SINGLE SERVER RETRIAL QUEUEING SYSTEM WITH VARIABLE SERVICE RATES IN PRIORITY SERVICE BY MATRIX GEOMETRIC METHOD

Consider a single server retrial queueing system with non-pre-emptive priority service and variable service rates in which two types of customers arrive in a Poisson process with arrival rate λ 1 for low priority customers and λ 2 for high priority customers.We assume that the regular service times follow an exponential distribution with parameters μ 1 and μ 2 for both types of customers respectively. The retrial is introduced for low priority customers only.The concept of variable service rate ( accelerated service ) is introduced in this paper and it follows the exponential distribution with parameter µ 3. The access from orbit to the service facility follows the classical retrial policy and the high priority customers will be governed by the non-pre-emptive priority service. 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, Truncation level (O_cut),Probability of server free and Probabilities of server busy with low and high priority customers for various values of λ 1 , λ 2 , μ 1 , µ 2 , µ 3 , σ and k in elaborate manne r and also various particular cases of this model have been discussed.