A recursive method for Bernoulli arrival queues and its application to partial buffer sharing in ATM

Abstract In this research, we first develop a recursive method to compute the state probabilities of Geo/G/1/K discrete-time queueing system directly from the system equations. Then, we model the partial buffer sharing scheme of ATM buffer control mechanism by Geo1, Geo2/G/1/K+1 queue and apply the recursive method to obtain the steady-state probabilities and loss probabilities. Scope and purpose Most results in queueing theory are given in the form of transforms. We need to invert the transform solution to obtain probabilities and various performance measures. This is a big burden not only to researchers but also to practitioners. In this research, we develop a recursive method for discrete-time finite queueing systems which enables us to compute the state probabilities not by inverting the transform solution, but directly from the system equations. The developed recursive method is simple enough (even though somewhat tedious) to implement in analyzing many discrete-time finite queueing systems with Bernoulli arrivals.