A Dynamic Analysis of Aloha Systems with Blocking and Carrier Sense

Abstract

A mathematical model of a proposed scheme to implement an ALOHA system with blocking and carrier sense is analyzed. New packets and blocked packets are each attempted to be sent at times which form a Poisson point process. A system of first order differential equations which describe the dynamic behavior of the system is obtained. These equations can be solved by conventional numerical techniques. If a steady state exists, the differential equations become a set of linear equations and a steady state solution is found with additional rate and normalization equations. Steady state solutions of simple examples for one and two user systems are given. It was found that throughput may approach 1/τ, but in that operating condition, the average delay approaches Nτ and the users are probably blocked most of the time. By reducing throughput, however, the average delay and average number of blocked users can be reduced.