Resit exam: COM 4515/6515
Network Performance Analysis, September 2022
You have been asked to model a queueing system for people checking in at an airport.
There is one queue and 10 check-in desks, and a customer proceeds to the first available desk. Assume that the
service rate of all the check-in assistants is the same and that the plane can seat 200 people. Assume steady state
conditions.
The answers to the following questions should be simplified by hand as far as possible. The answers should be
expressed in terms of λ, the arrival rate of the passengers, and the service rate µ of each check-in assistant.
Do not use a computer to simplify them further.
1. Derive an expression for the probability that there are k people in the system.
2. Derive an expression for the average number of people in the queue.
3. Derive an expression for the average waiting time of a customer in the queue.
The passengers proceed to security after they have checked-in. Explain if it is possible to construct a model for
the passengers as they proceed from check-in to security.
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