On a loss system with a given number of customers

Abstract

A one-server loss system with Poisson arrival stream and deterministic service times is considered conditional on the number of customers who appeared up to a given T. This condition implies that the arrival times form a sample of the uniform distribution on (0, T]. We derive several characteristics of interest, such as the blocking probability at any given time t ∈ (0, T], the probability that exactly i of the customers in (0, T] are served and, as a generalization, the distribution of the number of served customers arriving in any subinterval of (0, T]. © 1992 J.C. Baltzer A.G. Scientific Publishing Company.