TRANSIENT BEHAVIOUR OF M/G/1 RETRIAL QUEUEING SYSTEM WITH CONSTANT RETRIAL POLICY BY SUPPLEMENTARY VARIABLE TECHNIQUE

Consider a single server retrial queueing system in which customers arrive in a Poisson process with arrival rate λ. These customers are identified as primary calls. Further assume that the service time follows a general distribution with probability density function ()b x and cumulative distribution function ()B x. If the server is free at the time of a primary call arrival, the arriving call begins to be served immediately by the server and after completion of the service, the customer leaves the system and server becomes idle. If the server is busy, then the arriving customer goes to orbit of infinite capacity and makes a retrial at a later time. This pool of sources of repeated calls may be viewed as a sort of queue (FCFS). We assume that the access from the orbit to the service facility is governed by the constant retrial rate of policy, that is the retrial customer at the head of the retrial queue repeats its request for service with an exponentially distributed retrial times with retrial rate (1-δ0n)σ, where δ0n denotes Kronecker’s delta. If an incoming repeated call finds the server free, it is served in the same manner and leaves the system after service completion, while the source which produced this repeated call disappears. Otherwise, the system state does not change. The input flow of primary calls, interval between repetitions and service time are mutually independent. The transient behaviour of this model is analysed by Supplementary variable technique. Steady state probability distributions and system performance measures have been derived for various service time distributions (Exponential and Erlang). Numerica