Publication

Abstract : In this paper we consider the GI/M/1/1 retrial queue with finite number of retrials to each orbital customer and a finite number of orbits. The interarrival times from outside the system have a general distribution. The sojourn time of a unit in an orbit until its retrial for service and its service time are exponentially distributed with parameters depending on the orbit number. The maximum number of retrials any unit is permitted to take is restricted to k. There are a finite number, say m, of orbits with at most one customer in each orbit. At the time of an arrival if the server is busy and all orbits are occupied, then the customer is lost to the system. If the server is idle at an arrival epoch, the unit directly goes for service. If the server is busy and at least one of the orbits is empty then the arriving customer occupies the first empty orbit. A unit in the orbit retries for service which returns to the same orbit (if the server is busy) with probability P and leaves the system with probability 1−P, 0