SINGLE SERVER RETRIAL QUEUES WITH SECOND OPTIONAL SERVICE UNDER ERLANG SERVICES

Abstract

Consider a single server retrial queueing system in which customers arrive in a Poisson process with arrival rate λ. In this model the server provides two types of service namely Essential Service and Second Optional Service. The Essential service will be given to all customers through k-phases whereas the Second optional service is extended only to those optional customers as a single phase if they demand. The essential service time has Erlang-k distribution with service rate kμ1 for each phase. The second optional service has only one phase in it and the service time of second optional service follows an exponential distribution with parameter μ2. If the server is free at the time of a primary call arrival, the arriving call begins to be served in Phase 1of the essential service phase immediately by the server then progresses through the remaining phases and must complete the last phase and after completion of this essential service, this customer either demands a second optional service with probability p or leaves the system with probability (1-p) before the next customer enters the first phase of the essential service. 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 Matrix geometric Technique. Numerical studies have been done for Analysis of Mean number of customers in the orbit (MNCO),Truncation level (OCUT),Probability of server free and busy for various values of λ , μ1 , μ2 , p , k and σ.

KEYWORDS : Retrial queue - second optional service - classical retrial policy- Matrix Geometric Method

2010 Mathematics Subject Classification 60K25 65K30