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Consider a single server retrial queueing system with preemptive priority service and single working vacation in which two types of customers arrive in a Poisson process with arrival rates λ1 for low and λ2 for high priority customers. We assume that regular service times follow an exponential distribution with parameters μ1 and μ2 correspondingly. The retrial is introduced for low priority customers only. During working vacation the server serve's the arriving customers with lesser service rates µ3 and µ4 respectively. These service rates µ3 and µ4 follow an exponential distribution. However at any time the server may return from the working vacation with a working vacation rate α which follows the exponential distribution. The access from orbit to the service facility follows the classical retrial policy and the high priority customers will be governed by the pre-emptive priority service. This model is solved by using Matrix geometric Technique. Numerical study have been done in elaborate manner for finding the Mean number of customers in the orbit, Probabilities that server is idle, busy during working vacation and normal period.

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