I have an Operations Management queuing problem question. I need to understand how to use a queuing calculator like this Omni queuing one: https://www.omnicalculator.com/math/queueing-theory I need to use a M/M/S version with S=4 servers for my case here. Here is my case issue and questions: The average daily number of passengers in a certain airport terminal is 10,200 and 12% of them arrive to the terminal during 5-6 am. Suppose now that 30% of these passengers are enrolled in the Transportation Safety Administration’s (TSA) Pre-Check program. These passenger line up in a separate queue and go through separate security screening lanes called pre-check lanes for faster security screening. non pre-check passengers go through a different queue and security screening lanes. A pre-check processing lane is always staffed with 4 TSA officers (it costs $30 per TSA agent per hour, and then $40 per hour to operate (overhead costs) a pre-check lane), and they can process 250 passengers per hour. Note that, arrivals of passengers to the security check-in lines follow a Poisson distribution (like a traffic light that has high variability), and the service “times” provided follow an exponential distribution (this means that the Omni calculator mentioned above or a queuing software tool like STORM could be used and will provide valid answers for the length of the queue and for the system, and for the Wait times in the queue and in overall system. Question 1: To ensure that the Pre-check queue does not grow infinite (to be at 1 or above ratio), what is the least-cost lane opening and staffing plan for the 5-6 am period? Question 2: What is the average waiting time of a passenger in the pre-check queue? Question 3: What is the average queue length?
Queuing theory is a powerful tool when it comes to optimizing the operations of complex systems with unpredictable customer arrivals and service times. In this essay, we will address a specific operational issue at an airport terminal during the 5-6 am period. We will employ queuing theory, specifically the M/M/S queuing model with S = 4 servers, to analyze and solve this issue.
The first step in optimizing the staffing plan is to determine the average arrival rate of passengers during the specified time period. The arrival rate is calculated by multiplying the average daily number of passengers by the percentage of passengers arriving during 5-6 am. In this case, an arrival rate (λ) of 1,224 passengers per hour was calculated.
Next, we need to consider the service rate of the TSA officers in the Pre-Check lane. With 4 officers, each capable of processing 250 passengers per hour, the service rate (μ) for the Pre-Check lane is 1,000 passengers per hour. The aim is to maintain a certain probability (P0) that the Pre-Check queue remains empty, thus avoiding long queues.
To ensure that the Pre-Check queue does not grow infinitely, we iterate through different numbers of servers (S) to identify the minimum number of TSA officers required to achieve the desired P0. This optimization process helps strike a balance between staffing costs and passenger satisfaction.
The average waiting time (W) of a passenger in the Pre-Check queue is crucial for understanding passenger experience. It can be calculated using Little’s Law, which relates waiting time, queue length, and arrival rate. By determining the average number of passengers in the Pre-Check queue and dividing it by the arrival rate, we can find the average waiting time. This provides valuable insights into passenger wait times.
The average queue length (L) is another vital metric that helps in evaluating the efficiency of the Pre-Check lane. It represents the average number of passengers in the queue at any given time. The formula for calculating L is based on the M/M/S queuing model, considering the arrival rate, service rate, and the probability that the queue is empty (P0). A longer queue implies longer waiting times for passengers, which can lead to dissatisfaction.
In conclusion, queuing theory offers a systematic and data-driven approach to addressing operational challenges at the airport terminal during peak hours. By using mathematical models such as the M/M/S queuing model, airport managers can optimize their staffing plans, minimize wait times, and ensure a seamless experience for passengers, all while controlling costs. It’s a powerful tool for maintaining the delicate balance between operational efficiency and customer satisfaction in dynamic environments like airports. This optimization not only enhances the passenger experience but also contributes to the overall success of the airport’s operations, demonstrating the real-world application of queuing theory in solving complex operational problems.
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