The single server queueing system with Non-recurrent input-process and Erlang service time

Abstract

We consider a single server queueing system in which customers arrive at the instants t₀, t₁, …, t_m, …. We write τ_m = t_m+1 − t_m, m ≧ 0. There is a single server with distribution of service times B(x) given by where k is an integer not less than unity.