An Approximate Method for Design and Analysis of an ALOHA System

Abstract

We develop here an approximate method for the design and performance prediction of a multiaccess communication system which employs the ALOHA packet-switching technique. Our model is based on the use of a diffusion process approximation of an ALOHAlike system (with or without time-slotting). A simple closed-form solution for the variable <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q(t)</tex> , a variant of the number of backlog messages at time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</tex> , is given in terms of a few system and user parameters. Final results are expressed in terms of ordinary performance measures such as throughput and average delay. Several numerical examples are given to demonstrate the usefulness of the approximation technique developed.