Analysis on queueing systems having general inter-arrival time and service time distributions

Abstract

In this dissertation we consider queueing systems where the inter-arrival times and service times both have a general distribution. For a single-server queue, the aim is to find the waiting time probabilities. Through the use of Lindley's integral equation and the imbedded Markov chain, we construct a transition probability matrix. For the steady-state equations, we derive an iterative formula of Lindley's integral equation in discrete form using the Laplace-Stieltjes transform. By using Little's formula, we calculate the effective parameters. Then we compare results with simulation and with approximations and upper bounds. For the multi-server queueing model, we obtain equations which will give exact results for the number of customers in the queue. We then use approximation formulae, namely the Allen Cunneen Approximation formula, to obtain an estimation for the mean waiting time in the queue. Finally, we link multi-server queueing systems with a generalization of Lindley's equation. The software which is used in this dissertation is MATLAB where there are codes for both single-server and multi-server queues. Simulation is done by using provided simulators available on the internet, and QTS