M/G/1/∞(E,MV) Repairable Queueing System With N Dissimilar Units Series Structure

A repairable queueing system with vacation is an important model of queue theory. It extend the study of classical queueing system theory. In this article, we introduced the theoretical and practical situation about queueing system with vacation and queueing system with repairable service station all over the world. Base on the work, we study such problem: M / G/1/∞( E,MV) repairable queueing system with N dissimilar units series structure, in which it operates if and only if all of the N units operate. Assume that each unit has exponential distribution and its repair time has arbitrary distribution. By introducing "the generalized busy period"of the service station and using the method of renewal process, a new approach to analysis the reliability quantities of the service station is presented. By using the method of embedded Markov chains and the new approach, We do the following work: 1 queueing index of the M / G/1/∞( E,MV) repairable queueing system (1) getting the generated function of equilibrium distribution of embedded Markov chains of queue length and average queue length; (2) getting the expression of LS -transform of sojour time and waiting time and the average value; (3) getting the expression of the L -transform of the transient queue length distribution at arbitrary time t and the recursion expression of the limitation distribution when t →∞; (4) getting the expression of LS -transform of the expected number of departure number during the time interval (0 , t] and the steady-state result. 2 reliability index of the service station of the M / G/1/∞( E,MV) repairable queueing system (1) getting the expression of L -transform of the probability that the service...