Equilibrium behaviors of customers in a discrete-time queueing system

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Dr. Do Van Tien
Department of Networked Systems and Services

The popularity of queuing systems with negative customers, also called G-queues, has increased rapidly during the past two decades. G-queues have proven useful especially in systems where modeling data loss is essential. The study of the discrete time version has been neglected until the past few years but with the spread of packet level and slot based networks it is starting to get more attention. Only a few researches have been conducted on G-queues with game theoretical approaches.

In this thesis we studied an MMBP/Geo/1 queue in discrete time with game theoretical approach. In our system the incoming negative customers can remove other customers in a batch with a certain probability. We revised the progress and achievements of the field of G-queues and took a look at some previous works in detail to learn more about the models and methods used. We examined our queue in two separate cases: the fully observable case where incoming customers can see the state of the system and the length of the queue; and the partially observable case where incoming customers can only see the length of the queue but not the state of the system. After that we formulated our own systems of equations based on the Markov chain models to calculate the net rewards and the threshold value for the length of the queue.

A numerical analysis was conducted to see the effect of the system parameters on the threshold. Three different distributions were considered for the batch killings: geometric, Poisson and the distribution where a single customer is removed with probability 1. We found out that the service rate has a great impact on the threshold and that there are some cases where the threshold does not exist because it is worth for the customer to join at any length of the queue. Whereas the the increase in the cost of the time unit does not change the threshold that much.


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