Abstract: In this article, we consider a continuous review inventory system with Markovian demand. The operating policy is ( , ) s S policy, that is, the maximum inventory level is and whenever the inventory level drops to S , s an order for units is placed. The ordered items are received after a random time which is assumed to be exponential distribution. The server goes for a vacation of an e...

The research in the area of retrial queues focused mainly on the fact that the retrials operate under classical retrial policy, which suppose that the intervals between successive repeated attempts are exponentially distributed with total rate jθ (j is the number of customers in the orbit). There is another discipline, called constant retrial policy, where the total retrial rate does not depend...

In the previous chapter we assumed that replenishment is instantaneous and no shortage is permitted (shortage cost infinity).In this chapter we assume that replenishment of inventory does not materialize immediately as placement of order ,rather takes a random amount of time for order materialization .Thus we have now a finite shortage cost situation. Another salient feature of this chapter is ...

Abstract Define the traffic intensity as the ratio of the arrival rate to the service rate. This paper shows that the BMAP/PH/s/s+K retrial queue with PH-retrial times is ergodic if and only if its traffic intensity is less than one. The result implies that the BMAP/PH/s/s+K retrial queue with PH-retrial times and the corresponding BMAP/PH/s queue have the same condition for ergodicity, a fact ...

Retrial queueing systems are characterized by the requirement that customers finding the service area busy must join the retrial group and reapply for service at random intervals. This paper deals with the M/G/1 retrial queue subjected to breakdowns. We use its stochastic decomposition property to approximate the model performance in the case of general retrial times.

We study multi-class retrial queueing systems with Poisson inputs, general service times, and an arbitrary numbers of servers and waiting places. A class-i blocked customer joins orbit i and waits in the orbit for retrial. Orbit i works like a single-server ·/M/1 queueing system with exponential retrial time regardless of the orbit size. Such retrial systems are referred to as retrial systems w...

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...

Mean value analysis is an elegant tool for determining mean performance measures in queueing models. We use the technique to analyze the M/G/1 retrial queue with exponential retrial times. We also show how the relations can be adapted to obtain mean performance measures in more advanced M/G/1-type retrial queues.