Analytically simple and computationally efficient solution to GI[formula omitted]/Geom/1 queues involving heavy-tailed distributions

Abstract

This paper provides an analytically simple and computationally efficient solution to the discrete-time queueing model GIX /Geom/1. Using the imbedded Markov chain method, the analysis has been carried out for the late-arrival system and the results for the early-arrival system have been derived from those of the late-arrival system. The distributions of the numbers in the system at various epochs are all found in terms of roots of the underlying characteristic equation. Numerical results are also discussed.