Pushpa Publishing House

respectively for each phase. We assume that the services in all phases are independent and identical and only one customer at a time is in the service mechanism. 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 then progresses through the remaining phases and must complete the last phase and leave the system before the next customer enters the first phase. 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

and s in elaborate manner and also various particular cases of this model have been discussed.

Advances and Applications in Statistics
Volume 18, Issue 2, Pages 189 - 208 (October 2010)

M/M/1 RETRIAL QUEUEING SYSTEM WITH VARIABLE SERVICE RATES UNDER ERLANG k-TYPE SERVICES
G. Ayyappan, Gopal Sekar and A. Muthu Ganapathi Subramanian

Abstract:
Consider a Single server retrial queueing system with variable service rates under Erlang k-type services in which customers arrive in a Poisson process with arrival rate l. Let k be the number of phases in the service station. In this model, the server provides service in two different rates namely regular service rate and accelerated service rate. Both service times have Erlang k-type distribution with service rates

and

and s in elaborate manner and also various particular cases of this model have been discussed.

Keywords and phrases: single server, Erlang k-type services, variable service rates, matrix geometric method, classical retrial policy.

Number of Downloads: 417 | Number of Views: 1202