A multiple optional vacation policy for the unreliable server batch arrival queueing system with essential and multi optional services under N-policy is investigated. According to vacation policy, the server takes an essential phase of vacation after the completion of service of an individual customer when queue becomes empty. On returning from the vacation, if the server finds the queue empty,...

Abstract We consider an M/G/1 feedback queue with optional server vacations based on Bernoulli schedule and a single vacation policy. We assume that the server provides two types of service, type 1 with probability p1 and type 2 with probability p2 with the service times following general distribution and each arriving customer may choose either type of service. However after the completion of ...

the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract We consider an M [x] /G/1 queue with two types of service subject to random breakdowns having multiple server vacation, where the customers arrive to the system in batches of variable size. We assume that a single server p...

Consider a single server retrial queueing system with preemptive priority service and single working vacation in which two types of customers arrive in a Poisson process with arrival rates λ1 for low and λ2 for high priority customers. We assume that regular service times follow an exponential distribution with parameters μ1 and μ2 correspondingly. The retrial is introduced for low priority cus...

In this contribution we investigate discrete-time queueing systems with vacations. A framework is constructed that allows for studying numerous different vacation systems, including a.o. classical vacation systems like the exhaustive and limited vacation systems as well as queueing systems with service interruptions. Using a probability generating functions approach, we obtain steady-state perf...

This paper refers to some closed two-stage queueing systems with state-dcpendent vacation policy. By means of the markovian rcnewal process and the stochastic decomposition formulas of the quantities in equilibrium for M/Gjl vacation models, we derive both stationary distributions of the queue length and the cyclic time for the closed state-dependcnt vacation model. We try to so!\'e the problem...

Consider an M/M/1 queueing system with server vacations where the server is turned oo as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding co...

This paper deals with the transient analysis of batch arrival retrial queueing system with general retrial times, priority service, balking, second optional service, Bernoulli vacation, extended vacation, breakdown, delayed repair and stand by server. Here we assume that customers arrive in batches according to compound Poisson processes, where the blocked customers either with probability p jo...