Journal of Applied Mathematics and Stochastic Analysis
Volume 2009 (2009), Article ID 308025, 14 pages
doi:10.1155/2009/308025
Research Article

Interloss Time in M/M/1/1 Loss System

Pierpaolo Ferrante

Occupational Medicine Department (DML), National Institute for Occupational Safety and Prevention (ISPESL), Via Alessandria 220/E, 00198 Rome, Italy

Received 29 March 2009; Accepted 24 May 2009

Academic Editor: Ho Lee

Copyright © 2009 Pierpaolo Ferrante. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the interloss times in the M/M/1/1 Erlang Loss System. Here we present the explicit form of the probability density function of the time spent between two consecutive losses in the M/M/1/1 model. This density function solves a Cauchy problem for the second-order differential equations, which was used to evaluate the corresponding laplace transform. Finally the connection between the Erlang's loss rate and the evaluated probability density function is showed.