DATA 604 - Assignment 2

# M/G/1 with continuous service time distribution between 0.1 and 1.9
a = 0.1
b = 1.9
es = (a+b)/2 #Also known as 1
sd = sqrt(((b-a)^2)/12) # Thank you textbook
y = 1/1.25 #Reciprocal of interarrival
m = 1/es # Reciprocal of service time
p = y/m

Wq = (y *(sd^2+ (1 / m^2) ))    /    (2*(1-p))
Lq = Wq * y
W = Wq+es
L = W*y
data.frame('lambda' = y, 'mu' = m, 'p' = p, 'Wq' = Wq, 'W' = W, 'Lq' = Lq, 'L' = L, 'SD' = sd)

# M/G/1 with triangularly distrubted service times between 0.1 and 1.9; mode = 1.0
mode = 1
a = .1
b = 1.9
es = (a+m+b)/3 #also known as 1
sd = sqrt(   (a^2 + m^2 + b^2 - a*m - a*b - b*m   )/18  ) #Thank you textbook
y = 1/1.25
m = 1/es
p = y/m
# Copy paste from previous solution
Wq = (y *(sd^2+ (1 / m^2) ))    /    (2*(1-p))
Lq = Wq * y
W = Wq+es
L = W*y
data.frame('lambda' = y, 'mu' = m, 'p' = p, 'Wq' = Wq, 'W' = W, 'Lq' = Lq, 'L' = L, 'SD' = sd)

# M/M/3 Three servers, exponentially distributed arrival and service times.
#Right from the docs, this returns "the mean nubmer of customers in the M/M/c model"


library(queueing)

## create input parameters

i_mmc = NewInput.MMC(lambda=(1/1.25), mu=(1/3), c=3, n=0, method=0)

## Build the model

o_mmc <- QueueingModel(i_mmc)

l = L(o_mmc)

#From here can we use the function to give us everything we want;  
#but thats not the point of the exercise. Let us follow the book and apply little's law.

y= 1/1.25
m= 1/3
w = l/y
p = y/m
lq = l-(y/m)
wq = lq/y
data.frame('lambda' = y, 'mu' = m, 'p' = p, 'Wq' = wq, 'W' = w, 'Lq' = lq, 'L' = l)

# mInterarrival time = 6/minutes

# Sign In = M/M/2 - Service time 3/minutes - Probability 1.0
signin = NewInput.MMC(lambda=1/6,mu=1/3,c=2,n=0,method=0)
results = QueueingModel(signin)
signin =data.frame('station'='Sign in','p' = results$Pn,'L'= results$L, 'W' = results$W, 'Lq' = results$Lq, 'Wq' =results$Wq)

# Registration = M/M/1 - Service time 5/minutes - Probability .9
registration = NewInput.MMC(lambda=(1/6)*.9,mu=1/5,c=1,n=0,method=0)
results = QueueingModel(registration)
registration = data.frame('station'='Registration','p' = results$Pn,'L'= results$L, 'W' = results$W, 'Lq' = results$Lq, 'Wq' =results$Wq)

# Trauma = M/M/2 - Service time 90/minutes - Probability .1
trauma = NewInput.MMC(lambda=(1/6)*.1,mu=1/90,c=2,n=0,method=0)
results = QueueingModel(trauma)
trauma = data.frame('station'='Trauma rooms','p' = results$Pn,'L'= results$L, 'W' = results$W, 'Lq' = results$Lq, 'Wq' =results$Wq)

# Exam Rooms = M/M/3 - Service time 16/minutes - Probability .9
exam = NewInput.MMC(lambda=(1/6)*.9,mu=1/16,c=3,n=0,method=0)
results = QueueingModel(exam)
exam = data.frame('station' = 'Exam rooms','p' = results$Pn,'L'= results$L, 'W' = results$W, 'Lq' = results$Lq, 'Wq' =results$Wq)

# Treatment Rooms = M/M/2 - Service time 15/minutes  - Probability .9*.6+.1 (Both paths may lead towards here)
treatment = NewInput.MMC(lambda=(1/6)*( (.9*.6)+.1 ),mu=1/15,c=2,n=0,method=0)
results = QueueingModel(treatment)
treatment = data.frame('station' = 'Treatment Rooms','p' = results$Pn,'L'= results$L, 'W' = results$W, 'Lq' = results$Lq, 'Wq' =results$Wq)

results = rbind(signin,registration,trauma,exam,treatment)

results