Single Server Retrial Queueing System with Partial Breakdown by Computational Method

A single server retrial queueing with partial breakdown and repair is taken into considerations, in which customers arrive in a Poisson process with arrival rate λ. The time interval between partial breakdowns of server follows an exponential distribution with parameter α and the time interval between repairs of server follows an exponential distribution with parameter β. The server provides service with two different rates that are normal service rate µ1 and lesser service rate µ2 during a partial breakdown. If the server is free at the time of a primary call arrival, the arriving call begins to be served immediately as the server and customer leaves the system after service completion. Otherwise, if the server is busy then arriving customer goes to orbit and becomes a source of repeated calls. A pool of sources of repeated calls may be viewed as a sort of queue. Each such source produces a Poisson process of repeated calls with intensity σ. If an incoming repeated call finds the server free, it is served and leaves the system after service, while the source producing this repeated call disappears. If there is a partial breakdown of a server during the service (active breakdown), the server does the service with lesser service rate. It is assumed that the access from orbit to the service facility is governed by the classical retrial policy. This model is solved by using Direct Truncated Method. Numerical study have been done for analysis of Mean Number of Customers in the Orbit (MNCO), Truncation level (OCUT), Probabilities of server free in normal period and partial breakdown period, Probabilities of server busy in normal service period and in partial breakdown period for various values of λ, μ1 , μ2, α ,β and σ in elaborate manner ; in addition, various particular cases of this model have been discussed.