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 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 sin 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.
