As a generalization of classic queueing models with vacations,the working vacation queues were introduced in 2002, where the server serves customers at a lower rate rather than completely stopping service during the vacation period. This type of vacation models can be applied in performance evaluation of optical communication networks, production and service systems, and other fields. In recent...

We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there are no customers in the system, the server takes vacation consisting of K -phases, each phase is generally distributed. Here the first phase is compulsory where as the other phases are optional. For this model the supplementary var...

This paper deals with finite capacity single server queuing system with vacations. Vacation starts at rate nu if the system is empty. Also the server takes another vacation if upon his arrival to the system, finds the system empty. Customers arrive in the system in Poisson fashion at rate lamda0 during vacation, faster rate lamdaf during active service and slower rate lamdas during the breakdow...

This paper investigates an M [x] /G/1 queueing system with an unreliable server, where the server may take an additional vacation after the essential vacation. If the system becomes empty, the server leaves the system and takes the essential vacation. At the end of the essential vacation, the server may return to the system with probability p or take another vacation with probability 1-p. When ...

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, an M/M/1 queue with working vacation and vacation interruption is investigated. The server is supposed to take a working vacation whenever the system becomes empty and if there are at least N customers waiting in the system at a service completion instant, vacation interruption happens and the server resumes a normal working period. A matrix geometric approach is employed to obta...

In this paper we present the analysis of the BMAP/GI/1 phase dependent vacation model with decrementing-K service discipline. The exhaustive discipline is a special case of the decrementing-K discipline, where K = ∞. The generalization of the service discipline independent expressions of the vacation model [7] for phase dependent vacation enables the treatment of the BMAP/GI/1 queue as special ...

In this paper we present the analysis of BMAP/G/1 vacation models of non-M/G/1-type in a general framework. We provide new service discipline independent formulas for the vector generating function (GF) of the stationary number of customers and for its mean, both in terms of quantities at the start of vacation. We present new results for vacation models with gated and G-limited disciplines. For...