Abstract
Consider a single server retrial queueing system with pre-emptive priority service and vacation interruptions in which customers arrive in a Poisson process with arrival rate λ1 for low priority customers and λ2 for high priority customers. Further it is assume that the service times follow an exponential distribution with parameters μ1 and μ2 for low and high priority customers respectively. The retrial is introduced for low priority customers only. The server goes for vacation after exhaustively completing the service to both types of customers. The vacation rate follows an exponential distribution with parameter α. The concept of vacation interruption is used in this paper that is the server comes from the vacation into normal working condition without completing his vacation period subject to some conditions. Let k be the maximum number of waiting spaces for high priority customers in front of the service station. The high priority customers will be governed by the pre-emptive priority service. We assume that the access from orbit to the service facility is governed by the classical retrial policy. This model is solved by using Matrix geometric Technique. Numerical study have been done for Analysis of Mean number of low priority customers in the orbit (MNCO), Mean number of high priority customers in the queue(MPQL),Truncation level (OCUT),Probability of server free and Probabilities of server busy with low and high priority customers and probability of server in vacation for various values of λ1 , λ2 , μ1 , μ2, α and σ in elaborate manner and also various particular cases of this model have been discussed.
Highlights
Queueing systems in which arriving customers who find all servers and waiting positions occupied may retry for service after a period of time are called Retrial queues [1, 2, 7, 8]
The vacation interruption for priority service in retrial queueing system is governed by the following principle i.e. if the server is on vacation and if atleast one high priority customer enters the system, the server will be called back and he should immediately start to serve interrupting his vacation period
Consider a single server retrial queueing system with pre-emptive priority service [3, 5, 9], where the server goes for exhaustive service type vacation with vacation interruptions in which two types of customers arrive in a Poisson process with arrival rate λ1 for low priority customers and λ2 for high priority customers
Summary
Queueing systems in which arriving customers who find all servers and waiting positions (if any) occupied may retry for service after a period of time are called Retrial queues [1, 2, 7, 8]. In this paper we introduce this vacation interruption policy for retrial queueing system with priority service. Gopal Sekar vacation interruption was discussed by Jihong Li and Naishuo Tian [10] in the working vacation under classical queueing models who described it as “We introduce a new policy: the server can come back from the vacation to the normal working level once some indices of the system, such as the number of customers, achieve a certain value in the vacation period. The server may come back from the vacation without completing the vacation The vacation interruption for priority service in retrial queueing system is governed by the following principle i.e. if the server is on vacation and if atleast one high priority customer enters the system, the server will be called back and he should immediately start to serve interrupting his vacation period
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