Two Types Of Empty Exhaustive Service With Multiple Adaptive Vacation Repairable Queuing System

Based on the existing research harvest of queueing system with server vacation and repairable service station , this paper study two typical repairable queueing systems with exhaustive service and adaptive multistage vacation, we obtain the following indexes:1 Repairable queue MX/G(M/G)/1 with adaptive multistage vacationResuming the cutomers arrival intervals and the life of server are all exponential distributions, the service time and repair time are general distributions, we consider two types of customer arrival:1) the customers input rate is unchangablea. the expression of L - transform of the transient queue length distribution at arbitrary epoch t and the recursion expression of the steady distributionb. the distribution functions of"server-idle period"and"circular server-busy period"c. the expression of LS -transform for the expected number of departure during the interval (0 , t] and the asymptotic expansion of the expressiond. the expression of L -transform for the probability that the server failure happens at epoch t and the equilibrium resulte. the expression of LS -transform for expected number of the server failures during the interval (0 , t] and asymptotic expansion of the expressionf. the asymptotic expansion for the total downtime of the server during the interval (0 , t].2) the customers input rate is changeable——P-entering disciplinea. the expression of the L - transform for the transient queue length distribution at arbitrary epoch t and the recursion expression of the steady distributionb. the distribution functions of"server-idle period"and"circular server-busy period"2 Repairable queue Geom/G(Geom/G)/1 with adaptive multistage vacationBeing parallel to the consecutive distribution, resuming that the customers arrival intervals and the life of server are geometry distributions, the service time and repair...