Analysis Of M/G/1 (Repairable) Queueing System With Delayed D-Policy

This paper studies the M/G/1 (repairable) queueing system with delayed D-policy, which generalized the M/G/1 queueing system with D-policy. The main contents of the thesis are as follow:First of all, this paper discussed the queue length distribution for M/G/1 queueing system with delayed D-policy. By introducing the server busy period and using the total probability decomposition technique, we derived the recursion expression of the Laplace transform of the transient queue length distribution at any time t, and obtain the recursion expressions of the distribution and stochastic decomposition of the queue length at a random point in equilibrium3, and also the expression of average queue length. Furthermore, when P{C=0}=1, the queueing system which is studied is the M/G/1 queueing system with D-policy. When P{C=0}=1 and P{D=0}=1, the queueing system which is studied is the classic M/G/1 queueing system. So that the results that obtained in this paper can lead to some corresponding results under these some special cases.Secondly, this paper studies the M/G/1 repairable queueing system with delayed D-Policy. The generalized busy periods of the repair facility and service station are defined, and the stochastic decomposition is provided to obtain the following some reliability indices of the service station4:1) The Laplace-Stieltjes transform of the first failure time; 2) The point unavailability at time and the steady unavailability; 3) The average failure number.