N-policy M/g/1 Queuing System To Promote Research

The research about one aspect of the repairable queueing system and the vacation system has been done by many references and obtained in-depth research. But there has been little of the research about the union of them. During the research of the repairable system, it is usually assumed that the repair facility is reliable completely. But it is usual that the repair facility may be invalid during repairing trouble unit in practice. It will not keep on repairing a trouble unit until the repair facility has been changed.In this paper we consider the M/G/1 repairable queuing system with N-policy and a replaceable repair facility. First, we study the transient and equilibrium properties of the queue length. By introducing the server busy period and using the total probability decomposition technique we derive the recursion expression of the L-transformation of the transient queue length distribution at any time t, and also the expressions of the distribution and stochastic decomposition of the queue length at a random point in equilibrium. Especially we obtain some corresponding results under some special cases. Second, we consider some important reliability indexes of this system. The generalized busy periods of the service station and repair facility are defined, and the stochastic decomposition is provided to obtain some important reliability indexes of the service station and the repair facility.In addition, the import-rate of the system is usually related with whether the server is on guard or not. Customers who arrived the system did not always enter the system during the vacation of server. Based on the above, in this paper we consider another M/G/1 queue with N-policy in which the customers who arrive during server vacation enter the system with probability p (0 < p≤1). By using a simple method, the recursion expression of the Laplace transform of the transient queue-length distribution and equilibrium queue-length distribution are obtained.