Present investigation deals with optimal management policy for Markovian queue with server breakdowns, vacations and setup. The customers arrive in Poisson fashion to get the service. The server may breakdown during the service and goes for repair immediately. By applying probability generating function technique queue length distribution is obtain for different states of the server. Further we...

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...

Retrial queueing systems are characterized by the fact that a primary request, finding all servers and waiting positions busy upon arrival, leaves the service area but after some random time, repeats its demand. Between retrials, the customer is said to be in “Orbit”. So the repeated attempts for service from the group of blocked customers are super imposed on the normal stream of arrivals of p...

This paper investigates the concept of a Markovian queueing model with heterogeneous, intermittently available servers feedback under hybrid vacation policy. Both asymmetric transition representation and policy are addressed in this article. The necessary sufficient conditions for system stability presented. In addition, steady-state probability distribution was derived by employing matrix geom...

This paper presents the transient solution of a variant working vacation queue with balking. Customers arrive according to a Poisson process and decide to join the queue with probability $b$ or balk with $bar{b} = 1-b$. As soon as the system becomes empty, the server takes working vacation. The service times during regular busy period and working vacation period, and vacation times are assumed ...

We consider a finite-buffer single server queueing system with queue-length dependent vacations where arrivals occur according to a batch Markovian arrival process (BMAP). The service discipline is P-limited service, also called E-limited with limit variation (ELV) where the server serves until either the system is emptied or a randomly chosen limit of L customers has been served. Depending on ...

The study of unreliable server retrial bulk queue with multiphase optional service is analyzed by incorporating the features balking, Bernoulli vacation and feedback. On occasion when occupied customers, an arriving customer finding long queue, can join orbit receives its later on making re-attempt. system reinforced multi phase along essential joining opt any one services after getting service...

This paper deals with finite-population, single and multi-server queueing systems with two classes of vacation mechanisms : station vacation and server vacation. In the first one, all the servers take vacation simultaneously whenever the system becomes empty, and they also return to the system at the same time, i.e., station vacation is group vacation for all servers. For the second class of va...