M/M/1 Retrial Queueing System With Vacation Interruptions Under Pre‐Emptive Priority Service

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.