The Optimal Design For The Repairable Queueing System M/G/1 With Changeable Parameters

Optimal design is an important research field in queueing system. Recently, much work has been done on it while many important results have been received. On the foundation of the previous work, we mainly study optimal design of the queueing system M / G /1/L and the repairable queueing system M / G /1. Furthermore, we obtain their optimization methods.This paper is organized as follows. The first chapter is the introduction of the basic knowledge. Here we introduce the background, the research presentation of this field and the basic knowledge of queueing system. In chapter two, we introduce the supplementary variable method and the L-transform which are mainly concerned in this paper. In chapter three we study the M / G /1/L queueing system in which the arrivers enter the system with probability p . We obtain the solutions of its state transform rate equations by the supplementary variable method and the L-transform. Then we further obtain its optimization method by setting a N -threshold and constructing the cost function of the system. In chapter four, we study optimal design of the repairable M / G /1 queueing system with two service speeds. The discipline of the service speed change is that the server would first serve customers by speed 1, if the number of the customers exceeds the N -threshold the server works by speed 2 until there is no customer in the system. We obtain some probability index by the supplementary variable method and the L-transform. Finally, we get the optimization method by constructing the cost function of the system.