A Birth and Death Process Approximation for the Slotted ALOHA Algorithm.
MASSACHUSETTS UNIV AMHERST DEPT OF MATHEMATICS AND STATISTICS
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Many authors have concerned themselves with the bistable behavior of the finite-user slotted ALOHA protocol under heaving loading. Recently Nelson used a catastrophe-theoretic approach to demonstrate that under a fluctuating load the protocol suffers hysteresis as well as bistability. He uses results from catastrophe theory to give a possible improved control algorithm. Central to Nelsons approach is a diffusion approximation of the queue of backlogged users. This approximation has the advantage of yielding a continuing probability density for the process, thus allowing the use of stochastic catastrophe theory. Unfortunately, as will be seen later, the approximation requires difficult numerical integration and yields no closed form solution. It is being proposed here that the process should remain discrete, and that it can be approximated reasonably well as a birth-death process. This allows rapid computation of the approximate stationary distribution.
- Statistics and Probability