ANALYSIS OF BACKOFF PROTOCOLS FOR MULTIPLE-ACCESS CHANNELS

In this paper, we analyze the stochastic behavior of backoff protocols for multiple access channels such as the Ethernet. In particular, we prove that binary exponential backoff is unstable if the arrival rate of new messages at each stations is lambda/N for any lambda > 1/2 and the number of stations N is sufficiently large. For small N, we prove that lambda greater than or equal to lambda(0)+1/4N-2 implies instabil ity, where lambda(0) approximate to .567. More importantly, we also pr ove that any superlinear polynomial backoff protocol (e.g., quadratic backoff is stable for any set of arrival rates that sum to less than o ne and any number of stations. The results significantly extend the pr evious work in the area and provide the first examples of acknowledgme nt-based protocols known to be stable for a nonnegligible overall arri val rate distributed over an arbitrarily large number of stations. The results also disprove a popular assumption that exponential backoff i s the best choice among acknowledgment-based protocols for systems wit h large overall arrival rates. Finally, we prove that any linear or su blinear backoff protocol is unstable if the arrival rate at each stati on is lambda/N for any fixed lambda and sufficiently large N.