M/G/1 Repairable Queueing System With Delayed Single Vacation And Min(N,V)-Policy Control

In this thesis, we consider the M/G/1 repairable queueing system with delayed single vacation and Min(N, V)-policy. The content is divided into three chapters. In the first chapter, by using the total probability decomposition technique and the Laplace transform tool, we analyze the transient queue length distribution from the beginning of any initial state N(0) = i(i = 0,1,2, …), and obtain the expressions of the Laplace-transformation of the transient queue length distribution. Meanwhile, we obtain both the recursion expressions of the steady state queue length distribution and the explicit expression for the probability distribution of the additional queue length. Especially, we discuss the expected steady-state queue length for some special cases. In the second chapter, some reliability performance measures of the service station, such as the distribution of the service station's first failure time, the probability that the time t is in a "generalized busy period",the unavailability of the service station at the time t and the failure frequency of service station, are discussed by the renewal process theory.In the third chapter, by numerical examples in diagrams showing, we analyze the influence of the relevant parameters of the system on the expected additional queue length , and discuss the optimization design problem of system capacity, which indicates that the value of steady-state queue length distribution in the system capacity design. Finally, basing on the cost model and employing the renewal reward process, the explicit expression of the expected cost function per unit time is derived. The optimal threshold N* that makes the cost to the lowest is determined by the numerical example.