Some features of a finite-source M/GI/1 retrial queuing system with collisions of customers

In this paper a finite-source M/GI/1 retrial queuing system with collisions of customers is considered. The definition of throughput of the system as average number of customers, which are successfully served per unit time is introduced. It is shown that at some combinations of system parameter values and probability distribution of service time of customers the throughput can be arbitrarily small, and at another values of parameters throughput can be greater than the service intensity. Applying method of asymptotic analysis under the condition of unlimited growing number of sources it is proofed that limiting distribution of the number of retrials/transitions of the customer into the orbit is geometric and the sojourn/waiting time of the customer in the orbit follows a generalized exponential distribution. In addition, the mean sojourn time of the customer under service is obtained. © 2017, Springer International Publishing AG