Stability and Optimal Control of the Packet Switching Broadcast Channel

Abstract

The purpose of this paper is to analyze and optimize the behavior of the broadcast channel for a packet transmission operating in the slotted mode Mathematical methods of Markov chain theory are used to prove the inherent lnstablhty of the system If no control is apphed, the effective throughput of the system will tend to zero tf the population of user terminals ~s sufficiently large Two classes of control pohcles are examined, the first acts on admissions to the channel from active terminals, and the second modifies the retransmlss~on rate of packets In each case sufflc~ent conditions for channel stability are given. In the case of retransm~sslon controls it is shown that only pohcles which assure a rate of retransmlsslon from each blocked terminal of the form off = 1/n, where n is the total number of blocked terminals, will yield a stable channel It ts also proved that the optimal pohcy which maximizes the maximum achievable throughput wtth a stable channel IS of the formf = (1 - k)/n Simulations illustrating channel lnstabdlty and the effect of the opnmal control are prowded