On the overflow processes from the PH 1 + PH 2/M/ S/ K queue with two independent PH-renewal inputs

Abstract

This paper presents an analysis of overflow processes from a PH 1 + PH 2/M/ S/ K queue having two independent phase type renewal input streams. Both the superposed overflow process and individual overflow processes for the PH 1- and PH 2-streams are analyzed using first passage time distributions for the number of customers in the system. Each overflow process is characterized as a Markov renewal process. The nth moment of the number of customers in an infinite server group to which these overflows have been offered is derived using a theory for the MR/M/∞ queue with a Markov renewal input. The numerical examples for means and variance-to-mean ratios (peakednesses) of the individual overflow streams are given for an H 2 + H 2/ M/ S/ S queue with interrupted Poisson inputs, which is a vital model for telephone network planning. In addition, overflow traffic characteristics are discussed by using these examples.