M/G/1 Repairable Queueing System With Delay Min(N,D)-Control Policy And A Replaceable Repair Facility

In Chapter 1,we study the M/G/1 repairable queueing system with delay Min(N,D)-control policy,in which the repair facility may subject to breakdown and then be replaced during the period that the repair facility repairs the broken service station.First-ly,by using the total probability decomposition technique,the Laplace transform and renewal process theory,some reliability indices of the service station and the repair facility,such as the transient-state and steady-state unavailability,the expected failure number during(0,t]are discussed.Secondly,employing the standard results in renewal process,the optimal control policy(N*,D*)such that the long-run expected cost rate is minimum under a given cost struc-ture is obtained.In Chapter 2,We combine the "set-up time"with "delay Min(N,D)-control policy",and then establish a M/G/1 repairable queueing system model with set-up time and delay Min(N,D)-control policy and a replaceable repair facility.We discuss 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 transform of the transient queue length distribution.Meanwhile,the recursion expressions of the steady state queue length distribution is obtained.Furthermore,the reliability indexes of the server and repair facility are derived,for example,the server' s first failure time,unavailability and average failure number in(0,t]time,repair facility' s unavailability and average replaced number in(0,t]time.Finally,employing the standard results in renewal process,we get the optimal control policy(N*,D*)such that the long-run expected cost rate is minimum under a given cost structure.