Analysis of M/G/1 queues with disasters

Abstract

Recently there has been an increasing interest in queueing models with disasters. Upon arrival of a disaster, all the customers present are flushed out. Queueing models with disasters have been applied to the problems of failure recovery in many computer network systems, database systems and telecommunication networks. In this thesis, we assume that disasters arrive at the system with poisson process (δ) when the server is busy. Since disasters are considered as server breakdowns or reset orders of computer systems in many literatures, it might be appropriate to assume random repairing time right after a disaster``s arrival epoch. We consider the M/G/1 queueing system with disasters and general repair time during which customers can enter the system. In addition, as a generalization of the model proposed by Chen and Renshaw (1997), performance measures of the M/G/1 model with disasters and mass arrivals on empty system have been derived by the method used in the case of repair time model. In this thesis, we suggest the steady state and sojourn time distributions of the above two models in closed forms using Laplace-Stiltjes transform. In addition, we perform a cost analysis using the results of cycle analysis.