||Single Server Retrial Queuing System with Second Optional Service under Coxian Phase Type Services
||Muthu Ganapathi SUBRAMANIAN, G. AYYAPPAN and Gopal SEKAR
Consider a single server retrial queueing system with second optional service under Coxian phase type services in which customers arrive in a Poisson process with arrival rate λ. Let k be the number of phases in the service station. The server provides two types of services, namely Regular Service and Second Optional Service. The regular service time follows an exponential distribution with parameter μj; for jth phase ( j = 1, 2, 3 , . . . , k). The second optional service time follows an exponential distribution with parameter λ. The services in all phases are independent and only one customer at a time is in the service mechanism. Let qj ( j = 1,2,3,. . . , k-1) be the probability that the customer moves from jth phase to (j+1)st phase. If the server is free at the time of a primary call arrival, the arriving call begins to be served in Phase 1 immediately by the server. If the server is busy, then the arriving customer goes to orbit and becomes a source of repeated calls. We assume that the access from orbit to the service facility is governed by the classical retrial policy. This model is solved by using Direct Truncation Method. Numerical studies have been done for analysis of mean number of customers in the orbit (MNCO),Truncation level (OCUT), Probabilities of server free and busy and for various values of λ, q1, q2, . . . , qk-1, μ1, μ2, . . . , μk μ, p, k, and σ and also various particular cases of this model have been discussed.