Analysis of the discrete-time GI/Geom(n)/1/N queue

In this paper, we consider the discrete-time single-server finite-buffer late arrival with delayed access queue GI/Geom(n)/1/N. Whereas the interarrival times are independently identically distributed random variables with arbitrary probability mass function, the service times are geometrically distributed random variables with probability of a service completion during a slot dependent on the number of customers present in the system. Using the supplementary variable technique, we obtain probability distributions of numbers of customers in the system at arbitrary and prearrival epochs as well as an outside observerʹs distribution. In addition, we derive some important results which are used to develop relations between probabilities at prearrival and arbitrary epochs. Results obtained in this paper can be used in several areas such as performance evaluation of computer-communication systems.