Analysis of Practical Backo Protocols for Contention Resolution with Multiple Servers

  • Leslie Ann Goldbergy, Philip D. MacKenziez
  • Published 1995

Abstract

Backo protocols are probably the most widely used protocols for contention resolution in multiple access channels. In this paper, we analyze the stochastic behavior of backoo protocols for contention resolution among a set of clients and servers, each server being a multiple access channel that deals with contention like an Ethernet channel. We use the standard model in which each client generates requests for a given server according to a Bernoulli distribution with a specied mean. The client-server request rate of a system is the maximum over all client-server pairs (i; j) of the sum of all request rates associated with either client i or server j. (Having a sub-unit client-server request rate is a necessary condition for stability for single-server systems.) Our main result is that any superlinear polynomial backoo protocol is stable for any multiple-server system with a sub-unit client-server request rate. Our result is the rst proof of stability for any backoo protocol for contention resolution with multiple servers. (The multiple-server problem does not reduce to the single-server problem, because each client can only send a single message at any step.) Our result is also the rst proof that any weakly acknowledgment based protocol is stable for contention resolution with multiple servers and such high request rates. Two special cases of our result are of interest. Hastad, Leighton and Rogoo have shown that for a single-server system with a sub-unit client-server request rate any modied superlinear polynomial backoo protocol is stable. These modiied backoo protocols are similar to standard backoo protocols but require more random bits to implement. The special case of our result in which there is only one server extends the result of Hastad, Leighton and Rogoo to standard (practical) backoo protocols. Finally, our result applies to dynamic routing in optical networks. Speciically, a special case of our result demonstrates that superlinear polynomial backoo protocols are stable for dynamic routing in optical networks.

Cite this paper

@inproceedings{Goldbergy1995AnalysisOP, title={Analysis of Practical Backo Protocols for Contention Resolution with Multiple Servers}, author={Leslie Ann Goldbergy and Philip D. MacKenziez}, year={1995} }