On a Recurrence Equation Arising in the Analysis of Conflict Resolution Algorithms

Conflict resolution algorithms (eRA) for broadcast communications have become increasingly popular since the work of Capetanakis as well as Tsybakov and Mikhailov (CfM-algorithm). In this paper we consider a class of CfM algorithms for which a common recurrence equation for the expected length of the conflict resolution interval is found. An analysis of the equation is the primary goal of this paper. A closed fonn expression for the solution of the recurrence is given. Then we present an asymptotic approximation of it. In addition, we solve a functional equation associated with the recurrence and study a small value as well as an asymptotic approximation of the solution. Finally. we apply these approximations to compute maximum throughput of some eRA algorithms. We also point out that the studies are not only restricted to analysis of CRA algorithms, and a wide class of algorithms might be investigated by the proposed recurrence equation. Categories and Subject Descriptions: CA [performance of Systems]: Model Techniques: 0.4.8 [Operating Systems]: Perfonnance: Queueing theory; F2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical algorithms and Problems: computations on discrete structures. General Terms: Perfonnance. Theory, Algorithms Additional