For different airfield in the country, the Borealian Aeronautic Security Agency’s (BASA) is in charge of running the passenger pre-board screening process. Therefore to track passengers’ traffic, the BASA has to develop queuing model. In the context of the (BASA), a queuing system refers to the structured process through which passengers and crew members undergo security checks before boarding their flights at the nation’s airfields. It involves the management of queues or waiting lines, where individuals wait for their turn to be screened by security personnel.

In this scenario, the queuing system comprises several key elements:

Arrival Process: Passengers and crew members arrive at the beginning of the main queue, indicating the start of the screening process. The arrival process can vary based on factors such as the schedule intensity of departing flights and the passenger volume associated with these flights. It may also be influenced by trends, such as shifts in the number of passengers, flights, and destinations over time.

Main Queue: Once passengers and crew members arrive, they join the main queue, waiting for their turn to proceed with the screening process. The length of the queue can vary depending on the number of individuals present and the efficiency of the overall system.

Boarding Pass Scanning: At some point during the queueing process, passengers’ boarding passes are scanned. This step helps verify their travel details and ensures proper documentation before proceeding further.

Server Entry Position: After the boarding passes are scanned, passengers are directed to a server entry position. This position serves as the entry point for individuals to move from the queue to the screening area, where security personnel conduct thorough checks of both passengers and their carry-on luggage.

Screening by Servers: Once passengers reach the server entry position, they undergo screening by dedicated servers or security personnel. This step involves the inspection of individuals and their belongings to ensure compliance with safety and security regulations.

Factors influencing the wait time in the pre-board screening process can include the number of servers available, their processing rates, and the overall passenger volume. Additionally, interactions between yearly, seasonal, time-of-day, and day-of-week patterns may further impact the queuing system. For example, passenger traffic may differ between weekdays and weekends or vary based on the season. These patterns need to be considered in the analysis and optimization of the queuing system.

By understanding and analyzing the queuing system within the context of BASA’s pre-board screening process, the agency can optimize resource allocation, staffing levels, and operational strategies. This can lead to reduced wait times, improved efficiency, and enhanced passenger experiences while maintaining the highest standards of security and safety.

Data Cleaning

Prior to exploring and visualizing the data, we must first perform data cleaning to ensure an appropriate and seamless analysis. Below we can see a chunk of 5 rows of the original merged data sets, which contains multiples superfluous N/A values.

Since the dataset was original a combination of four others : 20262030.csv, BASA_AUC_2028_912.csv, dat_F_sub.csv, *dat_P_sub_c.csv, we have removed empty rows as they would create discrepancies when building pivot tables.

Concerning missing values, the variables Wait_Time(18421 missing values), C_avg(1370) and C_start(1370), compared to other variables, records higher number of missing values, which are of two types: some of them are recorded as missing values and some of them are recorded as NA.

## # of missing values for Wait_time is: 18241
## # of missing values for C_Start is: 1370
## # of missing values for C_avg is: 1370

We have also performed the following changes :

There are 4 majors airfields in the Airport:

However after the data transformation, and dropping all the NAs we notice that only 2 airfiels are left. The Auckland (AUC) and the Saint-François (SAF) airfields.

All those changes have resulted in the following data set.

Exploration and Visualization

While trying to look for seasonal pattern, we notice that most flights occur during autumn, followed by Summer at AUC airfield where as winter is the season of flight at SAF airfield.

Create the boxplot

This graph let us know that, on average, actual flight departures occur as previously schedules as the the most densed area is surrounded around zero being the time difference between Scheduled and Actual departure, with some exceptions as we see. They may be potential outliers needed to be investigated further.

This data set is mainly composed of travellers leaving AUC airfield and a relatively low number of passengers departing from SAF. Our analysis will then be more oriented towards the screening process of passengers in the former airfield. Though the latter will have a particular attention as well.

We will then try to look at the destination cities to see which is the most commonly visited.

BORQUE seems to be visited the most being more than twice as visited as BORCWL. The four majorairfields are the least frequented cities. Are domestic flights not really common compared to International ones?

Comparison of the Airfield AUC and SAF

Before we perform our queuing system analysis, we first compare our remaining two airfields traffic level and performance.

Average Number of Server

Number of Passenger

We notice that the Auckland airfields has a significantly higher number of passenger and consequently more servers.

By Average Arrival Rate

Here we have created a clusters by airfields and time period.

The clusters are as follow, the passengers are broken down by airfields, followed by the season of their flight departure, the period of the week, either being the weekday or the weekend, and finally the time frame in which the flights are departed, which are intervals of 4 hours.

We can see that in general the busiest periods are the ones in the early AM, for both weekends and weekdays.

Distribution of Active Server

The average number of survers seems to remain consistent through the days and hours. However we notice a higher average leaning closer to 1.5 servers, in the mornings.

Average Wait Time and Performance Levels

For both airfields, performance is higher when the wait time increases and is above 10 minutes. However their distributed wait times across time period seem to be similar. We can then assume that, although with a higher number of traffic, the line of the Auckland airfield seems to be performing as well as the line for Saint-François. That could mainly be due to the additional third server occasionally added to the line.

M/M/1 Queueing Model

In a queueing system where the number of servers varies with time, accurately estimating the service rates becomes challenging because the estimates typically depend on the number of open servers. However, to address this issue without resorting to vacation models, a different approach can be taken.

In this case, the queueing system is viewed as an M/M/1 queue, where the servers are concealed behind a generalized server. Instead of explicitly considering the specific number of open servers at any given time, the system is treated as if it has a single effective server that represents the overall service capacity of the system.

QoS Estimates — M/M/1

We have estimated service levels \(p_{M}\) and Service rates \(\mu_{M}\).

Validation

To validate we will compare the estimated performance rate and the actual performance rate per sequence of time. That is, \((p_{r},x\)) against \((p_{M,x},x)\).

By adopting the M/M/1 queueing perspective, the estimation of service rates becomes independent of the number of servers. The focus shifts to determining the average time it takes for the generalized server to process a customer. This average service time is a combination of the individual service times of the actual servers, accounting for their varying availability throughout the system’s operation.

Here , we can see that for example , with M/M/1 queue, the est. Service rate is really low during winter , and is only functional on weekend from 16:00 to 22:00 , During winter, airports and screening processes might experience higher passenger volumes due to holiday travel or adverse weather conditions. The increased passenger load could result in longer queues and slower service times. Additionally, factors like cold weather conditions or reduced staffing levels during the winter season could contribute to slower service rates.

Average Cross Entropy

Evaluating the average cross entropy, we can see that the model is a in general a fairly good estimates of our observations as it does not greatly deviate from our original mode.

Regression Model

Although the number of servers in the system may change dynamically, the core principles and theorems of queueing theory still hold when considering the effective M/M/1 queue with the hidden generalized server. These principles include the exponential distribution of inter-arrival times, the exponential distribution of service times, and the stability conditions for the queue.

Analyzing the system as an M/M/1 queue allows for easier computation of key performance metrics. Average wait times, queue lengths, and other important performance measures can be determined based on the estimated service rates, without explicitly considering the specific number of open servers at different times.

By using this approach, analysts can simplify the analysis of the queueing system, making it more tractable and avoiding the complexities associated with modeling the dynamic variations in the number of servers. It provides a practical way to estimate service rates and evaluate the system’s performance while still maintaining the fundamental principles of queueing theory.

However, it’s crucial to note that this approach assumes that the variability in the number of servers does not significantly affect the arrival and service processes. In our case, the average number of servers is not significantly high, which confirms theory.

Estimates — M/M/1 Regression

Predicted Mean Number of Servers

Conclusion

Overall, by treating the queueing system as an M/M/1 queue with a hidden generalized server, analysts can estimate service rates independently of the number of servers and simplify the analysis while still retaining the fundamental principles of queuing theory.

Contibutors

Amina Al-Nadjib : Quantitative Analysis and Interpretation, Data Cleaning

Alphone Marie Diatta : Interpretion of Quantitative Analysis, Introduction and Conclusion

Mohamed Diakhate : Visual analysis and Interpretation, Data Cleaning

Salma Chiheb : Graph Interpretation

Dictionnary

Field Name  Field Size  Data Type  Data Format  Description  Range
Airfield  3  String  ___  Departure Airfield Code  AUC, SAF, QUE, CWL
S2  14  Date and Time  YYYY-MM-DD hh:mm:ss  Time at which boarding passes are scanned at S2  2028-01-01 00:00 to 2030-12-31 23:59
Wait_Time  2  Integer  NN  Wait time in line in minutes 0 - 75
C_Start  1  Integer  N  Number of Serve at Start  0 - 3
C0  1  Integer  N  Number of Server at End  0 - 6
C_abg  1  Float  N.N  Average number of  Servers  0 - 3
Sch_Departure  14  Date and Time  YYYY-MM-DD hh:mm:ss   Scheduled Departure Date and Time  00:00:00 to 23:59:00
Act_Departure  14  Time  YYYY-MM-DD  Actual Departure Date and Time   00:00:00 to 23:59:01
BFO_Dest_City  6  String    or _NNN Destination Airfield Code  BOR, VEC, AUC, SAF, QUE, CWL
BFO_Destination_Country_Code  3  String  ___  Destination Country Code  BOR, VEC, WIS, SCO, NEN, GRC
order  7  Integer  NNNNNNN  Order at which passengers are served??  1186 -  9974043
Pass_ID  7  Integer  NNNNNNN  Passenger Pass ID  5 - 9903091
Departure_Date  8  Date  YYYY-MM-DD  Actual Departure Date  2028-01-01 to 2023-12-31 
Departure_Time  6  Time  hh:mm:ss  Actual Departure Time  00:00:00 to 23:59:00
Time_Of_Day  10  String  N – ______  Time of the day of flight departure  1 - NIGHT  2 - MORING 3 - AFTERNOON 4 - EVENING
Period_of_Week  9  Boolean  N – ______  Period of week of flight departure  1 - WEEKDAY 2 - WEEKEND 
Day_Of_Week  5  String  N – ___  Day of the week of flight departure  1 - MON to 7 - SUN
Month   6  String  NN – ___  Month of flight departure  January to December
Season   8  String  N – ______  Season of flight depature  1 - WINTER to 4 - AUTUMN
Year  4  Integer  NNNN  Year of flight Departure  2028 to 2030