A new type of equilibrium distributions

under specific assumptions

R. El Kouch

Institut National des Postes et Télécommunications, PO Box: 6241. Rabat-Instituts, Rabat, Maroc

* Corresponding author. E-mail: elkouch@inpt.ac.ma

Received : 19 July 2004; revised version accepted :14 January 2005

Abstract

This paper presents a new type of equilibrium distributions under specific assumptions. We generalize the result for arbitrary service times. We develop computationally efficient recursive formula for the equilibrium distributions for the number of customers in the system.

In studying queueing systems, we use not only several random variables but also several different sequences that are functions of time. All the works that have been done before were related to the Markovian Arrival Process (MAP) which is associated with a finite absorbing Markov, or were related to analog systems. Many authors have dealt with the property of insensitivity in queuing theory. We will not comment on these works, because they are published and are available in most teletraffic theory books.

For the queuing model considered in our approach, the stochastic process of the number of customers at time in the system is considered non-Markovian.

The mathematical derivations, used here, are easy to comprehend by network engineers. They are based on the well-known Erlang phase method.

Keywords: Equilibrium Distribution; Stochastic Process; Poisson distribution; Queuing model; AONP; PAP; Coaxian.

© 2015