In this paper a M /G(a,b)/|1 queuing system with multiple vacations, delayed service and setup time is considered. If the queue size is < ‘a’ after a service completion or after a vacation termination, the server goes for multiple vacation. Also after serving M batches continuously even if sufficient number of customers are there in the queue, the server goes for a vacation with probability α j...

In this paper, we consider an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy, where we examine the case that customer impatience is due to the servers’ vacation. Whenever a system becomes empty, the server takes a vacation. However, the server is allowed to take a maximum number of vacations, denoted by K vacations, if the system remains empty after the...

In the present paper, mathematical modeling for analyzing a Markovian queueing system with two heterogeneous servers and working vacation has been demonstrated. Keeping in view queueing situations in real life problems, here we consider service policy that initially both the heterogeneous servers take vacation when there are no customers waiting for service in the queue; however, after this ser...

In this paper, we analyze a machine repairable system with warm spares and two repairmen. The first repairman never takes vacations. The second repairman leaves for a vacation of random length when the number of the failed units is less than N. At the end of a vacation period, this repairman returns back if there are N or more failed units accumulated in the system. Otherwise this repairman goe...

We consider a two-heterogeneous-server queueing system with Bernoulli vacation in which customers arrive according to a Markovian arrival process MAP . Servers returning from vacation immediately take another vacation if no customer is waiting. Using matrix-geometric method, the steady-state probability of the number of customers in the system is investigated. Some important performance measure...

In this paper, the operating characteristics of an 1 / /G M X queueing system with unreliable server and single vacation are analyzed. The server is subjected to fail, while it is on, and the arrival rate depends on the up and down states of the server. The time to failure is exponentially distributed and the repair times follow general distribution. Server is assigned to a secondary job (vacat...

A batch arrival single-server queueing system of a general type is considered. At the end of each busy period the server begins a multiple vacation period when the service process is stopped. A new approach to the study of departure process in such a system is proposed. Using the formula of total probability and renewal theory we direct the analysis to that in the system without vacations. An e...

In this paper, we investigate an M/M/c queue with single working vacations of partial servers and setup times. During the vacation period, some of which servers are not entirely stop the service but service the new customers at a lower service rate, the other servers have a normal vacation and stop the service. Quasi-birth-and-death-process and infinitesimal generators for the process are obtai...

This paper studies a large class of M/C/l queues with vacations. By means of a probabilistic interpretation we obtain a functional equation which gives a unified approach to derive time-dependent results for the workload distribution. We also discuss application of our result to a number vacation models.