This notebook is provided as a template to help you get started with your assignments. It gives you an idea of how you might use R for your work, along with example exercises to help you practice and become more comfortable with R. Keep in mind that you are not required to follow this template exactly, and the material here is not the solution to your assignment, it is simply a resource to guide you, provide ideas, and give you a starting point for building your own solutions.
First, make sure you upload the CSV file to your R working directory. Once the file is in the right place, you can read it into R as follows:
# Read the CSV
df <- read.csv("Superior.csv")
head(df)
## InterArrival LoadingTime
## 1 1.57 2.18
## 2 1.05 2.53
## 3 1.93 2.24
## 4 0.74 2.10
## 5 6.51 2.24
## 6 7.56 2.62
In this step, we’ll simulate inter-arrival times and wait (service) times using the exponential distribution , just as an example to show the workflow. This choice may not be the right one for your assignment. Use the idea to pick and justify the distribution that best fits your data, and then generate numbers accordingly.
To generate numbers from an exponential distribution, we need the
rate parameter lambda. In this case, we will assume both inter-arrival
times and service times follow exponential distributions. For now, I
have set both lambda values to 1 as placeholders. Your task
is to calculate the correct values from the dataset using the
formula:
lambda_hat_inter_arrival <- 1
lambda_hat_service_time <- 1
# Now calculate the correct lambda from your dataset. Make sure to drop null values.
lambda_hat_inter_arrival <- 1 / mean(df$InterArrival) #calculate correct lambda_hat_inter_arrival
lambda_hat_service_time <- 1 / mean(df$LoadingTime) #calculate correct lambda_hat_inter_arrival
Now we are generating inter-arrival times and service times using the exponential distribution.
n=1000 # Total number of values to generate
r_interarrival <- rexp(n, rate = lambda_hat_inter_arrival)
r_service <- rexp(n, rate = lambda_hat_service_time)
If you would like to try other distributions for these variables, you can generate them in the next code block.
# Generate inter-arrival times and service times using the distribution you believe is most appropriate for the data.
We will simulate ships arriving at a port with multiple wharfs (servers). Each ship has an inter-arrival time (time between ships) and a service time (time needed to load/unload). The function below shows how to simulate the system once (one repetition).
# Function to simulate ships arriving at a port
# with c_servers wharfs and n_ships arrivals
simulate_one <- function(
c_servers, # number of servers (wharfs) available at the port
n_ships, # number of ships to simulate in one repetition
r_interarrival, # inter-arrival times
r_service, # service times
seed = NULL # optional random seed for reproducibility
) {
# Optional: set a random seed for reproducibility
if (!is.null(seed)) set.seed(seed)
# inter-arrival times and service times for 1000 ships
interarrivals <- r_interarrival
services <- r_service
# Compute arrival times as the cumulative sum of inter-arrivals
arrival_time <- cumsum(interarrivals)
# Track when each server (wharf) is next available
server_free <- rep(0.0, c_servers) # start all as free at time 0
# Create vectors to store results for each ship
server_id <- integer(n_ships) # which server each ship uses
start_time <- numeric(n_ships) # when service actually starts
wait_time <- numeric(n_ships) # how long each ship waits
depart_time <- numeric(n_ships) # when each ship departs
# Loop through ships one by one
for (i in seq_len(n_ships)) {
# Find the server that becomes free the earliest
j <- which.min(server_free)
# Assign this ship to that server
server_id[i] <- j
# Service can only start when both the ship has arrived
# and the server is free
start_time[i] <- max(arrival_time[i], server_free[j])
# Waiting time = start time - arrival time
wait_time[i] <- start_time[i] - arrival_time[i]
# Departure time = start time + service time
depart_time[i] <- start_time[i] + services[i]
# Update that server’s next free time
server_free[j] <- depart_time[i]
}
# Return results as a data frame
data.frame(
ship_id = seq_len(n_ships),
arrival_time = arrival_time,
server_assigned = server_id,
start_time = start_time,
wait_time = wait_time,
service_time = services,
depart_time = depart_time,
c_servers = c_servers
)
}
# Example: run one simulation with 2 wharfs, 1000 ships
result <- simulate_one(
c_servers = 2,
n_ships = 1000,
r_interarrival =r_interarrival, # exponential inter-arrival
r_service = r_service, # exponential service
seed = 123
)
print(result)
## ship_id arrival_time server_assigned start_time wait_time service_time
## 1 1 3.087574 1 3.087574 0.00000000 7.858988148
## 2 2 3.192694 2 3.192694 0.00000000 0.240353530
## 3 3 3.923205 2 3.923205 0.00000000 2.339502950
## 4 4 4.499135 2 6.262708 1.76357339 2.600784915
## 5 5 4.861432 2 8.863493 4.00206105 0.655596642
## 6 6 5.530262 2 9.519090 3.98882754 0.407647584
## 7 7 6.056305 2 9.926737 3.87043239 2.710720053
## 8 8 6.233902 1 10.946562 4.71265975 5.750932144
## 9 9 9.028394 2 12.637457 3.60906348 0.383570668
## 10 10 9.799312 2 13.021028 3.22171585 1.705309549
## 11 11 12.887240 2 14.726337 1.83909778 1.816747136
## 12 12 14.479051 2 16.543085 2.06403378 2.237538094
## 13 13 15.287167 1 16.697494 1.41032710 1.941103501
## 14 14 17.873723 1 18.638597 0.76487493 15.571429015
## 15 15 19.576498 2 19.576498 0.00000000 2.352234241
## 16 16 24.450535 2 24.450535 0.00000000 0.270207848
## 17 17 26.552349 2 26.552349 0.00000000 8.420794148
## 18 18 31.446294 1 34.210026 2.76373212 1.110528527
## 19 19 32.686542 2 34.973143 2.28660069 1.198265439
## 20 20 36.387368 1 36.387368 0.00000000 1.359912624
## 21 21 38.368416 2 38.368416 0.00000000 2.635485402
## 22 22 38.981508 1 38.981508 0.00000000 3.826330025
## 23 23 43.900782 2 43.900782 0.00000000 1.234829528
## 24 24 46.668569 1 46.668569 0.00000000 6.054317478
## 25 25 50.838580 2 50.838580 0.00000000 2.305348849
## 26 26 51.539764 1 52.722886 1.18312246 1.303937747
## 27 27 52.206211 2 53.143928 0.93771735 0.469964170
## 28 28 53.841404 2 53.841404 0.00000000 5.016547716
## 29 29 57.657857 1 57.657857 0.00000000 3.842501106
## 30 30 57.865842 2 58.857952 0.99210980 7.700468881
## 31 31 58.234750 1 61.500358 3.26560771 0.100846172
## 32 32 58.632652 1 61.601204 2.96855183 2.800207753
## 33 33 62.702309 1 64.401412 1.69910235 0.181467078
## 34 34 65.214619 1 65.214619 0.00000000 1.034000727
## 35 35 68.383515 1 68.383515 0.00000000 1.333469343
## 36 36 73.767421 2 73.767421 0.00000000 1.387372492
## 37 37 73.808449 1 73.808449 0.00000000 0.782754643
## 38 38 78.001984 1 78.001984 0.00000000 0.585328740
## 39 39 80.805942 2 80.805942 0.00000000 3.072951902
## 40 40 82.093083 1 82.093083 0.00000000 0.992378916
## 41 41 85.117379 1 85.117379 0.00000000 3.559569070
## 42 42 86.729713 2 86.729713 0.00000000 1.064608927
## 43 43 88.962654 2 88.962654 0.00000000 0.311766624
## 44 44 93.640096 1 93.640096 0.00000000 0.665572036
## 45 45 97.403074 2 97.403074 0.00000000 1.267347435
## 46 46 97.680860 1 97.680860 0.00000000 3.647234732
## 47 47 101.778686 2 101.778686 0.00000000 0.128655648
## 48 48 105.546421 1 105.546421 0.00000000 6.343744050
## 49 49 109.102289 2 109.102289 0.00000000 0.425418761
## 50 50 110.694495 2 110.694495 0.00000000 1.065437507
## 51 51 114.197407 2 114.197407 0.00000000 9.920379307
## 52 52 118.233050 1 118.233050 0.00000000 3.198046968
## 53 53 119.205228 1 121.431097 2.22586928 4.509732206
## 54 54 119.418807 2 124.117786 4.69897909 1.398535091
## 55 55 119.937513 2 125.516321 5.57880776 1.449023525
## 56 56 120.016570 1 125.940829 5.92425952 2.358385905
## 57 57 120.466709 2 126.965345 6.49863584 1.618779853
## 58 58 121.258166 1 128.299215 7.04104958 6.869352132
## 59 59 131.295221 2 131.295221 0.00000000 1.760192640
## 60 60 132.310750 2 133.055414 0.74466411 0.426947583
## 61 61 132.599568 2 133.482362 0.88279323 3.628063856
## 62 62 132.862692 1 135.168567 2.30587504 0.112988860
## 63 63 135.222640 1 135.281556 0.05891587 0.800526803
## 64 64 139.307188 1 139.307188 0.00000000 1.851358616
## 65 65 141.926333 2 141.926333 0.00000000 1.109283623
## 66 66 142.321889 1 142.321889 0.00000000 0.040605054
## 67 67 142.680407 1 142.680407 0.00000000 2.303907548
## 68 68 151.782389 2 151.782389 0.00000000 3.410703518
## 69 69 152.927239 1 152.927239 0.00000000 1.425475826
## 70 70 154.944050 1 154.944050 0.00000000 2.399854009
## 71 71 156.937404 2 156.937404 0.00000000 0.399842276
## 72 72 158.131390 2 158.131390 0.00000000 5.874150976
## 73 73 159.459460 1 159.459460 0.00000000 0.213786421
## 74 74 159.768033 1 159.768033 0.00000000 3.858147599
## 75 75 161.372603 1 163.626181 2.25357772 1.688682715
## 76 76 162.784904 2 164.005541 1.22063765 0.572093078
## 77 77 164.407019 2 164.577634 0.17061514 2.463268217
## 78 78 165.525322 1 165.525322 0.00000000 4.281815163
## 79 79 170.968659 2 170.968659 0.00000000 2.220611020
## 80 80 173.027380 1 173.027380 0.00000000 0.691831507
## 81 81 173.905877 2 173.905877 0.00000000 1.843811640
## 82 82 175.402198 1 175.402198 0.00000000 1.913556031
## 83 83 175.693389 2 175.749689 0.05629976 0.307557188
## 84 84 176.414560 2 176.414560 0.00000000 0.754114846
## 85 85 176.736669 2 177.168675 0.43200568 4.372227797
## 86 86 178.697578 1 178.697578 0.00000000 0.517510604
## 87 87 181.953902 1 181.953902 0.00000000 0.126692515
## 88 88 182.012620 2 182.012620 0.00000000 0.308683721
## 89 89 182.502448 1 182.502448 0.00000000 3.751089325
## 90 90 184.277129 2 184.277129 0.00000000 2.167055972
## 91 91 184.508366 1 186.253537 1.74517078 1.798096653
## 92 92 186.552672 2 186.552672 0.00000000 7.312699177
## 93 93 190.777024 1 190.777024 0.00000000 2.483952988
## 94 94 200.050667 1 200.050667 0.00000000 2.716206527
## 95 95 200.109219 2 200.109219 0.00000000 0.845572578
## 96 96 200.575091 2 200.954792 0.37970072 2.459909196
## 97 97 200.896653 1 202.766874 1.87022054 0.200804656
## 98 98 201.855047 1 202.967678 1.11263172 1.985212182
## 99 99 205.192225 2 205.192225 0.00000000 5.098255356
## 100 100 205.702407 1 205.702407 0.00000000 3.497090041
## 101 101 211.630108 1 211.630108 0.00000000 0.580401801
## 102 102 211.743037 2 211.743037 0.00000000 2.250858773
## 103 103 219.580604 1 219.580604 0.00000000 2.366547952
## 104 104 221.952579 2 221.952579 0.00000000 4.116635728
## 105 105 222.527411 1 222.527411 0.00000000 4.726268866
## 106 106 223.115407 2 226.069215 2.95380773 1.187761154
## 107 107 225.669466 1 227.253680 1.58421438 1.613819773
## 108 108 228.065225 2 228.065225 0.00000000 0.676457758
## 109 109 235.432555 2 235.432555 0.00000000 0.240355434
## 110 110 236.603783 1 236.603783 0.00000000 0.886178371
## 111 111 238.192644 2 238.192644 0.00000000 1.075826873
## 112 112 238.637718 1 238.637718 0.00000000 2.091106311
## 113 113 239.239709 2 239.268471 0.02876111 0.992445717
## 114 114 240.766366 2 240.766366 0.00000000 2.359536376
## 115 115 246.169185 1 246.169185 0.00000000 0.818505359
## 116 116 246.287027 2 246.287027 0.00000000 1.134698594
## 117 117 247.300977 1 247.300977 0.00000000 1.713051681
## 118 118 249.313003 2 249.313003 0.00000000 1.417975761
## 119 119 249.602335 1 249.602335 0.00000000 2.157011076
## 120 120 249.692612 2 250.730979 1.03836688 0.706025426
## 121 121 252.506203 2 252.506203 0.00000000 0.516081466
## 122 122 256.497786 1 256.497786 0.00000000 0.074081768
## 123 123 256.531599 2 256.531599 0.00000000 0.430897103
## 124 124 256.858940 1 256.858940 0.00000000 2.195821696
## 125 125 257.167113 2 257.167113 0.00000000 3.499859960
## 126 126 258.136813 1 259.054762 0.91794871 3.461256771
## 127 127 258.654613 2 260.666973 2.01235929 0.810743042
## 128 128 259.185609 2 261.477716 2.29210620 0.269021941
## 129 129 265.701676 2 265.701676 0.00000000 1.653128260
## 130 130 265.888250 1 265.888250 0.00000000 0.721183357
## 131 131 267.609260 1 267.609260 0.00000000 3.400692222
## 132 132 270.826657 2 270.826657 0.00000000 0.213759153
## 133 133 271.441025 1 271.441025 0.00000000 3.982240341
## 134 134 271.668450 2 271.668450 0.00000000 0.483655003
## 135 135 271.961521 2 272.152105 0.19058377 0.959602117
## 136 136 273.150923 2 273.150923 0.00000000 0.996750046
## 137 137 276.723291 2 276.723291 0.00000000 0.209780066
## 138 138 280.431677 1 280.431677 0.00000000 2.880560999
## 139 139 281.374897 2 281.374897 0.00000000 1.533813754
## 140 140 282.104189 2 282.908710 0.80452186 5.830884227
## 141 141 282.713104 1 283.312238 0.59913390 0.508512887
## 142 142 282.870307 1 283.820751 0.95044388 1.845567294
## 143 143 282.881923 1 285.666318 2.78439560 0.696746441
## 144 144 285.432513 1 286.363065 0.93055141 1.606991326
## 145 145 288.288881 1 288.288881 0.00000000 0.853139260
## 146 146 294.083657 2 294.083657 0.00000000 0.157435579
## 147 147 298.232471 1 298.232471 0.00000000 0.880168899
## 148 148 298.834926 2 298.834926 0.00000000 0.950125099
## 149 149 298.967317 1 299.112640 0.14532318 0.310143280
## 150 150 304.340179 1 304.340179 0.00000000 3.471357011
## 151 151 309.473234 2 309.473234 0.00000000 0.606388889
## 152 152 310.550878 1 310.550878 0.00000000 0.051463930
## 153 153 311.565764 2 311.565764 0.00000000 2.150648952
## 154 154 312.100132 1 312.100132 0.00000000 9.734345168
## 155 155 314.130777 2 314.130777 0.00000000 0.370679006
## 156 156 314.228700 2 314.501456 0.27275558 6.106088045
## 157 157 314.731756 2 320.607544 5.87578762 7.301467981
## 158 158 318.123776 1 321.834478 3.71070158 2.508231015
## 159 159 324.961375 1 324.961375 0.00000000 3.894265785
## 160 160 326.586677 2 327.909012 1.32233526 2.218185962
## 161 161 327.012043 1 328.855641 1.84359715 1.455721817
## 162 162 329.616249 2 330.127198 0.51094872 0.239377358
## 163 163 329.928690 1 330.311362 0.38267198 0.040667505
## 164 164 331.655639 1 331.655639 0.00000000 1.845885508
## 165 165 337.813024 2 337.813024 0.00000000 3.535229435
## 166 166 338.491855 1 338.491855 0.00000000 0.515755493
## 167 167 348.928731 1 348.928731 0.00000000 3.175339463
## 168 168 350.295652 2 350.295652 0.00000000 3.309586781
## 169 169 351.154659 1 352.104070 0.94941158 9.490261865
## 170 170 353.225979 2 353.605239 0.37925997 0.212200726
## 171 171 354.515559 2 354.515559 0.00000000 3.324240570
## 172 172 355.757595 2 357.839799 2.08220384 1.351243730
## 173 173 359.868992 2 359.868992 0.00000000 1.246697284
## 174 174 361.056507 2 361.115689 0.05918147 2.109115390
## 175 175 362.455967 1 362.455967 0.00000000 0.295289876
## 176 176 364.464836 1 364.464836 0.00000000 4.329740276
## 177 177 365.752145 2 365.752145 0.00000000 0.145515078
## 178 178 368.592532 2 368.592532 0.00000000 0.261051887
## 179 179 369.313325 1 369.313325 0.00000000 2.928683315
## 180 180 382.076981 2 382.076981 0.00000000 0.786133548
## 181 181 384.397429 1 384.397429 0.00000000 6.401733258
## 182 182 387.357483 2 387.357483 0.00000000 2.496581005
## 183 183 388.406082 2 389.854064 1.44798167 4.616681384
## 184 184 394.746701 1 394.746701 0.00000000 4.469733631
## 185 185 395.123209 2 395.123209 0.00000000 2.824662092
## 186 186 397.129778 2 397.947871 0.81809389 2.275401304
## 187 187 397.519750 1 399.216434 1.69668403 1.455792914
## 188 188 405.730668 2 405.730668 0.00000000 0.466923742
## 189 189 405.888529 1 405.888529 0.00000000 3.775347421
## 190 190 408.395998 2 408.395998 0.00000000 0.352393597
## 191 191 410.884786 2 410.884786 0.00000000 5.050728211
## 192 192 411.267923 1 411.267923 0.00000000 11.696996990
## 193 193 414.249461 2 415.935515 1.68605314 0.616120006
## 194 194 414.260728 2 416.551635 2.29090694 1.789465931
## 195 195 417.330663 2 418.341101 1.01043763 0.143043883
## 196 196 423.169071 2 423.169071 0.00000000 1.987093566
## 197 197 424.143900 1 424.143900 0.00000000 1.473961462
## 198 198 430.649007 2 430.649007 0.00000000 1.921290682
## 199 199 433.909699 1 433.909699 0.00000000 0.453778602
## 200 200 441.015443 2 441.015443 0.00000000 1.050057687
## 201 201 442.780094 1 442.780094 0.00000000 0.893033401
## 202 202 444.670021 2 444.670021 0.00000000 1.612494853
## 203 203 444.932138 1 444.932138 0.00000000 2.177733872
## 204 204 450.385663 2 450.385663 0.00000000 1.436040140
## 205 205 454.177984 1 454.177984 0.00000000 0.124463848
## 206 206 455.636744 2 455.636744 0.00000000 1.673594891
## 207 207 455.681865 1 455.681865 0.00000000 1.939749953
## 208 208 457.051978 2 457.310339 0.25836040 0.338126861
## 209 209 458.218695 1 458.218695 0.00000000 0.055370270
## 210 210 465.497718 2 465.497718 0.00000000 6.820489238
## 211 211 466.356001 1 466.356001 0.00000000 6.268676846
## 212 212 469.848791 2 472.318208 2.46941684 6.641071828
## 213 213 476.115429 1 476.115429 0.00000000 3.967643568
## 214 214 479.207696 2 479.207696 0.00000000 0.121155196
## 215 215 480.070440 2 480.070440 0.00000000 3.544848018
## 216 216 480.984939 1 480.984939 0.00000000 0.888045859
## 217 217 485.323043 1 485.323043 0.00000000 5.353370893
## 218 218 485.358643 2 485.358643 0.00000000 1.061609231
## 219 219 486.832659 2 486.832659 0.00000000 1.156582317
## 220 220 490.493343 2 490.493343 0.00000000 1.906744388
## 221 221 495.637483 1 495.637483 0.00000000 1.192728819
## 222 222 496.693230 2 496.693230 0.00000000 0.639829447
## 223 223 497.802713 1 497.802713 0.00000000 3.521164142
## 224 224 500.158921 2 500.158921 0.00000000 1.285730378
## 225 225 501.117141 1 501.323877 0.20673656 0.752677843
## 226 226 501.963141 2 501.963141 0.00000000 0.765375092
## 227 227 502.705317 1 502.705317 0.00000000 3.143251030
## 228 228 503.934041 2 503.934041 0.00000000 0.858845032
## 229 229 507.279820 2 507.279820 0.00000000 1.203875774
## 230 230 520.070634 1 520.070634 0.00000000 1.735620141
## 231 231 520.183640 2 520.183640 0.00000000 2.721770915
## 232 232 522.641118 1 522.641118 0.00000000 5.598969540
## 233 233 523.331913 2 523.331913 0.00000000 3.600615071
## 234 234 523.564683 2 526.932528 3.36784556 0.533136717
## 235 235 528.826463 2 528.826463 0.00000000 6.757978226
## 236 236 535.354846 1 535.354846 0.00000000 0.152631178
## 237 237 535.443070 1 535.507477 0.06440699 0.001869328
## 238 238 536.243567 1 536.243567 0.00000000 0.544620540
## 239 239 540.956532 2 540.956532 0.00000000 1.437215994
## 240 240 543.300023 1 543.300023 0.00000000 2.608857608
## 241 241 543.446107 2 543.446107 0.00000000 6.180217049
## 242 242 544.466721 1 545.908881 1.44215941 0.569119065
## 243 243 545.743934 1 546.478000 0.73406553 3.579247086
## 244 244 546.471552 2 549.626324 3.15477168 1.144474450
## 245 245 547.903965 1 550.057247 2.15328158 0.238669716
## 246 246 549.366021 1 550.295917 0.92989579 2.336254018
## 247 247 551.784018 2 551.784018 0.00000000 3.114428840
## 248 248 556.816847 1 556.816847 0.00000000 4.755694967
## 249 249 557.223992 2 557.223992 0.00000000 5.272069641
## 250 250 559.557482 1 561.572542 2.01505991 0.606969066
## 251 251 563.768474 1 563.768474 0.00000000 3.325761176
## 252 252 564.267915 2 564.267915 0.00000000 1.401717548
## 253 253 566.451743 2 566.451743 0.00000000 3.816534203
## 254 254 568.699856 1 568.699856 0.00000000 11.661440907
## 255 255 572.867925 2 572.867925 0.00000000 2.285912966
## 256 256 580.835880 2 580.835880 0.00000000 0.346580252
## 257 257 585.101377 1 585.101377 0.00000000 0.660881915
## 258 258 586.101055 2 586.101055 0.00000000 4.025270543
## 259 259 589.881412 1 589.881412 0.00000000 14.163959972
## 260 260 590.198662 2 590.198662 0.00000000 0.868483569
## 261 261 590.975551 2 591.067145 0.09159394 1.082804159
## 262 262 591.596030 2 592.149949 0.55391993 3.759785001
## 263 263 592.308360 2 595.909734 3.60137474 1.874322212
## 264 264 593.905066 2 597.784057 3.87899095 1.973649732
## 265 265 596.041769 2 599.757706 3.71593752 8.125261471
## 266 266 597.383238 1 604.045372 6.66213378 1.166147980
## 267 267 598.506461 1 605.211520 6.70505886 0.576341717
## 268 268 601.854120 1 605.787862 3.93374176 0.549364594
## 269 269 602.363693 1 606.337226 3.97353302 2.141315298
## 270 270 603.126724 2 607.882968 4.75624424 0.397494791
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## 856 856 1822.399514 1 1823.571330 1.17181553 1.601990228
## 857 857 1822.893058 1 1825.173320 2.28026217 3.138798283
## 858 858 1826.599075 2 1826.599075 0.00000000 4.504485434
## 859 859 1829.466838 1 1829.466838 0.00000000 6.771147904
## 860 860 1832.887706 2 1832.887706 0.00000000 5.126724004
## 861 861 1832.988658 1 1836.237986 3.24932866 3.514848007
## 862 862 1835.721120 2 1838.014430 2.29330982 1.073754028
## 863 863 1838.200832 2 1839.088184 0.88735124 0.676333502
## 864 864 1841.582765 1 1841.582765 0.00000000 6.277542230
## 865 865 1842.842993 2 1842.842993 0.00000000 0.961476793
## 866 866 1844.723438 2 1844.723438 0.00000000 3.979365923
## 867 867 1845.405256 1 1847.860308 2.45505144 1.217102603
## 868 868 1845.678942 2 1848.702804 3.02386271 0.196168906
## 869 869 1850.375773 2 1850.375773 0.00000000 3.499921264
## 870 870 1852.542252 1 1852.542252 0.00000000 4.314270284
## 871 871 1856.863762 2 1856.863762 0.00000000 7.633384202
## 872 872 1857.263698 1 1857.263698 0.00000000 0.218005620
## 873 873 1858.228697 1 1858.228697 0.00000000 1.106484928
## 874 874 1861.728557 1 1861.728557 0.00000000 6.013141361
## 875 875 1862.589085 2 1864.497146 1.90806108 7.462816851
## 876 876 1865.815361 1 1867.741698 1.92633716 0.762013706
## 877 877 1867.029591 1 1868.503712 1.47412066 3.528119329
## 878 878 1867.363272 2 1871.959963 4.59669113 7.296611892
## 879 879 1869.328823 1 1872.031831 2.70300809 1.339909698
## 880 880 1870.859631 1 1873.371741 2.51210961 0.071609232
## 881 881 1872.393416 1 1873.443350 1.04993475 2.972202589
## 882 882 1878.864731 1 1878.864731 0.00000000 3.244034118
## 883 883 1882.332872 2 1882.332872 0.00000000 0.897491697
## 884 884 1884.036196 1 1884.036196 0.00000000 0.227153997
## 885 885 1889.682971 2 1889.682971 0.00000000 0.020815310
## 886 886 1890.868557 1 1890.868557 0.00000000 5.583704148
## 887 887 1894.324642 2 1894.324642 0.00000000 0.466440332
## 888 888 1896.340472 2 1896.340472 0.00000000 3.953295483
## 889 889 1899.856455 1 1899.856455 0.00000000 1.241258229
## 890 890 1900.397887 2 1900.397887 0.00000000 3.712496779
## 891 891 1905.052911 1 1905.052911 0.00000000 7.445580945
## 892 892 1908.146787 2 1908.146787 0.00000000 9.190022955
## 893 893 1909.324986 1 1912.498492 3.17350539 5.368866859
## 894 894 1916.177465 2 1917.336810 1.15934448 10.279648031
## 895 895 1917.950117 1 1917.950117 0.00000000 1.773987215
## 896 896 1920.856647 1 1920.856647 0.00000000 1.455310850
## 897 897 1924.277629 1 1924.277629 0.00000000 8.084709713
## 898 898 1928.386163 2 1928.386163 0.00000000 5.179490887
## 899 899 1933.236413 1 1933.236413 0.00000000 2.216978621
## 900 900 1933.405523 2 1933.565653 0.16013057 4.811690026
## 901 901 1934.088396 1 1935.453391 1.36499503 4.922936222
## 902 902 1935.149669 2 1938.377344 3.22767461 2.273238515
## 903 903 1939.161503 1 1940.376328 1.21482409 0.358080401
## 904 904 1939.480307 2 1940.650582 1.17027502 6.373391064
## 905 905 1940.752952 1 1940.752952 0.00000000 0.305839664
## 906 906 1946.011407 1 1946.011407 0.00000000 0.166398003
## 907 907 1948.053322 1 1948.053322 0.00000000 4.253881707
## 908 908 1948.462636 2 1948.462636 0.00000000 1.566084442
## 909 909 1948.961378 2 1950.028721 1.06734259 2.354906858
## 910 910 1950.999917 1 1952.307204 1.30728640 8.804146563
## 911 911 1951.909545 2 1952.383627 0.47408273 0.110284747
## 912 912 1954.547469 2 1954.547469 0.00000000 2.357356270
## 913 913 1955.060743 2 1956.904826 1.84408240 2.656698910
## 914 914 1955.684437 2 1959.561524 3.87708737 0.284677234
## 915 915 1956.215078 2 1959.846202 3.63112387 5.086121080
## 916 916 1959.527183 1 1961.111350 1.58416737 0.770399201
## 917 917 1960.497430 1 1961.881750 1.38431920 0.088234708
## 918 918 1961.658680 1 1961.969984 0.31130407 4.005502081
## 919 919 1962.692205 2 1964.932323 2.24011780 0.063784944
## 920 920 1966.669078 2 1966.669078 0.00000000 19.154997876
## 921 921 1971.635321 1 1971.635321 0.00000000 3.222287645
## 922 922 1972.563245 1 1974.857609 2.29436360 0.777321527
## 923 923 1974.465708 1 1975.634931 1.16922252 1.051985674
## 924 924 1976.771498 1 1976.771498 0.00000000 3.955465970
## 925 925 1977.198867 1 1980.726964 3.52809774 2.226911026
## 926 926 1977.814765 1 1982.953875 5.13911026 3.437392367
## 927 927 1977.932344 2 1985.824076 7.89173151 0.344394269
## 928 928 1981.123636 2 1986.168470 5.04483437 1.160937537
## 929 929 1983.886552 1 1986.391268 2.50471567 1.633826495
## 930 930 1984.093667 2 1987.329407 3.23574029 1.278709243
## 931 931 1985.691563 1 1988.025094 2.33353084 3.513199441
## 932 932 1986.257492 2 1988.608117 2.35062449 6.833960287
## 933 933 1987.877378 1 1991.538294 3.66091551 1.607751528
## 934 934 1996.371952 1 1996.371952 0.00000000 0.726023100
## 935 935 1996.804853 2 1996.804853 0.00000000 0.647260634
## 936 936 1998.096495 1 1998.096495 0.00000000 5.074824461
## 937 937 1998.298116 2 1998.298116 0.00000000 14.150962631
## 938 938 1998.621127 1 2003.171319 4.55019223 0.454965291
## 939 939 2000.386067 1 2003.626284 3.24021773 1.928151741
## 940 940 2002.404060 1 2005.554436 3.15037623 3.150287365
## 941 941 2003.727712 1 2008.704723 4.97701192 1.403168016
## 942 942 2006.911912 1 2010.107891 3.19597914 8.115969464
## 943 943 2012.842246 2 2012.842246 0.00000000 2.037750755
## 944 944 2013.531940 2 2014.879997 1.34805650 2.501028690
## 945 945 2016.496241 2 2017.381025 0.88478436 1.757177394
## 946 946 2019.300439 1 2019.300439 0.00000000 1.294322768
## 947 947 2019.622862 2 2019.622862 0.00000000 0.468443918
## 948 948 2020.057962 2 2020.091306 0.03334465 6.588457510
## 949 949 2023.159320 1 2023.159320 0.00000000 4.895517830
## 950 950 2023.284080 2 2026.679764 3.39568411 9.130386499
## 951 951 2025.579799 1 2028.054838 2.47503868 2.148094150
## 952 952 2027.349136 1 2030.202932 2.85379590 4.771737626
## 953 953 2027.976602 1 2034.974670 6.99806764 2.502191317
## 954 954 2030.223071 2 2035.810150 5.58707896 1.363874764
## 955 955 2034.435436 2 2037.174025 2.73858913 2.548432018
## 956 956 2037.104276 1 2037.476861 0.37258452 0.559717106
## 957 957 2037.353855 1 2038.036578 0.68272322 3.287108536
## 958 958 2040.718065 2 2040.718065 0.00000000 0.927577261
## 959 959 2048.646879 1 2048.646879 0.00000000 1.636948479
## 960 960 2049.336103 2 2049.336103 0.00000000 1.689016072
## 961 961 2050.912905 1 2050.912905 0.00000000 2.275006048
## 962 962 2053.075831 2 2053.075831 0.00000000 2.330097341
## 963 963 2055.081939 1 2055.081939 0.00000000 0.861095003
## 964 964 2056.978144 2 2056.978144 0.00000000 0.322007059
## 965 965 2058.592525 1 2058.592525 0.00000000 2.820678875
## 966 966 2059.275290 2 2059.275290 0.00000000 1.775694343
## 967 967 2063.866808 2 2063.866808 0.00000000 4.268238462
## 968 968 2064.722860 1 2064.722860 0.00000000 4.374627812
## 969 969 2065.371490 2 2068.135047 2.76355700 2.786321206
## 970 970 2066.832560 1 2069.097488 2.26492793 1.207734958
## 971 971 2069.956493 1 2070.305223 0.34872984 3.351608751
## 972 972 2071.685304 2 2071.685304 0.00000000 6.926306659
## 973 973 2077.250284 1 2077.250284 0.00000000 0.950619126
## 974 974 2080.882692 1 2080.882692 0.00000000 2.015788518
## 975 975 2084.333755 2 2084.333755 0.00000000 0.390362191
## 976 976 2085.530542 1 2085.530542 0.00000000 0.479862175
## 977 977 2087.434442 2 2087.434442 0.00000000 6.967035072
## 978 978 2089.745438 1 2089.745438 0.00000000 1.390737959
## 979 979 2090.281966 1 2091.136176 0.85420977 3.171373567
## 980 980 2092.669296 1 2094.307549 1.63825303 3.343184017
## 981 981 2100.338987 2 2100.338987 0.00000000 1.788816710
## 982 982 2105.966014 1 2105.966014 0.00000000 7.878976996
## 983 983 2106.603983 2 2106.603983 0.00000000 1.346945097
## 984 984 2110.126785 2 2110.126785 0.00000000 0.762594097
## 985 985 2110.935138 2 2110.935138 0.00000000 0.113221382
## 986 986 2121.004549 2 2121.004549 0.00000000 1.601284046
## 987 987 2121.989204 1 2121.989204 0.00000000 0.302320392
## 988 988 2123.519520 1 2123.519520 0.00000000 0.546256236
## 989 989 2131.152583 2 2131.152583 0.00000000 8.749552522
## 990 990 2134.719230 1 2134.719230 0.00000000 2.226004833
## 991 991 2136.070104 1 2136.945235 0.87513130 2.385398517
## 992 992 2138.125704 1 2139.330633 1.20492919 2.184604051
## 993 993 2147.233717 2 2147.233717 0.00000000 3.085745445
## 994 994 2149.648847 1 2149.648847 0.00000000 1.988942457
## 995 995 2151.031276 2 2151.031276 0.00000000 2.654672872
## 996 996 2152.953743 1 2152.953743 0.00000000 1.355608495
## 997 997 2156.023804 2 2156.023804 0.00000000 0.760319738
## 998 998 2158.758074 1 2158.758074 0.00000000 2.217244248
## 999 999 2159.662817 2 2159.662817 0.00000000 6.367852778
## 1000 1000 2161.351034 1 2161.351034 0.00000000 0.428189446
## depart_time c_servers
## 1 10.946562 2
## 2 3.433047 2
## 3 6.262708 2
## 4 8.863493 2
## 5 9.519090 2
## 6 9.926737 2
## 7 12.637457 2
## 8 16.697494 2
## 9 13.021028 2
## 10 14.726337 2
## 11 16.543085 2
## 12 18.780623 2
## 13 18.638597 2
## 14 34.210026 2
## 15 21.928732 2
## 16 24.720742 2
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## 18 35.320555 2
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## 20 37.747280 2
## 21 41.003902 2
## 22 42.807838 2
## 23 45.135611 2
## 24 52.722886 2
## 25 53.143928 2
## 26 54.026824 2
## 27 53.613893 2
## 28 58.857952 2
## 29 61.500358 2
## 30 66.558421 2
## 31 61.601204 2
## 32 64.401412 2
## 33 64.582879 2
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## 35 69.716984 2
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## 999 2166.030670 2
## 1000 2161.779223 2
# Use the simulate_one function to run one simulation with 3 wharfs and 1000 ships
So far, we have simulated the system once (one repetition) using
simulate_one(). In practice, a single simulation run only
gives us one possible outcome. Because randomness is involved, we need
to repeat the simulation many times to get a better understanding of the
system’s overall performance (e.g., average waiting time, variation in
service times, probability of long queues, etc.).
As an exercise, you are asked to extend the one-run simulation into a function that can perform multiple replications. Your function could have the following inputs:
reps → number of times to repeat the
simulation
c_servers → number of servers (wharfs)
in the system.
n_ships → number of ships to simulate
in each replication.
r_interarrival → function to generate
inter-arrival times.
r_service → function to generate
service times.
seed → optional random seed so results
can be reproduced.
Hint: Think about wrapping
simulate_one() inside a loop.
# create a function for multi-replication simulation here
# =================================
# 2) Multi-replication convenience
# =================================
# Runs 'reps' independent simulations and binds rows with rep_id.
simulate_many <- function(reps, c_servers, n_ships, r_interarrival, r_service, seed = NULL) {
if (!is.null(seed)) set.seed(seed)
out <- vector("list", reps)
for (r in seq_len(reps)) {
df <- simulate_one(c_servers, n_ships, r_interarrival, r_service)
df$rep_id <- r
out[[r]] <- df[, c("rep_id", names(df)[names(df)!="rep_id"])]
}
do.call(rbind, out)
}
big2 <- simulate_many(reps = 1000, c_servers = 2, n_ships = 1000, r_interarrival, r_service, seed = 999)
big2
## rep_id ship_id arrival_time server_assigned start_time wait_time
## 1 1 1 3.087574 1 3.087574 0.00000000
## 2 1 2 3.192694 2 3.192694 0.00000000
## 3 1 3 3.923205 2 3.923205 0.00000000
## 4 1 4 4.499135 2 6.262708 1.76357339
## 5 1 5 4.861432 2 8.863493 4.00206105
## 6 1 6 5.530262 2 9.519090 3.98882754
## 7 1 7 6.056305 2 9.926737 3.87043239
## 8 1 8 6.233902 1 10.946562 4.71265975
## 9 1 9 9.028394 2 12.637457 3.60906348
## 10 1 10 9.799312 2 13.021028 3.22171585
## 11 1 11 12.887240 2 14.726337 1.83909778
## 12 1 12 14.479051 2 16.543085 2.06403378
## 13 1 13 15.287167 1 16.697494 1.41032710
## 14 1 14 17.873723 1 18.638597 0.76487493
## 15 1 15 19.576498 2 19.576498 0.00000000
## 16 1 16 24.450535 2 24.450535 0.00000000
## 17 1 17 26.552349 2 26.552349 0.00000000
## 18 1 18 31.446294 1 34.210026 2.76373212
## 19 1 19 32.686542 2 34.973143 2.28660069
## 20 1 20 36.387368 1 36.387368 0.00000000
## 21 1 21 38.368416 2 38.368416 0.00000000
## 22 1 22 38.981508 1 38.981508 0.00000000
## 23 1 23 43.900782 2 43.900782 0.00000000
## 24 1 24 46.668569 1 46.668569 0.00000000
## 25 1 25 50.838580 2 50.838580 0.00000000
## 26 1 26 51.539764 1 52.722886 1.18312246
## 27 1 27 52.206211 2 53.143928 0.93771735
## 28 1 28 53.841404 2 53.841404 0.00000000
## 29 1 29 57.657857 1 57.657857 0.00000000
## 30 1 30 57.865842 2 58.857952 0.99210980
## 31 1 31 58.234750 1 61.500358 3.26560771
## 32 1 32 58.632652 1 61.601204 2.96855183
## 33 1 33 62.702309 1 64.401412 1.69910235
## 34 1 34 65.214619 1 65.214619 0.00000000
## 35 1 35 68.383515 1 68.383515 0.00000000
## 36 1 36 73.767421 2 73.767421 0.00000000
## 37 1 37 73.808449 1 73.808449 0.00000000
## 38 1 38 78.001984 1 78.001984 0.00000000
## 39 1 39 80.805942 2 80.805942 0.00000000
## 40 1 40 82.093083 1 82.093083 0.00000000
## 41 1 41 85.117379 1 85.117379 0.00000000
## 42 1 42 86.729713 2 86.729713 0.00000000
## 43 1 43 88.962654 2 88.962654 0.00000000
## 44 1 44 93.640096 1 93.640096 0.00000000
## 45 1 45 97.403074 2 97.403074 0.00000000
## 46 1 46 97.680860 1 97.680860 0.00000000
## 47 1 47 101.778686 2 101.778686 0.00000000
## 48 1 48 105.546421 1 105.546421 0.00000000
## 49 1 49 109.102289 2 109.102289 0.00000000
## 50 1 50 110.694495 2 110.694495 0.00000000
## 51 1 51 114.197407 2 114.197407 0.00000000
## 52 1 52 118.233050 1 118.233050 0.00000000
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## 1858 2 858 1826.599075 2 1826.599075 0.00000000
## 1859 2 859 1829.466838 1 1829.466838 0.00000000
## 1860 2 860 1832.887706 2 1832.887706 0.00000000
## 1861 2 861 1832.988658 1 1836.237986 3.24932866
## 1862 2 862 1835.721120 2 1838.014430 2.29330982
## 1863 2 863 1838.200832 2 1839.088184 0.88735124
## 1864 2 864 1841.582765 1 1841.582765 0.00000000
## 1865 2 865 1842.842993 2 1842.842993 0.00000000
## 1866 2 866 1844.723438 2 1844.723438 0.00000000
## 1867 2 867 1845.405256 1 1847.860308 2.45505144
## 1868 2 868 1845.678942 2 1848.702804 3.02386271
## 1869 2 869 1850.375773 2 1850.375773 0.00000000
## 1870 2 870 1852.542252 1 1852.542252 0.00000000
## 1871 2 871 1856.863762 2 1856.863762 0.00000000
## 1872 2 872 1857.263698 1 1857.263698 0.00000000
## 1873 2 873 1858.228697 1 1858.228697 0.00000000
## 1874 2 874 1861.728557 1 1861.728557 0.00000000
## 1875 2 875 1862.589085 2 1864.497146 1.90806108
## 1876 2 876 1865.815361 1 1867.741698 1.92633716
## 1877 2 877 1867.029591 1 1868.503712 1.47412066
## 1878 2 878 1867.363272 2 1871.959963 4.59669113
## 1879 2 879 1869.328823 1 1872.031831 2.70300809
## 1880 2 880 1870.859631 1 1873.371741 2.51210961
## 1881 2 881 1872.393416 1 1873.443350 1.04993475
## 1882 2 882 1878.864731 1 1878.864731 0.00000000
## 1883 2 883 1882.332872 2 1882.332872 0.00000000
## 1884 2 884 1884.036196 1 1884.036196 0.00000000
## 1885 2 885 1889.682971 2 1889.682971 0.00000000
## 1886 2 886 1890.868557 1 1890.868557 0.00000000
## 1887 2 887 1894.324642 2 1894.324642 0.00000000
## 1888 2 888 1896.340472 2 1896.340472 0.00000000
## 1889 2 889 1899.856455 1 1899.856455 0.00000000
## 1890 2 890 1900.397887 2 1900.397887 0.00000000
## 1891 2 891 1905.052911 1 1905.052911 0.00000000
## 1892 2 892 1908.146787 2 1908.146787 0.00000000
## 1893 2 893 1909.324986 1 1912.498492 3.17350539
## 1894 2 894 1916.177465 2 1917.336810 1.15934448
## 1895 2 895 1917.950117 1 1917.950117 0.00000000
## 1896 2 896 1920.856647 1 1920.856647 0.00000000
## 1897 2 897 1924.277629 1 1924.277629 0.00000000
## 1898 2 898 1928.386163 2 1928.386163 0.00000000
## 1899 2 899 1933.236413 1 1933.236413 0.00000000
## 1900 2 900 1933.405523 2 1933.565653 0.16013057
## 1901 2 901 1934.088396 1 1935.453391 1.36499503
## 1902 2 902 1935.149669 2 1938.377344 3.22767461
## 1903 2 903 1939.161503 1 1940.376328 1.21482409
## 1904 2 904 1939.480307 2 1940.650582 1.17027502
## 1905 2 905 1940.752952 1 1940.752952 0.00000000
## 1906 2 906 1946.011407 1 1946.011407 0.00000000
## 1907 2 907 1948.053322 1 1948.053322 0.00000000
## 1908 2 908 1948.462636 2 1948.462636 0.00000000
## 1909 2 909 1948.961378 2 1950.028721 1.06734259
## 1910 2 910 1950.999917 1 1952.307204 1.30728640
## 1911 2 911 1951.909545 2 1952.383627 0.47408273
## 1912 2 912 1954.547469 2 1954.547469 0.00000000
## 1913 2 913 1955.060743 2 1956.904826 1.84408240
## 1914 2 914 1955.684437 2 1959.561524 3.87708737
## 1915 2 915 1956.215078 2 1959.846202 3.63112387
## 1916 2 916 1959.527183 1 1961.111350 1.58416737
## 1917 2 917 1960.497430 1 1961.881750 1.38431920
## 1918 2 918 1961.658680 1 1961.969984 0.31130407
## 1919 2 919 1962.692205 2 1964.932323 2.24011780
## 1920 2 920 1966.669078 2 1966.669078 0.00000000
## 1921 2 921 1971.635321 1 1971.635321 0.00000000
## 1922 2 922 1972.563245 1 1974.857609 2.29436360
## 1923 2 923 1974.465708 1 1975.634931 1.16922252
## 1924 2 924 1976.771498 1 1976.771498 0.00000000
## 1925 2 925 1977.198867 1 1980.726964 3.52809774
## 1926 2 926 1977.814765 1 1982.953875 5.13911026
## 1927 2 927 1977.932344 2 1985.824076 7.89173151
## 1928 2 928 1981.123636 2 1986.168470 5.04483437
## 1929 2 929 1983.886552 1 1986.391268 2.50471567
## 1930 2 930 1984.093667 2 1987.329407 3.23574029
## 1931 2 931 1985.691563 1 1988.025094 2.33353084
## 1932 2 932 1986.257492 2 1988.608117 2.35062449
## 1933 2 933 1987.877378 1 1991.538294 3.66091551
## 1934 2 934 1996.371952 1 1996.371952 0.00000000
## 1935 2 935 1996.804853 2 1996.804853 0.00000000
## 1936 2 936 1998.096495 1 1998.096495 0.00000000
## 1937 2 937 1998.298116 2 1998.298116 0.00000000
## 1938 2 938 1998.621127 1 2003.171319 4.55019223
## 1939 2 939 2000.386067 1 2003.626284 3.24021773
## 1940 2 940 2002.404060 1 2005.554436 3.15037623
## 1941 2 941 2003.727712 1 2008.704723 4.97701192
## 1942 2 942 2006.911912 1 2010.107891 3.19597914
## 1943 2 943 2012.842246 2 2012.842246 0.00000000
## 1944 2 944 2013.531940 2 2014.879997 1.34805650
## 1945 2 945 2016.496241 2 2017.381025 0.88478436
## 1946 2 946 2019.300439 1 2019.300439 0.00000000
## 1947 2 947 2019.622862 2 2019.622862 0.00000000
## 1948 2 948 2020.057962 2 2020.091306 0.03334465
## 1949 2 949 2023.159320 1 2023.159320 0.00000000
## 1950 2 950 2023.284080 2 2026.679764 3.39568411
## 1951 2 951 2025.579799 1 2028.054838 2.47503868
## 1952 2 952 2027.349136 1 2030.202932 2.85379590
## 1953 2 953 2027.976602 1 2034.974670 6.99806764
## 1954 2 954 2030.223071 2 2035.810150 5.58707896
## 1955 2 955 2034.435436 2 2037.174025 2.73858913
## 1956 2 956 2037.104276 1 2037.476861 0.37258452
## 1957 2 957 2037.353855 1 2038.036578 0.68272322
## 1958 2 958 2040.718065 2 2040.718065 0.00000000
## 1959 2 959 2048.646879 1 2048.646879 0.00000000
## 1960 2 960 2049.336103 2 2049.336103 0.00000000
## 1961 2 961 2050.912905 1 2050.912905 0.00000000
## 1962 2 962 2053.075831 2 2053.075831 0.00000000
## 1963 2 963 2055.081939 1 2055.081939 0.00000000
## 1964 2 964 2056.978144 2 2056.978144 0.00000000
## 1965 2 965 2058.592525 1 2058.592525 0.00000000
## 1966 2 966 2059.275290 2 2059.275290 0.00000000
## 1967 2 967 2063.866808 2 2063.866808 0.00000000
## 1968 2 968 2064.722860 1 2064.722860 0.00000000
## 1969 2 969 2065.371490 2 2068.135047 2.76355700
## 1970 2 970 2066.832560 1 2069.097488 2.26492793
## 1971 2 971 2069.956493 1 2070.305223 0.34872984
## 1972 2 972 2071.685304 2 2071.685304 0.00000000
## 1973 2 973 2077.250284 1 2077.250284 0.00000000
## 1974 2 974 2080.882692 1 2080.882692 0.00000000
## 1975 2 975 2084.333755 2 2084.333755 0.00000000
## 1976 2 976 2085.530542 1 2085.530542 0.00000000
## 1977 2 977 2087.434442 2 2087.434442 0.00000000
## 1978 2 978 2089.745438 1 2089.745438 0.00000000
## 1979 2 979 2090.281966 1 2091.136176 0.85420977
## 1980 2 980 2092.669296 1 2094.307549 1.63825303
## 1981 2 981 2100.338987 2 2100.338987 0.00000000
## 1982 2 982 2105.966014 1 2105.966014 0.00000000
## 1983 2 983 2106.603983 2 2106.603983 0.00000000
## 1984 2 984 2110.126785 2 2110.126785 0.00000000
## 1985 2 985 2110.935138 2 2110.935138 0.00000000
## 1986 2 986 2121.004549 2 2121.004549 0.00000000
## 1987 2 987 2121.989204 1 2121.989204 0.00000000
## 1988 2 988 2123.519520 1 2123.519520 0.00000000
## 1989 2 989 2131.152583 2 2131.152583 0.00000000
## 1990 2 990 2134.719230 1 2134.719230 0.00000000
## 1991 2 991 2136.070104 1 2136.945235 0.87513130
## 1992 2 992 2138.125704 1 2139.330633 1.20492919
## 1993 2 993 2147.233717 2 2147.233717 0.00000000
## 1994 2 994 2149.648847 1 2149.648847 0.00000000
## 1995 2 995 2151.031276 2 2151.031276 0.00000000
## 1996 2 996 2152.953743 1 2152.953743 0.00000000
## 1997 2 997 2156.023804 2 2156.023804 0.00000000
## 1998 2 998 2158.758074 1 2158.758074 0.00000000
## 1999 2 999 2159.662817 2 2159.662817 0.00000000
## 2000 2 1000 2161.351034 1 2161.351034 0.00000000
## 2001 3 1 3.087574 1 3.087574 0.00000000
## 2002 3 2 3.192694 2 3.192694 0.00000000
## 2003 3 3 3.923205 2 3.923205 0.00000000
## 2004 3 4 4.499135 2 6.262708 1.76357339
## 2005 3 5 4.861432 2 8.863493 4.00206105
## 2006 3 6 5.530262 2 9.519090 3.98882754
## 2007 3 7 6.056305 2 9.926737 3.87043239
## 2008 3 8 6.233902 1 10.946562 4.71265975
## 2009 3 9 9.028394 2 12.637457 3.60906348
## 2010 3 10 9.799312 2 13.021028 3.22171585
## 2011 3 11 12.887240 2 14.726337 1.83909778
## 2012 3 12 14.479051 2 16.543085 2.06403378
## 2013 3 13 15.287167 1 16.697494 1.41032710
## 2014 3 14 17.873723 1 18.638597 0.76487493
## 2015 3 15 19.576498 2 19.576498 0.00000000
## 2016 3 16 24.450535 2 24.450535 0.00000000
## 2017 3 17 26.552349 2 26.552349 0.00000000
## 2018 3 18 31.446294 1 34.210026 2.76373212
## 2019 3 19 32.686542 2 34.973143 2.28660069
## 2020 3 20 36.387368 1 36.387368 0.00000000
## 2021 3 21 38.368416 2 38.368416 0.00000000
## 2022 3 22 38.981508 1 38.981508 0.00000000
## 2023 3 23 43.900782 2 43.900782 0.00000000
## 2024 3 24 46.668569 1 46.668569 0.00000000
## 2025 3 25 50.838580 2 50.838580 0.00000000
## 2026 3 26 51.539764 1 52.722886 1.18312246
## 2027 3 27 52.206211 2 53.143928 0.93771735
## 2028 3 28 53.841404 2 53.841404 0.00000000
## 2029 3 29 57.657857 1 57.657857 0.00000000
## 2030 3 30 57.865842 2 58.857952 0.99210980
## 2031 3 31 58.234750 1 61.500358 3.26560771
## 2032 3 32 58.632652 1 61.601204 2.96855183
## 2033 3 33 62.702309 1 64.401412 1.69910235
## 2034 3 34 65.214619 1 65.214619 0.00000000
## 2035 3 35 68.383515 1 68.383515 0.00000000
## 2036 3 36 73.767421 2 73.767421 0.00000000
## 2037 3 37 73.808449 1 73.808449 0.00000000
## 2038 3 38 78.001984 1 78.001984 0.00000000
## 2039 3 39 80.805942 2 80.805942 0.00000000
## 2040 3 40 82.093083 1 82.093083 0.00000000
## 2041 3 41 85.117379 1 85.117379 0.00000000
## 2042 3 42 86.729713 2 86.729713 0.00000000
## 2043 3 43 88.962654 2 88.962654 0.00000000
## 2044 3 44 93.640096 1 93.640096 0.00000000
## 2045 3 45 97.403074 2 97.403074 0.00000000
## 2046 3 46 97.680860 1 97.680860 0.00000000
## 2047 3 47 101.778686 2 101.778686 0.00000000
## 2048 3 48 105.546421 1 105.546421 0.00000000
## 2049 3 49 109.102289 2 109.102289 0.00000000
## 2050 3 50 110.694495 2 110.694495 0.00000000
## 2051 3 51 114.197407 2 114.197407 0.00000000
## 2052 3 52 118.233050 1 118.233050 0.00000000
## 2053 3 53 119.205228 1 121.431097 2.22586928
## 2054 3 54 119.418807 2 124.117786 4.69897909
## 2055 3 55 119.937513 2 125.516321 5.57880776
## 2056 3 56 120.016570 1 125.940829 5.92425952
## 2057 3 57 120.466709 2 126.965345 6.49863584
## 2058 3 58 121.258166 1 128.299215 7.04104958
## 2059 3 59 131.295221 2 131.295221 0.00000000
## 2060 3 60 132.310750 2 133.055414 0.74466411
## 2061 3 61 132.599568 2 133.482362 0.88279323
## 2062 3 62 132.862692 1 135.168567 2.30587504
## 2063 3 63 135.222640 1 135.281556 0.05891587
## 2064 3 64 139.307188 1 139.307188 0.00000000
## 2065 3 65 141.926333 2 141.926333 0.00000000
## 2066 3 66 142.321889 1 142.321889 0.00000000
## 2067 3 67 142.680407 1 142.680407 0.00000000
## 2068 3 68 151.782389 2 151.782389 0.00000000
## 2069 3 69 152.927239 1 152.927239 0.00000000
## 2070 3 70 154.944050 1 154.944050 0.00000000
## 2071 3 71 156.937404 2 156.937404 0.00000000
## 2072 3 72 158.131390 2 158.131390 0.00000000
## 2073 3 73 159.459460 1 159.459460 0.00000000
## 2074 3 74 159.768033 1 159.768033 0.00000000
## 2075 3 75 161.372603 1 163.626181 2.25357772
## 2076 3 76 162.784904 2 164.005541 1.22063765
## 2077 3 77 164.407019 2 164.577634 0.17061514
## 2078 3 78 165.525322 1 165.525322 0.00000000
## 2079 3 79 170.968659 2 170.968659 0.00000000
## 2080 3 80 173.027380 1 173.027380 0.00000000
## 2081 3 81 173.905877 2 173.905877 0.00000000
## 2082 3 82 175.402198 1 175.402198 0.00000000
## 2083 3 83 175.693389 2 175.749689 0.05629976
## 2084 3 84 176.414560 2 176.414560 0.00000000
## 2085 3 85 176.736669 2 177.168675 0.43200568
## 2086 3 86 178.697578 1 178.697578 0.00000000
## 2087 3 87 181.953902 1 181.953902 0.00000000
## 2088 3 88 182.012620 2 182.012620 0.00000000
## 2089 3 89 182.502448 1 182.502448 0.00000000
## 2090 3 90 184.277129 2 184.277129 0.00000000
## 2091 3 91 184.508366 1 186.253537 1.74517078
## 2092 3 92 186.552672 2 186.552672 0.00000000
## 2093 3 93 190.777024 1 190.777024 0.00000000
## 2094 3 94 200.050667 1 200.050667 0.00000000
## 2095 3 95 200.109219 2 200.109219 0.00000000
## 2096 3 96 200.575091 2 200.954792 0.37970072
## 2097 3 97 200.896653 1 202.766874 1.87022054
## 2098 3 98 201.855047 1 202.967678 1.11263172
## 2099 3 99 205.192225 2 205.192225 0.00000000
## 2100 3 100 205.702407 1 205.702407 0.00000000
## 2101 3 101 211.630108 1 211.630108 0.00000000
## 2102 3 102 211.743037 2 211.743037 0.00000000
## 2103 3 103 219.580604 1 219.580604 0.00000000
## 2104 3 104 221.952579 2 221.952579 0.00000000
## 2105 3 105 222.527411 1 222.527411 0.00000000
## 2106 3 106 223.115407 2 226.069215 2.95380773
## 2107 3 107 225.669466 1 227.253680 1.58421438
## 2108 3 108 228.065225 2 228.065225 0.00000000
## 2109 3 109 235.432555 2 235.432555 0.00000000
## 2110 3 110 236.603783 1 236.603783 0.00000000
## 2111 3 111 238.192644 2 238.192644 0.00000000
## 2112 3 112 238.637718 1 238.637718 0.00000000
## 2113 3 113 239.239709 2 239.268471 0.02876111
## 2114 3 114 240.766366 2 240.766366 0.00000000
## 2115 3 115 246.169185 1 246.169185 0.00000000
## 2116 3 116 246.287027 2 246.287027 0.00000000
## 2117 3 117 247.300977 1 247.300977 0.00000000
## 2118 3 118 249.313003 2 249.313003 0.00000000
## 2119 3 119 249.602335 1 249.602335 0.00000000
## 2120 3 120 249.692612 2 250.730979 1.03836688
## 2121 3 121 252.506203 2 252.506203 0.00000000
## 2122 3 122 256.497786 1 256.497786 0.00000000
## 2123 3 123 256.531599 2 256.531599 0.00000000
## 2124 3 124 256.858940 1 256.858940 0.00000000
## 2125 3 125 257.167113 2 257.167113 0.00000000
## 2126 3 126 258.136813 1 259.054762 0.91794871
## 2127 3 127 258.654613 2 260.666973 2.01235929
## 2128 3 128 259.185609 2 261.477716 2.29210620
## 2129 3 129 265.701676 2 265.701676 0.00000000
## 2130 3 130 265.888250 1 265.888250 0.00000000
## 2131 3 131 267.609260 1 267.609260 0.00000000
## 2132 3 132 270.826657 2 270.826657 0.00000000
## 2133 3 133 271.441025 1 271.441025 0.00000000
## 2134 3 134 271.668450 2 271.668450 0.00000000
## 2135 3 135 271.961521 2 272.152105 0.19058377
## 2136 3 136 273.150923 2 273.150923 0.00000000
## 2137 3 137 276.723291 2 276.723291 0.00000000
## 2138 3 138 280.431677 1 280.431677 0.00000000
## 2139 3 139 281.374897 2 281.374897 0.00000000
## 2140 3 140 282.104189 2 282.908710 0.80452186
## 2141 3 141 282.713104 1 283.312238 0.59913390
## 2142 3 142 282.870307 1 283.820751 0.95044388
## 2143 3 143 282.881923 1 285.666318 2.78439560
## 2144 3 144 285.432513 1 286.363065 0.93055141
## 2145 3 145 288.288881 1 288.288881 0.00000000
## 2146 3 146 294.083657 2 294.083657 0.00000000
## 2147 3 147 298.232471 1 298.232471 0.00000000
## 2148 3 148 298.834926 2 298.834926 0.00000000
## 2149 3 149 298.967317 1 299.112640 0.14532318
## 2150 3 150 304.340179 1 304.340179 0.00000000
## 2151 3 151 309.473234 2 309.473234 0.00000000
## 2152 3 152 310.550878 1 310.550878 0.00000000
## 2153 3 153 311.565764 2 311.565764 0.00000000
## 2154 3 154 312.100132 1 312.100132 0.00000000
## 2155 3 155 314.130777 2 314.130777 0.00000000
## 2156 3 156 314.228700 2 314.501456 0.27275558
## 2157 3 157 314.731756 2 320.607544 5.87578762
## 2158 3 158 318.123776 1 321.834478 3.71070158
## 2159 3 159 324.961375 1 324.961375 0.00000000
## 2160 3 160 326.586677 2 327.909012 1.32233526
## 2161 3 161 327.012043 1 328.855641 1.84359715
## 2162 3 162 329.616249 2 330.127198 0.51094872
## 2163 3 163 329.928690 1 330.311362 0.38267198
## 2164 3 164 331.655639 1 331.655639 0.00000000
## 2165 3 165 337.813024 2 337.813024 0.00000000
## 2166 3 166 338.491855 1 338.491855 0.00000000
## 2167 3 167 348.928731 1 348.928731 0.00000000
## 2168 3 168 350.295652 2 350.295652 0.00000000
## 2169 3 169 351.154659 1 352.104070 0.94941158
## 2170 3 170 353.225979 2 353.605239 0.37925997
## 2171 3 171 354.515559 2 354.515559 0.00000000
## 2172 3 172 355.757595 2 357.839799 2.08220384
## 2173 3 173 359.868992 2 359.868992 0.00000000
## 2174 3 174 361.056507 2 361.115689 0.05918147
## 2175 3 175 362.455967 1 362.455967 0.00000000
## 2176 3 176 364.464836 1 364.464836 0.00000000
## 2177 3 177 365.752145 2 365.752145 0.00000000
## 2178 3 178 368.592532 2 368.592532 0.00000000
## 2179 3 179 369.313325 1 369.313325 0.00000000
## 2180 3 180 382.076981 2 382.076981 0.00000000
## 2181 3 181 384.397429 1 384.397429 0.00000000
## 2182 3 182 387.357483 2 387.357483 0.00000000
## 2183 3 183 388.406082 2 389.854064 1.44798167
## 2184 3 184 394.746701 1 394.746701 0.00000000
## 2185 3 185 395.123209 2 395.123209 0.00000000
## 2186 3 186 397.129778 2 397.947871 0.81809389
## 2187 3 187 397.519750 1 399.216434 1.69668403
## 2188 3 188 405.730668 2 405.730668 0.00000000
## 2189 3 189 405.888529 1 405.888529 0.00000000
## 2190 3 190 408.395998 2 408.395998 0.00000000
## 2191 3 191 410.884786 2 410.884786 0.00000000
## 2192 3 192 411.267923 1 411.267923 0.00000000
## 2193 3 193 414.249461 2 415.935515 1.68605314
## 2194 3 194 414.260728 2 416.551635 2.29090694
## 2195 3 195 417.330663 2 418.341101 1.01043763
## 2196 3 196 423.169071 2 423.169071 0.00000000
## 2197 3 197 424.143900 1 424.143900 0.00000000
## 2198 3 198 430.649007 2 430.649007 0.00000000
## 2199 3 199 433.909699 1 433.909699 0.00000000
## 2200 3 200 441.015443 2 441.015443 0.00000000
## 2201 3 201 442.780094 1 442.780094 0.00000000
## 2202 3 202 444.670021 2 444.670021 0.00000000
## 2203 3 203 444.932138 1 444.932138 0.00000000
## 2204 3 204 450.385663 2 450.385663 0.00000000
## 2205 3 205 454.177984 1 454.177984 0.00000000
## 2206 3 206 455.636744 2 455.636744 0.00000000
## 2207 3 207 455.681865 1 455.681865 0.00000000
## 2208 3 208 457.051978 2 457.310339 0.25836040
## 2209 3 209 458.218695 1 458.218695 0.00000000
## 2210 3 210 465.497718 2 465.497718 0.00000000
## 2211 3 211 466.356001 1 466.356001 0.00000000
## 2212 3 212 469.848791 2 472.318208 2.46941684
## 2213 3 213 476.115429 1 476.115429 0.00000000
## 2214 3 214 479.207696 2 479.207696 0.00000000
## 2215 3 215 480.070440 2 480.070440 0.00000000
## 2216 3 216 480.984939 1 480.984939 0.00000000
## 2217 3 217 485.323043 1 485.323043 0.00000000
## 2218 3 218 485.358643 2 485.358643 0.00000000
## 2219 3 219 486.832659 2 486.832659 0.00000000
## 2220 3 220 490.493343 2 490.493343 0.00000000
## 2221 3 221 495.637483 1 495.637483 0.00000000
## 2222 3 222 496.693230 2 496.693230 0.00000000
## 2223 3 223 497.802713 1 497.802713 0.00000000
## 2224 3 224 500.158921 2 500.158921 0.00000000
## 2225 3 225 501.117141 1 501.323877 0.20673656
## 2226 3 226 501.963141 2 501.963141 0.00000000
## 2227 3 227 502.705317 1 502.705317 0.00000000
## 2228 3 228 503.934041 2 503.934041 0.00000000
## 2229 3 229 507.279820 2 507.279820 0.00000000
## 2230 3 230 520.070634 1 520.070634 0.00000000
## 2231 3 231 520.183640 2 520.183640 0.00000000
## 2232 3 232 522.641118 1 522.641118 0.00000000
## 2233 3 233 523.331913 2 523.331913 0.00000000
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## 10766 11 766 1638.730136 2 1638.730136 0.00000000
## 10767 11 767 1639.364249 1 1639.364249 0.00000000
## 10768 11 768 1639.934781 2 1639.934781 0.00000000
## 10769 11 769 1641.846606 1 1641.846606 0.00000000
## 10770 11 770 1643.009808 1 1643.009808 0.00000000
## 10771 11 771 1648.447326 2 1648.447326 0.00000000
## 10772 11 772 1651.503738 1 1651.503738 0.00000000
## 10773 11 773 1652.778520 2 1652.778520 0.00000000
## 10774 11 774 1652.840055 1 1652.840055 0.00000000
## 10775 11 775 1652.851921 1 1653.500860 0.64893961
## 10776 11 776 1652.986134 2 1655.048250 2.06211592
## 10777 11 777 1656.284133 1 1656.284133 0.00000000
## 10778 11 778 1657.457774 1 1658.074934 0.61716010
## 10779 11 779 1661.720246 1 1661.720246 0.00000000
## 10780 11 780 1663.126995 1 1663.309047 0.18205278
## 10781 11 781 1664.670971 2 1664.670971 0.00000000
## 10782 11 782 1664.982722 2 1664.982722 0.00000000
## 10783 11 783 1668.701569 2 1668.701569 0.00000000
## 10784 11 784 1671.229280 1 1671.229280 0.00000000
## 10785 11 785 1672.618473 2 1672.618473 0.00000000
## 10786 11 786 1675.219844 2 1675.219844 0.00000000
## 10787 11 787 1675.868737 2 1678.274849 2.40611230
## 10788 11 788 1677.640063 2 1681.286667 3.64660435
## 10789 11 789 1678.218316 1 1682.467907 4.24959147
## 10790 11 790 1680.484099 1 1682.482608 1.99850857
## 10791 11 791 1680.554477 2 1683.750386 3.19590925
## 10792 11 792 1686.507429 2 1686.507429 0.00000000
## 10793 11 793 1687.799451 2 1687.799451 0.00000000
## 10794 11 794 1689.503710 2 1689.503710 0.00000000
## 10795 11 795 1689.529350 1 1689.529350 0.00000000
## 10796 11 796 1690.847883 1 1690.847883 0.00000000
## 10797 11 797 1692.227805 1 1692.227805 0.00000000
## 10798 11 798 1693.010641 2 1693.010641 0.00000000
## 10799 11 799 1696.386700 1 1696.386700 0.00000000
## 10800 11 800 1697.673201 1 1698.358992 0.68579118
## 10801 11 801 1699.133792 1 1699.133792 0.00000000
## 10802 11 802 1701.062315 1 1701.062315 0.00000000
## 10803 11 803 1701.390882 1 1701.390882 0.00000000
## 10804 11 804 1704.875638 1 1704.875638 0.00000000
## 10805 11 805 1709.441858 2 1709.441858 0.00000000
## 10806 11 806 1709.896260 1 1709.896260 0.00000000
## 10807 11 807 1710.889035 2 1710.889035 0.00000000
## 10808 11 808 1713.827327 2 1713.827327 0.00000000
## 10809 11 809 1714.241042 1 1714.241042 0.00000000
## 10810 11 810 1715.184996 1 1715.184996 0.00000000
## 10811 11 811 1718.268957 1 1718.268957 0.00000000
## 10812 11 812 1719.092028 2 1719.092028 0.00000000
## 10813 11 813 1722.132414 2 1722.132414 0.00000000
## 10814 11 814 1722.190048 1 1722.190048 0.00000000
## 10815 11 815 1725.088380 1 1725.088380 0.00000000
## 10816 11 816 1726.440960 2 1726.440960 0.00000000
## 10817 11 817 1729.981482 2 1729.981482 0.00000000
## 10818 11 818 1731.584152 2 1731.584152 0.00000000
## 10819 11 819 1737.602725 1 1737.602725 0.00000000
## 10820 11 820 1738.734697 2 1738.734697 0.00000000
## 10821 11 821 1740.840585 2 1740.840585 0.00000000
## 10822 11 822 1742.361237 2 1742.361237 0.00000000
## 10823 11 823 1742.970692 2 1742.970692 0.00000000
## 10824 11 824 1745.332300 2 1745.332300 0.00000000
## 10825 11 825 1745.573438 2 1746.026779 0.45334095
## 10826 11 826 1746.099943 1 1746.175550 0.07560645
## 10827 11 827 1754.521315 1 1754.521315 0.00000000
## 10828 11 828 1757.134510 2 1757.134510 0.00000000
## 10829 11 829 1757.451806 1 1757.451806 0.00000000
## 10830 11 830 1758.916208 2 1758.916208 0.00000000
## 10831 11 831 1759.241742 2 1760.005440 0.76369820
## 10832 11 832 1759.379132 1 1761.592656 2.21352376
## 10833 11 833 1761.052247 1 1761.807207 0.75495977
## 10834 11 834 1764.551316 1 1764.551316 0.00000000
## 10835 11 835 1767.002170 1 1767.002170 0.00000000
## 10836 11 836 1773.511279 2 1773.511279 0.00000000
## 10837 11 837 1776.119127 1 1776.119127 0.00000000
## 10838 11 838 1776.933136 2 1776.933136 0.00000000
## 10839 11 839 1778.451892 2 1778.451892 0.00000000
## 10840 11 840 1778.999189 1 1778.999189 0.00000000
## 10841 11 841 1779.264414 1 1781.020881 1.75646673
## 10842 11 842 1782.667660 1 1782.667660 0.00000000
## 10843 11 843 1786.432404 1 1786.432404 0.00000000
## 10844 11 844 1787.539145 2 1787.539145 0.00000000
## 10845 11 845 1791.199635 1 1791.199635 0.00000000
## 10846 11 846 1796.905193 2 1796.905193 0.00000000
## 10847 11 847 1797.109807 1 1797.109807 0.00000000
## 10848 11 848 1799.404796 2 1799.404796 0.00000000
## 10849 11 849 1801.963747 1 1801.963747 0.00000000
## 10850 11 850 1807.915943 2 1807.915943 0.00000000
## 10851 11 851 1809.389327 1 1809.389327 0.00000000
## 10852 11 852 1815.830709 2 1815.830709 0.00000000
## 10853 11 853 1819.976646 1 1819.976646 0.00000000
## 10854 11 854 1820.832450 2 1820.832450 0.00000000
## 10855 11 855 1821.036564 1 1821.977151 0.94058740
## 10856 11 856 1822.399514 1 1823.571330 1.17181553
## 10857 11 857 1822.893058 1 1825.173320 2.28026217
## 10858 11 858 1826.599075 2 1826.599075 0.00000000
## 10859 11 859 1829.466838 1 1829.466838 0.00000000
## 10860 11 860 1832.887706 2 1832.887706 0.00000000
## 10861 11 861 1832.988658 1 1836.237986 3.24932866
## 10862 11 862 1835.721120 2 1838.014430 2.29330982
## 10863 11 863 1838.200832 2 1839.088184 0.88735124
## 10864 11 864 1841.582765 1 1841.582765 0.00000000
## 10865 11 865 1842.842993 2 1842.842993 0.00000000
## 10866 11 866 1844.723438 2 1844.723438 0.00000000
## 10867 11 867 1845.405256 1 1847.860308 2.45505144
## 10868 11 868 1845.678942 2 1848.702804 3.02386271
## 10869 11 869 1850.375773 2 1850.375773 0.00000000
## 10870 11 870 1852.542252 1 1852.542252 0.00000000
## 10871 11 871 1856.863762 2 1856.863762 0.00000000
## 10872 11 872 1857.263698 1 1857.263698 0.00000000
## 10873 11 873 1858.228697 1 1858.228697 0.00000000
## 10874 11 874 1861.728557 1 1861.728557 0.00000000
## 10875 11 875 1862.589085 2 1864.497146 1.90806108
## 10876 11 876 1865.815361 1 1867.741698 1.92633716
## 10877 11 877 1867.029591 1 1868.503712 1.47412066
## 10878 11 878 1867.363272 2 1871.959963 4.59669113
## 10879 11 879 1869.328823 1 1872.031831 2.70300809
## 10880 11 880 1870.859631 1 1873.371741 2.51210961
## 10881 11 881 1872.393416 1 1873.443350 1.04993475
## 10882 11 882 1878.864731 1 1878.864731 0.00000000
## 10883 11 883 1882.332872 2 1882.332872 0.00000000
## 10884 11 884 1884.036196 1 1884.036196 0.00000000
## 10885 11 885 1889.682971 2 1889.682971 0.00000000
## 10886 11 886 1890.868557 1 1890.868557 0.00000000
## 10887 11 887 1894.324642 2 1894.324642 0.00000000
## 10888 11 888 1896.340472 2 1896.340472 0.00000000
## 10889 11 889 1899.856455 1 1899.856455 0.00000000
## 10890 11 890 1900.397887 2 1900.397887 0.00000000
## 10891 11 891 1905.052911 1 1905.052911 0.00000000
## 10892 11 892 1908.146787 2 1908.146787 0.00000000
## 10893 11 893 1909.324986 1 1912.498492 3.17350539
## 10894 11 894 1916.177465 2 1917.336810 1.15934448
## 10895 11 895 1917.950117 1 1917.950117 0.00000000
## 10896 11 896 1920.856647 1 1920.856647 0.00000000
## 10897 11 897 1924.277629 1 1924.277629 0.00000000
## 10898 11 898 1928.386163 2 1928.386163 0.00000000
## 10899 11 899 1933.236413 1 1933.236413 0.00000000
## 10900 11 900 1933.405523 2 1933.565653 0.16013057
## 10901 11 901 1934.088396 1 1935.453391 1.36499503
## 10902 11 902 1935.149669 2 1938.377344 3.22767461
## 10903 11 903 1939.161503 1 1940.376328 1.21482409
## 10904 11 904 1939.480307 2 1940.650582 1.17027502
## 10905 11 905 1940.752952 1 1940.752952 0.00000000
## 10906 11 906 1946.011407 1 1946.011407 0.00000000
## 10907 11 907 1948.053322 1 1948.053322 0.00000000
## 10908 11 908 1948.462636 2 1948.462636 0.00000000
## 10909 11 909 1948.961378 2 1950.028721 1.06734259
## 10910 11 910 1950.999917 1 1952.307204 1.30728640
## 10911 11 911 1951.909545 2 1952.383627 0.47408273
## 10912 11 912 1954.547469 2 1954.547469 0.00000000
## 10913 11 913 1955.060743 2 1956.904826 1.84408240
## 10914 11 914 1955.684437 2 1959.561524 3.87708737
## 10915 11 915 1956.215078 2 1959.846202 3.63112387
## 10916 11 916 1959.527183 1 1961.111350 1.58416737
## 10917 11 917 1960.497430 1 1961.881750 1.38431920
## 10918 11 918 1961.658680 1 1961.969984 0.31130407
## 10919 11 919 1962.692205 2 1964.932323 2.24011780
## 10920 11 920 1966.669078 2 1966.669078 0.00000000
## 10921 11 921 1971.635321 1 1971.635321 0.00000000
## 10922 11 922 1972.563245 1 1974.857609 2.29436360
## 10923 11 923 1974.465708 1 1975.634931 1.16922252
## 10924 11 924 1976.771498 1 1976.771498 0.00000000
## 10925 11 925 1977.198867 1 1980.726964 3.52809774
## 10926 11 926 1977.814765 1 1982.953875 5.13911026
## 10927 11 927 1977.932344 2 1985.824076 7.89173151
## 10928 11 928 1981.123636 2 1986.168470 5.04483437
## 10929 11 929 1983.886552 1 1986.391268 2.50471567
## 10930 11 930 1984.093667 2 1987.329407 3.23574029
## 10931 11 931 1985.691563 1 1988.025094 2.33353084
## 10932 11 932 1986.257492 2 1988.608117 2.35062449
## 10933 11 933 1987.877378 1 1991.538294 3.66091551
## 10934 11 934 1996.371952 1 1996.371952 0.00000000
## 10935 11 935 1996.804853 2 1996.804853 0.00000000
## 10936 11 936 1998.096495 1 1998.096495 0.00000000
## 10937 11 937 1998.298116 2 1998.298116 0.00000000
## 10938 11 938 1998.621127 1 2003.171319 4.55019223
## 10939 11 939 2000.386067 1 2003.626284 3.24021773
## 10940 11 940 2002.404060 1 2005.554436 3.15037623
## 10941 11 941 2003.727712 1 2008.704723 4.97701192
## 10942 11 942 2006.911912 1 2010.107891 3.19597914
## 10943 11 943 2012.842246 2 2012.842246 0.00000000
## 10944 11 944 2013.531940 2 2014.879997 1.34805650
## 10945 11 945 2016.496241 2 2017.381025 0.88478436
## 10946 11 946 2019.300439 1 2019.300439 0.00000000
## 10947 11 947 2019.622862 2 2019.622862 0.00000000
## 10948 11 948 2020.057962 2 2020.091306 0.03334465
## 10949 11 949 2023.159320 1 2023.159320 0.00000000
## 10950 11 950 2023.284080 2 2026.679764 3.39568411
## 10951 11 951 2025.579799 1 2028.054838 2.47503868
## 10952 11 952 2027.349136 1 2030.202932 2.85379590
## 10953 11 953 2027.976602 1 2034.974670 6.99806764
## 10954 11 954 2030.223071 2 2035.810150 5.58707896
## 10955 11 955 2034.435436 2 2037.174025 2.73858913
## 10956 11 956 2037.104276 1 2037.476861 0.37258452
## 10957 11 957 2037.353855 1 2038.036578 0.68272322
## 10958 11 958 2040.718065 2 2040.718065 0.00000000
## 10959 11 959 2048.646879 1 2048.646879 0.00000000
## 10960 11 960 2049.336103 2 2049.336103 0.00000000
## 10961 11 961 2050.912905 1 2050.912905 0.00000000
## 10962 11 962 2053.075831 2 2053.075831 0.00000000
## 10963 11 963 2055.081939 1 2055.081939 0.00000000
## 10964 11 964 2056.978144 2 2056.978144 0.00000000
## 10965 11 965 2058.592525 1 2058.592525 0.00000000
## 10966 11 966 2059.275290 2 2059.275290 0.00000000
## 10967 11 967 2063.866808 2 2063.866808 0.00000000
## 10968 11 968 2064.722860 1 2064.722860 0.00000000
## 10969 11 969 2065.371490 2 2068.135047 2.76355700
## 10970 11 970 2066.832560 1 2069.097488 2.26492793
## 10971 11 971 2069.956493 1 2070.305223 0.34872984
## 10972 11 972 2071.685304 2 2071.685304 0.00000000
## 10973 11 973 2077.250284 1 2077.250284 0.00000000
## 10974 11 974 2080.882692 1 2080.882692 0.00000000
## 10975 11 975 2084.333755 2 2084.333755 0.00000000
## 10976 11 976 2085.530542 1 2085.530542 0.00000000
## 10977 11 977 2087.434442 2 2087.434442 0.00000000
## 10978 11 978 2089.745438 1 2089.745438 0.00000000
## 10979 11 979 2090.281966 1 2091.136176 0.85420977
## 10980 11 980 2092.669296 1 2094.307549 1.63825303
## 10981 11 981 2100.338987 2 2100.338987 0.00000000
## 10982 11 982 2105.966014 1 2105.966014 0.00000000
## 10983 11 983 2106.603983 2 2106.603983 0.00000000
## 10984 11 984 2110.126785 2 2110.126785 0.00000000
## 10985 11 985 2110.935138 2 2110.935138 0.00000000
## 10986 11 986 2121.004549 2 2121.004549 0.00000000
## 10987 11 987 2121.989204 1 2121.989204 0.00000000
## 10988 11 988 2123.519520 1 2123.519520 0.00000000
## 10989 11 989 2131.152583 2 2131.152583 0.00000000
## 10990 11 990 2134.719230 1 2134.719230 0.00000000
## 10991 11 991 2136.070104 1 2136.945235 0.87513130
## 10992 11 992 2138.125704 1 2139.330633 1.20492919
## 10993 11 993 2147.233717 2 2147.233717 0.00000000
## 10994 11 994 2149.648847 1 2149.648847 0.00000000
## 10995 11 995 2151.031276 2 2151.031276 0.00000000
## 10996 11 996 2152.953743 1 2152.953743 0.00000000
## 10997 11 997 2156.023804 2 2156.023804 0.00000000
## 10998 11 998 2158.758074 1 2158.758074 0.00000000
## 10999 11 999 2159.662817 2 2159.662817 0.00000000
## 11000 11 1000 2161.351034 1 2161.351034 0.00000000
## 11001 12 1 3.087574 1 3.087574 0.00000000
## 11002 12 2 3.192694 2 3.192694 0.00000000
## 11003 12 3 3.923205 2 3.923205 0.00000000
## 11004 12 4 4.499135 2 6.262708 1.76357339
## 11005 12 5 4.861432 2 8.863493 4.00206105
## 11006 12 6 5.530262 2 9.519090 3.98882754
## 11007 12 7 6.056305 2 9.926737 3.87043239
## 11008 12 8 6.233902 1 10.946562 4.71265975
## 11009 12 9 9.028394 2 12.637457 3.60906348
## 11010 12 10 9.799312 2 13.021028 3.22171585
## 11011 12 11 12.887240 2 14.726337 1.83909778
## 11012 12 12 14.479051 2 16.543085 2.06403378
## 11013 12 13 15.287167 1 16.697494 1.41032710
## 11014 12 14 17.873723 1 18.638597 0.76487493
## 11015 12 15 19.576498 2 19.576498 0.00000000
## 11016 12 16 24.450535 2 24.450535 0.00000000
## 11017 12 17 26.552349 2 26.552349 0.00000000
## 11018 12 18 31.446294 1 34.210026 2.76373212
## 11019 12 19 32.686542 2 34.973143 2.28660069
## 11020 12 20 36.387368 1 36.387368 0.00000000
## 11021 12 21 38.368416 2 38.368416 0.00000000
## 11022 12 22 38.981508 1 38.981508 0.00000000
## 11023 12 23 43.900782 2 43.900782 0.00000000
## 11024 12 24 46.668569 1 46.668569 0.00000000
## 11025 12 25 50.838580 2 50.838580 0.00000000
## 11026 12 26 51.539764 1 52.722886 1.18312246
## 11027 12 27 52.206211 2 53.143928 0.93771735
## 11028 12 28 53.841404 2 53.841404 0.00000000
## 11029 12 29 57.657857 1 57.657857 0.00000000
## 11030 12 30 57.865842 2 58.857952 0.99210980
## 11031 12 31 58.234750 1 61.500358 3.26560771
## 11032 12 32 58.632652 1 61.601204 2.96855183
## 11033 12 33 62.702309 1 64.401412 1.69910235
## 11034 12 34 65.214619 1 65.214619 0.00000000
## 11035 12 35 68.383515 1 68.383515 0.00000000
## 11036 12 36 73.767421 2 73.767421 0.00000000
## 11037 12 37 73.808449 1 73.808449 0.00000000
## 11038 12 38 78.001984 1 78.001984 0.00000000
## 11039 12 39 80.805942 2 80.805942 0.00000000
## 11040 12 40 82.093083 1 82.093083 0.00000000
## 11041 12 41 85.117379 1 85.117379 0.00000000
## 11042 12 42 86.729713 2 86.729713 0.00000000
## 11043 12 43 88.962654 2 88.962654 0.00000000
## 11044 12 44 93.640096 1 93.640096 0.00000000
## 11045 12 45 97.403074 2 97.403074 0.00000000
## 11046 12 46 97.680860 1 97.680860 0.00000000
## 11047 12 47 101.778686 2 101.778686 0.00000000
## 11048 12 48 105.546421 1 105.546421 0.00000000
## 11049 12 49 109.102289 2 109.102289 0.00000000
## 11050 12 50 110.694495 2 110.694495 0.00000000
## 11051 12 51 114.197407 2 114.197407 0.00000000
## 11052 12 52 118.233050 1 118.233050 0.00000000
## 11053 12 53 119.205228 1 121.431097 2.22586928
## 11054 12 54 119.418807 2 124.117786 4.69897909
## 11055 12 55 119.937513 2 125.516321 5.57880776
## 11056 12 56 120.016570 1 125.940829 5.92425952
## 11057 12 57 120.466709 2 126.965345 6.49863584
## 11058 12 58 121.258166 1 128.299215 7.04104958
## 11059 12 59 131.295221 2 131.295221 0.00000000
## 11060 12 60 132.310750 2 133.055414 0.74466411
## 11061 12 61 132.599568 2 133.482362 0.88279323
## 11062 12 62 132.862692 1 135.168567 2.30587504
## 11063 12 63 135.222640 1 135.281556 0.05891587
## 11064 12 64 139.307188 1 139.307188 0.00000000
## 11065 12 65 141.926333 2 141.926333 0.00000000
## 11066 12 66 142.321889 1 142.321889 0.00000000
## 11067 12 67 142.680407 1 142.680407 0.00000000
## 11068 12 68 151.782389 2 151.782389 0.00000000
## 11069 12 69 152.927239 1 152.927239 0.00000000
## 11070 12 70 154.944050 1 154.944050 0.00000000
## 11071 12 71 156.937404 2 156.937404 0.00000000
## 11072 12 72 158.131390 2 158.131390 0.00000000
## 11073 12 73 159.459460 1 159.459460 0.00000000
## 11074 12 74 159.768033 1 159.768033 0.00000000
## 11075 12 75 161.372603 1 163.626181 2.25357772
## 11076 12 76 162.784904 2 164.005541 1.22063765
## 11077 12 77 164.407019 2 164.577634 0.17061514
## 11078 12 78 165.525322 1 165.525322 0.00000000
## 11079 12 79 170.968659 2 170.968659 0.00000000
## 11080 12 80 173.027380 1 173.027380 0.00000000
## 11081 12 81 173.905877 2 173.905877 0.00000000
## 11082 12 82 175.402198 1 175.402198 0.00000000
## 11083 12 83 175.693389 2 175.749689 0.05629976
## 11084 12 84 176.414560 2 176.414560 0.00000000
## 11085 12 85 176.736669 2 177.168675 0.43200568
## 11086 12 86 178.697578 1 178.697578 0.00000000
## 11087 12 87 181.953902 1 181.953902 0.00000000
## 11088 12 88 182.012620 2 182.012620 0.00000000
## 11089 12 89 182.502448 1 182.502448 0.00000000
## 11090 12 90 184.277129 2 184.277129 0.00000000
## 11091 12 91 184.508366 1 186.253537 1.74517078
## 11092 12 92 186.552672 2 186.552672 0.00000000
## 11093 12 93 190.777024 1 190.777024 0.00000000
## 11094 12 94 200.050667 1 200.050667 0.00000000
## 11095 12 95 200.109219 2 200.109219 0.00000000
## 11096 12 96 200.575091 2 200.954792 0.37970072
## 11097 12 97 200.896653 1 202.766874 1.87022054
## 11098 12 98 201.855047 1 202.967678 1.11263172
## 11099 12 99 205.192225 2 205.192225 0.00000000
## 11100 12 100 205.702407 1 205.702407 0.00000000
## 11101 12 101 211.630108 1 211.630108 0.00000000
## 11102 12 102 211.743037 2 211.743037 0.00000000
## 11103 12 103 219.580604 1 219.580604 0.00000000
## 11104 12 104 221.952579 2 221.952579 0.00000000
## 11105 12 105 222.527411 1 222.527411 0.00000000
## 11106 12 106 223.115407 2 226.069215 2.95380773
## 11107 12 107 225.669466 1 227.253680 1.58421438
## 11108 12 108 228.065225 2 228.065225 0.00000000
## 11109 12 109 235.432555 2 235.432555 0.00000000
## 11110 12 110 236.603783 1 236.603783 0.00000000
## 11111 12 111 238.192644 2 238.192644 0.00000000
## service_time depart_time c_servers
## 1 7.858988148 10.946562 2
## 2 0.240353530 3.433047 2
## 3 2.339502950 6.262708 2
## 4 2.600784915 8.863493 2
## 5 0.655596642 9.519090 2
## 6 0.407647584 9.926737 2
## 7 2.710720053 12.637457 2
## 8 5.750932144 16.697494 2
## 9 0.383570668 13.021028 2
## 10 1.705309549 14.726337 2
## 11 1.816747136 16.543085 2
## 12 2.237538094 18.780623 2
## 13 1.941103501 18.638597 2
## 14 15.571429015 34.210026 2
## 15 2.352234241 21.928732 2
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## 1775 2.463531656 1655.964392 2
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## 1778 1.582713720 1659.657648 2
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## 1781 0.119021115 1664.789992 2
## 1782 0.134757688 1665.117480 2
## 1783 2.855228039 1671.556797 2
## 1784 11.238627019 1682.467907 2
## 1785 0.303491133 1672.921964 2
## 1786 3.055005208 1678.274849 2
## 1787 3.011818176 1681.286667 2
## 1788 2.463719049 1683.750386 2
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## 1790 6.577316445 1689.059924 2
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## 1794 2.509734230 1692.013444 2
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## 1796 0.743799996 1691.591683 2
## 1797 3.700682057 1695.928487 2
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## 1800 0.532432326 1698.891425 2
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## 1803 0.423640295 1701.814522 2
## 1804 1.329656204 1706.205294 2
## 1805 0.634775171 1710.076633 2
## 1806 3.799684865 1713.695945 2
## 1807 0.536883647 1711.425918 2
## 1808 2.724145176 1716.551472 2
## 1809 0.048858217 1714.289900 2
## 1810 0.243811868 1715.428808 2
## 1811 3.854608195 1722.123565 2
## 1812 2.647815550 1721.739844 2
## 1813 0.966752760 1723.099167 2
## 1814 0.497466740 1722.687515 2
## 1815 6.511201344 1731.599582 2
## 1816 0.969978829 1727.410938 2
## 1817 0.586043372 1730.567526 2
## 1818 0.636714905 1732.220867 2
## 1819 8.572824983 1746.175550 2
## 1820 0.461283123 1739.195980 2
## 1821 0.523923224 1741.364508 2
## 1822 0.550083840 1742.911320 2
## 1823 0.046668841 1743.017361 2
## 1824 0.694478810 1746.026779 2
## 1825 3.026641308 1749.053421 2
## 1826 0.043645352 1746.219195 2
## 1827 2.498406118 1757.019721 2
## 1828 1.690725801 1758.825236 2
## 1829 4.140849753 1761.592656 2
## 1830 1.089231868 1760.005440 2
## 1831 5.525146660 1765.530587 2
## 1832 0.214550460 1761.807207 2
## 1833 2.253250118 1764.060457 2
## 1834 0.667038039 1765.218354 2
## 1835 2.183208838 1769.185379 2
## 1836 1.290926198 1774.802205 2
## 1837 2.081834752 1778.200962 2
## 1838 0.903211611 1777.836347 2
## 1839 6.645767367 1785.097660 2
## 1840 2.021691213 1781.020881 2
## 1841 0.940562813 1781.961443 2
## 1842 2.092501670 1784.760161 2
## 1843 0.058455750 1786.490859 2
## 1844 2.255451683 1789.794596 2
## 1845 3.078387480 1794.278023 2
## 1846 0.322951676 1797.228144 2
## 1847 1.445301715 1798.555109 2
## 1848 1.567434983 1800.972231 2
## 1849 2.720049864 1804.683796 2
## 1850 0.320162466 1808.236106 2
## 1851 0.361563987 1809.750891 2
## 1852 1.216514460 1817.047223 2
## 1853 2.000505069 1821.977151 2
## 1854 4.672802384 1825.505253 2
## 1855 1.594178357 1823.571330 2
## 1856 1.601990228 1825.173320 2
## 1857 3.138798283 1828.312118 2
## 1858 4.504485434 1831.103560 2
## 1859 6.771147904 1836.237986 2
## 1860 5.126724004 1838.014430 2
## 1861 3.514848007 1839.752834 2
## 1862 1.073754028 1839.088184 2
## 1863 0.676333502 1839.764517 2
## 1864 6.277542230 1847.860308 2
## 1865 0.961476793 1843.804470 2
## 1866 3.979365923 1848.702804 2
## 1867 1.217102603 1849.077410 2
## 1868 0.196168906 1848.898973 2
## 1869 3.499921264 1853.875694 2
## 1870 4.314270284 1856.856522 2
## 1871 7.633384202 1864.497146 2
## 1872 0.218005620 1857.481704 2
## 1873 1.106484928 1859.335182 2
## 1874 6.013141361 1867.741698 2
## 1875 7.462816851 1871.959963 2
## 1876 0.762013706 1868.503712 2
## 1877 3.528119329 1872.031831 2
## 1878 7.296611892 1879.256575 2
## 1879 1.339909698 1873.371741 2
## 1880 0.071609232 1873.443350 2
## 1881 2.972202589 1876.415553 2
## 1882 3.244034118 1882.108765 2
## 1883 0.897491697 1883.230364 2
## 1884 0.227153997 1884.263350 2
## 1885 0.020815310 1889.703786 2
## 1886 5.583704148 1896.452262 2
## 1887 0.466440332 1894.791083 2
## 1888 3.953295483 1900.293767 2
## 1889 1.241258229 1901.097713 2
## 1890 3.712496779 1904.110384 2
## 1891 7.445580945 1912.498492 2
## 1892 9.190022955 1917.336810 2
## 1893 5.368866859 1917.867359 2
## 1894 10.279648031 1927.616458 2
## 1895 1.773987215 1919.724104 2
## 1896 1.455310850 1922.311958 2
## 1897 8.084709713 1932.362339 2
## 1898 5.179490887 1933.565653 2
## 1899 2.216978621 1935.453391 2
## 1900 4.811690026 1938.377344 2
## 1901 4.922936222 1940.376328 2
## 1902 2.273238515 1940.650582 2
## 1903 0.358080401 1940.734408 2
## 1904 6.373391064 1947.023973 2
## 1905 0.305839664 1941.058792 2
## 1906 0.166398003 1946.177805 2
## 1907 4.253881707 1952.307204 2
## 1908 1.566084442 1950.028721 2
## 1909 2.354906858 1952.383627 2
## 1910 8.804146563 1961.111350 2
## 1911 0.110284747 1952.493912 2
## 1912 2.357356270 1956.904826 2
## 1913 2.656698910 1959.561524 2
## 1914 0.284677234 1959.846202 2
## 1915 5.086121080 1964.932323 2
## 1916 0.770399201 1961.881750 2
## 1917 0.088234708 1961.969984 2
## 1918 4.005502081 1965.975486 2
## 1919 0.063784944 1964.996108 2
## 1920 19.154997876 1985.824076 2
## 1921 3.222287645 1974.857609 2
## 1922 0.777321527 1975.634931 2
## 1923 1.051985674 1976.686916 2
## 1924 3.955465970 1980.726964 2
## 1925 2.226911026 1982.953875 2
## 1926 3.437392367 1986.391268 2
## 1927 0.344394269 1986.168470 2
## 1928 1.160937537 1987.329407 2
## 1929 1.633826495 1988.025094 2
## 1930 1.278709243 1988.608117 2
## 1931 3.513199441 1991.538294 2
## 1932 6.833960287 1995.442077 2
## 1933 1.607751528 1993.146045 2
## 1934 0.726023100 1997.097975 2
## 1935 0.647260634 1997.452114 2
## 1936 5.074824461 2003.171319 2
## 1937 14.150962631 2012.449079 2
## 1938 0.454965291 2003.626284 2
## 1939 1.928151741 2005.554436 2
## 1940 3.150287365 2008.704723 2
## 1941 1.403168016 2010.107891 2
## 1942 8.115969464 2018.223861 2
## 1943 2.037750755 2014.879997 2
## 1944 2.501028690 2017.381025 2
## 1945 1.757177394 2019.138203 2
## 1946 1.294322768 2020.594761 2
## 1947 0.468443918 2020.091306 2
## 1948 6.588457510 2026.679764 2
## 1949 4.895517830 2028.054838 2
## 1950 9.130386499 2035.810150 2
## 1951 2.148094150 2030.202932 2
## 1952 4.771737626 2034.974670 2
## 1953 2.502191317 2037.476861 2
## 1954 1.363874764 2037.174025 2
## 1955 2.548432018 2039.722457 2
## 1956 0.559717106 2038.036578 2
## 1957 3.287108536 2041.323687 2
## 1958 0.927577261 2041.645643 2
## 1959 1.636948479 2050.283828 2
## 1960 1.689016072 2051.025120 2
## 1961 2.275006048 2053.187911 2
## 1962 2.330097341 2055.405928 2
## 1963 0.861095003 2055.943034 2
## 1964 0.322007059 2057.300151 2
## 1965 2.820678875 2061.413204 2
## 1966 1.775694343 2061.050984 2
## 1967 4.268238462 2068.135047 2
## 1968 4.374627812 2069.097488 2
## 1969 2.786321206 2070.921368 2
## 1970 1.207734958 2070.305223 2
## 1971 3.351608751 2073.656832 2
## 1972 6.926306659 2078.611611 2
## 1973 0.950619126 2078.200903 2
## 1974 2.015788518 2082.898480 2
## 1975 0.390362191 2084.724118 2
## 1976 0.479862175 2086.010404 2
## 1977 6.967035072 2094.401477 2
## 1978 1.390737959 2091.136176 2
## 1979 3.171373567 2094.307549 2
## 1980 3.343184017 2097.650733 2
## 1981 1.788816710 2102.127804 2
## 1982 7.878976996 2113.844991 2
## 1983 1.346945097 2107.950928 2
## 1984 0.762594097 2110.889379 2
## 1985 0.113221382 2111.048359 2
## 1986 1.601284046 2122.605833 2
## 1987 0.302320392 2122.291525 2
## 1988 0.546256236 2124.065777 2
## 1989 8.749552522 2139.902136 2
## 1990 2.226004833 2136.945235 2
## 1991 2.385398517 2139.330633 2
## 1992 2.184604051 2141.515238 2
## 1993 3.085745445 2150.319463 2
## 1994 1.988942457 2151.637790 2
## 1995 2.654672872 2153.685949 2
## 1996 1.355608495 2154.309352 2
## 1997 0.760319738 2156.784124 2
## 1998 2.217244248 2160.975319 2
## 1999 6.367852778 2166.030670 2
## 2000 0.428189446 2161.779223 2
## 2001 7.858988148 10.946562 2
## 2002 0.240353530 3.433047 2
## 2003 2.339502950 6.262708 2
## 2004 2.600784915 8.863493 2
## 2005 0.655596642 9.519090 2
## 2006 0.407647584 9.926737 2
## 2007 2.710720053 12.637457 2
## 2008 5.750932144 16.697494 2
## 2009 0.383570668 13.021028 2
## 2010 1.705309549 14.726337 2
## 2011 1.816747136 16.543085 2
## 2012 2.237538094 18.780623 2
## 2013 1.941103501 18.638597 2
## 2014 15.571429015 34.210026 2
## 2015 2.352234241 21.928732 2
## 2016 0.270207848 24.720742 2
## 2017 8.420794148 34.973143 2
## 2018 1.110528527 35.320555 2
## 2019 1.198265439 36.171409 2
## 2020 1.359912624 37.747280 2
## 2021 2.635485402 41.003902 2
## 2022 3.826330025 42.807838 2
## 2023 1.234829528 45.135611 2
## 2024 6.054317478 52.722886 2
## 2025 2.305348849 53.143928 2
## 2026 1.303937747 54.026824 2
## 2027 0.469964170 53.613893 2
## 2028 5.016547716 58.857952 2
## 2029 3.842501106 61.500358 2
## 2030 7.700468881 66.558421 2
## 2031 0.100846172 61.601204 2
## 2032 2.800207753 64.401412 2
## 2033 0.181467078 64.582879 2
## 2034 1.034000727 66.248619 2
## 2035 1.333469343 69.716984 2
## 2036 1.387372492 75.154794 2
## 2037 0.782754643 74.591203 2
## 2038 0.585328740 78.587313 2
## 2039 3.072951902 83.878894 2
## 2040 0.992378916 83.085462 2
## 2041 3.559569070 88.676948 2
## 2042 1.064608927 87.794322 2
## 2043 0.311766624 89.274421 2
## 2044 0.665572036 94.305668 2
## 2045 1.267347435 98.670421 2
## 2046 3.647234732 101.328095 2
## 2047 0.128655648 101.907341 2
## 2048 6.343744050 111.890165 2
## 2049 0.425418761 109.527708 2
## 2050 1.065437507 111.759933 2
## 2051 9.920379307 124.117786 2
## 2052 3.198046968 121.431097 2
## 2053 4.509732206 125.940829 2
## 2054 1.398535091 125.516321 2
## 2055 1.449023525 126.965345 2
## 2056 2.358385905 128.299215 2
## 2057 1.618779853 128.584124 2
## 2058 6.869352132 135.168567 2
## 2059 1.760192640 133.055414 2
## 2060 0.426947583 133.482362 2
## 2061 3.628063856 137.110425 2
## 2062 0.112988860 135.281556 2
## 2063 0.800526803 136.082083 2
## 2064 1.851358616 141.158546 2
## 2065 1.109283623 143.035617 2
## 2066 0.040605054 142.362494 2
## 2067 2.303907548 144.984315 2
## 2068 3.410703518 155.193093 2
## 2069 1.425475826 154.352715 2
## 2070 2.399854009 157.343904 2
## 2071 0.399842276 157.337246 2
## 2072 5.874150976 164.005541 2
## 2073 0.213786421 159.673246 2
## 2074 3.858147599 163.626181 2
## 2075 1.688682715 165.314864 2
## 2076 0.572093078 164.577634 2
## 2077 2.463268217 167.040902 2
## 2078 4.281815163 169.807138 2
## 2079 2.220611020 173.189270 2
## 2080 0.691831507 173.719211 2
## 2081 1.843811640 175.749689 2
## 2082 1.913556031 177.315754 2
## 2083 0.307557188 176.057246 2
## 2084 0.754114846 177.168675 2
## 2085 4.372227797 181.540902 2
## 2086 0.517510604 179.215088 2
## 2087 0.126692515 182.080595 2
## 2088 0.308683721 182.321303 2
## 2089 3.751089325 186.253537 2
## 2090 2.167055972 186.444185 2
## 2091 1.798096653 188.051634 2
## 2092 7.312699177 193.865371 2
## 2093 2.483952988 193.260977 2
## 2094 2.716206527 202.766874 2
## 2095 0.845572578 200.954792 2
## 2096 2.459909196 203.414701 2
## 2097 0.200804656 202.967678 2
## 2098 1.985212182 204.952891 2
## 2099 5.098255356 210.290480 2
## 2100 3.497090041 209.199497 2
## 2101 0.580401801 212.210510 2
## 2102 2.250858773 213.993896 2
## 2103 2.366547952 221.947152 2
## 2104 4.116635728 226.069215 2
## 2105 4.726268866 227.253680 2
## 2106 1.187761154 227.256976 2
## 2107 1.613819773 228.867500 2
## 2108 0.676457758 228.741682 2
## 2109 0.240355434 235.672910 2
## 2110 0.886178371 237.489962 2
## 2111 1.075826873 239.268471 2
## 2112 2.091106311 240.728824 2
## 2113 0.992445717 240.260916 2
## 2114 2.359536376 243.125903 2
## 2115 0.818505359 246.987691 2
## 2116 1.134698594 247.421725 2
## 2117 1.713051681 249.014028 2
## 2118 1.417975761 250.730979 2
## 2119 2.157011076 251.759346 2
## 2120 0.706025426 251.437004 2
## 2121 0.516081466 253.022285 2
## 2122 0.074081768 256.571868 2
## 2123 0.430897103 256.962496 2
## 2124 2.195821696 259.054762 2
## 2125 3.499859960 260.666973 2
## 2126 3.461256771 262.516019 2
## 2127 0.810743042 261.477716 2
## 2128 0.269021941 261.746738 2
## 2129 1.653128260 267.354804 2
## 2130 0.721183357 266.609434 2
## 2131 3.400692222 271.009952 2
## 2132 0.213759153 271.040416 2
## 2133 3.982240341 275.423265 2
## 2134 0.483655003 272.152105 2
## 2135 0.959602117 273.111707 2
## 2136 0.996750046 274.147673 2
## 2137 0.209780066 276.933071 2
## 2138 2.880560999 283.312238 2
## 2139 1.533813754 282.908710 2
## 2140 5.830884227 288.739595 2
## 2141 0.508512887 283.820751 2
## 2142 1.845567294 285.666318 2
## 2143 0.696746441 286.363065 2
## 2144 1.606991326 287.970056 2
## 2145 0.853139260 289.142021 2
## 2146 0.157435579 294.241092 2
## 2147 0.880168899 299.112640 2
## 2148 0.950125099 299.785051 2
## 2149 0.310143280 299.422783 2
## 2150 3.471357011 307.811536 2
## 2151 0.606388889 310.079623 2
## 2152 0.051463930 310.602342 2
## 2153 2.150648952 313.716413 2
## 2154 9.734345168 321.834478 2
## 2155 0.370679006 314.501456 2
## 2156 6.106088045 320.607544 2
## 2157 7.301467981 327.909012 2
## 2158 2.508231015 324.342709 2
## 2159 3.894265785 328.855641 2
## 2160 2.218185962 330.127198 2
## 2161 1.455721817 330.311362 2
## 2162 0.239377358 330.366575 2
## 2163 0.040667505 330.352030 2
## 2164 1.845885508 333.501524 2
## 2165 3.535229435 341.348253 2
## 2166 0.515755493 339.007610 2
## 2167 3.175339463 352.104070 2
## 2168 3.309586781 353.605239 2
## 2169 9.490261865 361.594332 2
## 2170 0.212200726 353.817440 2
## 2171 3.324240570 357.839799 2
## 2172 1.351243730 359.191043 2
## 2173 1.246697284 361.115689 2
## 2174 2.109115390 363.224804 2
## 2175 0.295289876 362.751256 2
## 2176 4.329740276 368.794577 2
## 2177 0.145515078 365.897660 2
## 2178 0.261051887 368.853584 2
## 2179 2.928683315 372.242008 2
## 2180 0.786133548 382.863114 2
## 2181 6.401733258 390.799162 2
## 2182 2.496581005 389.854064 2
## 2183 4.616681384 394.470746 2
## 2184 4.469733631 399.216434 2
## 2185 2.824662092 397.947871 2
## 2186 2.275401304 400.223273 2
## 2187 1.455792914 400.672227 2
## 2188 0.466923742 406.197592 2
## 2189 3.775347421 409.663876 2
## 2190 0.352393597 408.748392 2
## 2191 5.050728211 415.935515 2
## 2192 11.696996990 422.964920 2
## 2193 0.616120006 416.551635 2
## 2194 1.789465931 418.341101 2
## 2195 0.143043883 418.484144 2
## 2196 1.987093566 425.156164 2
## 2197 1.473961462 425.617861 2
## 2198 1.921290682 432.570298 2
## 2199 0.453778602 434.363478 2
## 2200 1.050057687 442.065501 2
## 2201 0.893033401 443.673127 2
## 2202 1.612494853 446.282516 2
## 2203 2.177733872 447.109872 2
## 2204 1.436040140 451.821703 2
## 2205 0.124463848 454.302448 2
## 2206 1.673594891 457.310339 2
## 2207 1.939749953 457.621615 2
## 2208 0.338126861 457.648465 2
## 2209 0.055370270 458.274065 2
## 2210 6.820489238 472.318208 2
## 2211 6.268676846 472.624678 2
## 2212 6.641071828 478.959280 2
## 2213 3.967643568 480.083072 2
## 2214 0.121155196 479.328851 2
## 2215 3.544848018 483.615288 2
## 2216 0.888045859 481.872985 2
## 2217 5.353370893 490.676413 2
## 2218 1.061609231 486.420252 2
## 2219 1.156582317 487.989242 2
## 2220 1.906744388 492.400088 2
## 2221 1.192728819 496.830212 2
## 2222 0.639829447 497.333060 2
## 2223 3.521164142 501.323877 2
## 2224 1.285730378 501.444651 2
## 2225 0.752677843 502.076555 2
## 2226 0.765375092 502.728516 2
## 2227 3.143251030 505.848569 2
## 2228 0.858845032 504.792887 2
## 2229 1.203875774 508.483696 2
## 2230 1.735620141 521.806254 2
## 2231 2.721770915 522.905410 2
## 2232 5.598969540 528.240087 2
## 2233 3.600615071 526.932528 2
## 2234 0.533136717 527.465665 2
## 2235 6.757978226 535.584441 2
## 2236 0.152631178 535.507477 2
## 2237 0.001869328 535.509346 2
## 2238 0.544620540 536.788187 2
## 2239 1.437215994 542.393748 2
## 2240 2.608857608 545.908881 2
## 2241 6.180217049 549.626324 2
## 2242 0.569119065 546.478000 2
## 2243 3.579247086 550.057247 2
## 2244 1.144474450 550.770798 2
## 2245 0.238669716 550.295917 2
## 2246 2.336254018 552.632171 2
## 2247 3.114428840 554.898447 2
## 2248 4.755694967 561.572542 2
## 2249 5.272069641 562.496062 2
## 2250 0.606969066 562.179511 2
## 2251 3.325761176 567.094235 2
## 2252 1.401717548 565.669632 2
## 2253 3.816534203 570.268278 2
## 2254 11.661440907 580.361297 2
## 2255 2.285912966 575.153837 2
## 2256 0.346580252 581.182460 2
## 2257 0.660881915 585.762259 2
## 2258 4.025270543 590.126325 2
## 2259 14.163959972 604.045372 2
## 2260 0.868483569 591.067145 2
## 2261 1.082804159 592.149949 2
## 2262 3.759785001 595.909734 2
## 2263 1.874322212 597.784057 2
## 2264 1.973649732 599.757706 2
## 2265 8.125261471 607.882968 2
## 2266 1.166147980 605.211520 2
## 2267 0.576341717 605.787862 2
## 2268 0.549364594 606.337226 2
## 2269 2.141315298 608.478541 2
## 2270 0.397494791 608.280463 2
## 2271 2.212725452 610.493188 2
## 2272 0.406785839 608.885327 2
## 2273 1.097640416 609.982968 2
## 2274 0.551247102 610.534215 2
## 2275 2.258239621 612.751428 2
## 2276 7.428613270 617.962828 2
## 2277 0.284338449 613.035766 2
## 2278 2.538313660 615.574080 2
## 2279 0.508836770 616.082917 2
## 2280 4.468946800 625.571175 2
## 2281 1.287808417 627.224993 2
## 2282 0.959908525 630.326748 2
## 2283 1.277138902 630.845599 2
## 2284 2.778269844 636.903514 2
## 2285 2.620458131 636.940780 2
## 2286 8.954730566 648.453031 2
## 2287 6.710633657 648.380380 2
## 2288 5.645605442 654.025985 2
## 2289 0.032631267 648.485662 2
## 2290 2.234984776 650.720647 2
## 2291 0.233579016 650.954226 2
## 2292 0.738270688 651.692496 2
## 2293 1.593721178 659.011986 2
## 2294 1.175870884 661.945648 2
## 2295 0.292709283 661.529314 2
## 2296 2.835058146 665.154579 2
## 2297 2.832095822 674.815743 2
## 2298 4.013376021 676.537484 2
## 2299 7.101908880 681.917652 2
## 2300 4.429310113 680.966795 2
## 2301 0.919095165 681.885890 2
## 2302 5.145162769 687.031053 2
## 2303 2.026152009 683.943804 2
## 2304 0.717464506 684.661269 2
## 2305 0.348590381 685.009859 2
## 2306 2.332584880 687.342444 2
## 2307 0.291641138 687.322694 2
## 2308 2.119899319 689.442593 2
## 2309 1.239093599 689.419075 2
## 2310 3.668288267 694.136275 2
## 2311 0.284232706 691.980325 2
## 2312 10.632832801 706.644803 2
## 2313 0.398169840 700.958277 2
## 2314 0.035379840 702.197153 2
## 2315 8.009415363 710.959317 2
## 2316 1.070799217 707.715602 2
## 2317 2.136162701 713.846817 2
## 2318 6.993451232 719.274031 2
## 2319 6.855180292 723.393353 2
## 2320 0.175260623 719.449292 2
## 2321 0.731975905 720.181267 2
## 2322 2.033420003 722.214687 2
## 2323 0.907604817 725.326057 2
## 2324 0.153378444 727.225223 2
## 2325 2.290409413 731.627265 2
## 2326 2.031606526 733.945146 2
## 2327 0.403285205 735.813920 2
## 2328 5.623955212 742.466325 2
## 2329 5.061435495 745.682675 2
## 2330 5.509767297 749.050650 2
## 2331 0.289876479 745.972551 2
## 2332 0.934963689 748.475382 2
## 2333 3.815056200 752.290439 2
## 2334 3.133231137 752.793122 2
## 2335 0.575418813 753.089284 2
## 2336 4.536456766 761.200727 2
## 2337 3.003139423 760.695474 2
## 2338 1.117749377 761.813223 2
## 2339 1.022606953 762.223334 2
## 2340 0.801815946 763.602123 2
## 2341 1.868614748 766.547172 2
## 2342 7.137500552 775.636013 2
## 2343 1.636545151 771.349301 2
## 2344 0.868538218 772.217840 2
## 2345 2.255741075 775.938955 2
## 2346 6.810054075 782.446067 2
## 2347 0.690681761 778.143680 2
## 2348 0.171808529 781.141271 2
## 2349 7.426078619 789.840678 2
## 2350 2.685665998 785.493111 2
## 2351 0.198239339 786.368391 2
## 2352 0.655200849 788.496683 2
## 2353 0.657978220 791.968510 2
## 2354 1.247660917 793.699446 2
## 2355 2.853916856 796.666828 2
## 2356 1.811829355 795.848525 2
## 2357 1.333575783 800.083185 2
## 2358 1.505643468 803.085667 2
## 2359 0.447288145 808.901886 2
## 2360 0.372428202 808.890630 2
## 2361 0.105963067 811.638423 2
## 2362 1.810720479 820.459532 2
## 2363 0.181981214 820.468558 2
## 2364 1.973686744 824.152582 2
## 2365 1.895425281 824.090073 2
## 2366 0.237020391 826.715717 2
## 2367 2.925567392 829.969057 2
## 2368 4.350378000 833.746091 2
## 2369 3.735228244 833.817284 2
## 2370 1.888870502 835.634962 2
## 2371 0.127655319 834.610289 2
## 2372 1.032160286 849.310793 2
## 2373 3.460207910 853.799343 2
## 2374 0.092460360 851.007096 2
## 2375 1.566213134 853.133080 2
## 2376 1.988737697 855.121818 2
## 2377 4.282937734 862.329463 2
## 2378 5.458391811 863.947124 2
## 2379 10.466400170 872.795863 2
## 2380 1.045017013 875.115153 2
## 2381 0.175324093 875.099173 2
## 2382 1.676619987 880.992750 2
## 2383 0.768340310 882.340279 2
## 2384 1.951271189 886.587603 2
## 2385 4.273524206 896.406284 2
## 2386 5.369727310 900.496208 2
## 2387 0.772079667 900.623320 2
## 2388 0.065608665 902.814386 2
## 2389 0.405503456 903.431661 2
## 2390 2.200073602 909.623436 2
## 2391 2.820455754 910.485274 2
## 2392 1.728313983 911.843449 2
## 2393 1.867728336 914.924812 2
## 2394 6.317224171 921.762608 2
## 2395 4.001838373 921.643445 2
## 2396 9.561433850 931.204879 2
## 2397 1.588348381 924.552137 2
## 2398 0.285479867 924.837616 2
## 2399 2.020072339 926.857689 2
## 2400 0.042797439 926.900486 2
## 2401 1.181136215 929.070244 2
## 2402 3.409535636 932.697389 2
## 2403 0.969535075 932.355400 2
## 2404 1.282894503 933.638294 2
## 2405 1.420645291 934.118034 2
## 2406 8.754791910 942.393086 2
## 2407 2.241937077 936.359971 2
## 2408 2.264720730 939.099213 2
## 2409 0.086332872 942.143924 2
## 2410 0.065409150 946.078250 2
## 2411 4.296114168 952.250026 2
## 2412 3.381004793 953.992652 2
## 2413 4.772490491 957.022517 2
## 2414 4.881982195 958.874634 2
## 2415 0.374996407 957.397513 2
## 2416 1.977981866 959.375495 2
## 2417 0.135325152 959.009959 2
## 2418 0.985509020 959.995468 2
## 2419 1.301112770 960.676608 2
## 2420 6.539306130 969.972284 2
## 2421 4.079416395 967.564021 2
## 2422 0.999759597 968.563781 2
## 2423 2.156515012 970.720296 2
## 2424 0.084274692 970.056558 2
## 2425 0.683145957 970.739704 2
## 2426 1.031888467 971.752184 2
## 2427 0.418779552 971.158484 2
## 2428 4.085559535 975.244043 2
## 2429 11.084607413 985.880444 2
## 2430 0.050484669 979.476439 2
## 2431 2.159636637 982.559486 2
## 2432 2.004353484 984.563840 2
## 2433 4.172633531 988.736473 2
## 2434 0.280854412 986.161298 2
## 2435 1.747458395 989.365505 2
## 2436 0.720396102 991.708450 2
## 2437 2.475390784 995.768087 2
## 2438 0.621364064 994.555123 2
## 2439 2.859127125 997.414250 2
## 2440 0.268369263 996.036456 2
## 2441 1.353191912 997.389648 2
## 2442 1.762372488 1002.325622 2
## 2443 0.082510782 1004.585586 2
## 2444 2.427523023 1007.565519 2
## 2445 1.491648937 1008.700262 2
## 2446 2.566631385 1010.684177 2
## 2447 3.488038408 1015.370709 2
## 2448 0.037245714 1014.645436 2
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## 11007 2.710720053 12.637457 2
## 11008 5.750932144 16.697494 2
## 11009 0.383570668 13.021028 2
## 11010 1.705309549 14.726337 2
## 11011 1.816747136 16.543085 2
## 11012 2.237538094 18.780623 2
## 11013 1.941103501 18.638597 2
## 11014 15.571429015 34.210026 2
## 11015 2.352234241 21.928732 2
## 11016 0.270207848 24.720742 2
## 11017 8.420794148 34.973143 2
## 11018 1.110528527 35.320555 2
## 11019 1.198265439 36.171409 2
## 11020 1.359912624 37.747280 2
## 11021 2.635485402 41.003902 2
## 11022 3.826330025 42.807838 2
## 11023 1.234829528 45.135611 2
## 11024 6.054317478 52.722886 2
## 11025 2.305348849 53.143928 2
## 11026 1.303937747 54.026824 2
## 11027 0.469964170 53.613893 2
## 11028 5.016547716 58.857952 2
## 11029 3.842501106 61.500358 2
## 11030 7.700468881 66.558421 2
## 11031 0.100846172 61.601204 2
## 11032 2.800207753 64.401412 2
## 11033 0.181467078 64.582879 2
## 11034 1.034000727 66.248619 2
## 11035 1.333469343 69.716984 2
## 11036 1.387372492 75.154794 2
## 11037 0.782754643 74.591203 2
## 11038 0.585328740 78.587313 2
## 11039 3.072951902 83.878894 2
## 11040 0.992378916 83.085462 2
## 11041 3.559569070 88.676948 2
## 11042 1.064608927 87.794322 2
## 11043 0.311766624 89.274421 2
## 11044 0.665572036 94.305668 2
## 11045 1.267347435 98.670421 2
## 11046 3.647234732 101.328095 2
## 11047 0.128655648 101.907341 2
## 11048 6.343744050 111.890165 2
## 11049 0.425418761 109.527708 2
## 11050 1.065437507 111.759933 2
## 11051 9.920379307 124.117786 2
## 11052 3.198046968 121.431097 2
## 11053 4.509732206 125.940829 2
## 11054 1.398535091 125.516321 2
## 11055 1.449023525 126.965345 2
## 11056 2.358385905 128.299215 2
## 11057 1.618779853 128.584124 2
## 11058 6.869352132 135.168567 2
## 11059 1.760192640 133.055414 2
## 11060 0.426947583 133.482362 2
## 11061 3.628063856 137.110425 2
## 11062 0.112988860 135.281556 2
## 11063 0.800526803 136.082083 2
## 11064 1.851358616 141.158546 2
## 11065 1.109283623 143.035617 2
## 11066 0.040605054 142.362494 2
## 11067 2.303907548 144.984315 2
## 11068 3.410703518 155.193093 2
## 11069 1.425475826 154.352715 2
## 11070 2.399854009 157.343904 2
## 11071 0.399842276 157.337246 2
## 11072 5.874150976 164.005541 2
## 11073 0.213786421 159.673246 2
## 11074 3.858147599 163.626181 2
## 11075 1.688682715 165.314864 2
## 11076 0.572093078 164.577634 2
## 11077 2.463268217 167.040902 2
## 11078 4.281815163 169.807138 2
## 11079 2.220611020 173.189270 2
## 11080 0.691831507 173.719211 2
## 11081 1.843811640 175.749689 2
## 11082 1.913556031 177.315754 2
## 11083 0.307557188 176.057246 2
## 11084 0.754114846 177.168675 2
## 11085 4.372227797 181.540902 2
## 11086 0.517510604 179.215088 2
## 11087 0.126692515 182.080595 2
## 11088 0.308683721 182.321303 2
## 11089 3.751089325 186.253537 2
## 11090 2.167055972 186.444185 2
## 11091 1.798096653 188.051634 2
## 11092 7.312699177 193.865371 2
## 11093 2.483952988 193.260977 2
## 11094 2.716206527 202.766874 2
## 11095 0.845572578 200.954792 2
## 11096 2.459909196 203.414701 2
## 11097 0.200804656 202.967678 2
## 11098 1.985212182 204.952891 2
## 11099 5.098255356 210.290480 2
## 11100 3.497090041 209.199497 2
## 11101 0.580401801 212.210510 2
## 11102 2.250858773 213.993896 2
## 11103 2.366547952 221.947152 2
## 11104 4.116635728 226.069215 2
## 11105 4.726268866 227.253680 2
## 11106 1.187761154 227.256976 2
## 11107 1.613819773 228.867500 2
## 11108 0.676457758 228.741682 2
## 11109 0.240355434 235.672910 2
## 11110 0.886178371 237.489962 2
## 11111 1.075826873 239.268471 2
## [ reached 'max' / getOption("max.print") -- omitted 988889 rows ]
The next step is to analyze your simulation results by looking at measures such as average waiting time, cost, and other performance indicators. Then, use this analysis to decide whether adding a third wharf would be a reasonable choice.
# Analyze the simulation results