Contention resolution with constant expected delay
Leslie Ann Goldberg, PHILIP D. MACKENZIE, Mike Paterson, Aravind Srinivasan · Journal of the ACM · 2000
We study contention resolution in a multiple-access channel such as the Ethernet channel. In the model that we consider,nusers generate messages for the channel according to a probability distribution. Raghavan and Upfal have given a protocol in which the expecteddelay(time to get serviced) of every message is O(logn) when messages are generated according to a Bernoulli distribution with generation rate up to about 1/10. Our main results are the following protocols: (a) one in which the expected average message delay is O(1) when messages are generated according to a Bernoulli distribution with a generation rate smaller than 1/e, and (b) one in which the expected delay of any message is O(1) for an analogous model in which users are synchronized (i.e., they agree about the time), there are potentially an infinite number of users, and messages are generated according to a Poisson distribution with generation rate up to 1/e. (Each message constitutes a new user.) To achieve (a), we first show how to simulate (b) usingnsynchronized users, and then show how to build the synchronization into the protocol.