SOME CHARACTERISTICS OF OUTPUT STREAM OF UNSERVED CUSTOMERS IN \(G^X/G/1\) AND \(G_D^X/G_D/1\) SYSTEM

Abstract

In this paper, an output stream of unserved customers is considered. Namely, during the service of a customer or a group of customers, other customers which wait in the system lose some properties and cannot be accepted for servicing. Therefore, they leave the system unserved. We determinate the Laplace-Stieltjes transformation and the probability generating function of the inter-output times between two groups of unserved customers in \(G^X/G/1\) and \(G_D^X/G_D/1\) system, respectively. As a special case, we find the distribution of this characteristic for \(M/M/1\) and \(Geo/Geo/1\) systems.