PERFORMANCE ANALYSIS OF SINGLE-SERVER MARKOVIAN QUEUE WITH CUSTOMER BALKING, RENEGING AND INTERJECTION

Abstract

In this thesis, an infinite capacity single-server Markovian queue with customer balking, reneging and interjection was investigated. The steady-state analysis of the model was performed by the Markov process method. The governing steady-state difference-differential Chapman-Kolmogorov equations of the model were derived. Steady-state probabilities in explicit closed form expressions were obtained. This has been carried out by using the recursive method. Once we had the steady-state probabilities different performance measures of the system were obtained and a cost model was formulated. Then different performance measure values of the system were computed and analyzed using tables and graphs for better elaboration. All the computations were performed using MATLAB software by writing the MATLAB codes. The present investigation can be extended to customer’s behaviour balking, reneging and interjection in combined form in more general queueing systems such as M/G/1, G/M/1 or G/G/1, which are left for future research.