We consider a queueing system with c servers and a threshold type vacation policy. In this system, when a certain number d<c of servers become idle at a service completion instant, these d servers will take a synchronous vacation of random length together. After each vacation, the number of customers in the system is checked. If that number is N or more, these d servers will resume serving the ...

In this paper, we study an M/G/1 queue with two phases of heterogeneous service. A first essential service is provided to all arriving customers. Upon completion of this service, a customer can either opt for a second phase of service or can leave the system. A customer, who finds the server busy, either leaves the system with probability (1-α) or joins an orbit with probability α. From the orb...

In many industrial situations, machines are subjected to random breakdowns. In this paper, we consider the asynchronous vacation policy for the multi-server machine repair problem with server breakdown and two types of spares. According to this policy, when a certain number of servers become idle at a service completion instant, the servers will take an asynchronous vacation of random length to...

Retrial queues have been widely used to model many problems arising in telephone switching systems, telecommunication networks, computer networks and computer systems, etc. It is of basic importance to study reliability of retrial queues with server breakdowns and repairs because of limited ability of repairs and heavy influence of the breakdowns on the performance measure of the system. Howeve...

Abstract This paper studies a batch arrival queueing system in which the server may face occasional random breakdowns. The repair process does not start immediately after a breakdown and there is a delay time waiting for repairs to start. Further, after every service completion the server has the option to leave for a vacation with probability p or continue serving with probability1 − p. The ma...

Consumers often have to join a queue before they can obtain a service; however, they suffer disutility in waiting for the service. When consumers can self-organize the timing of their service visits, they may avoid long queues and choose to retry later. Nevertheless, the existing research on decision-making in queues has focused mainly on join or balk decisions, while acknowledging that some co...

The present paper deals with the problem of calculating queue length distributions in a priority queueing model with a preemptive-resume policy under the assumption of general arrival and service distributions. The multi-queue priority system is decomposed into single-queue vacation systems, for which the visit and inter-visit distributions are approximated by the idle and busy period of a ΣGI/...