A bound on the capacity of backoff and acknowledgment-based protocols

We study contention-resolution protocols for multiple-access channels. We show that every backoff protocol is transient if the arrival rate, $\lambda$, is at least 0.42 and that the capacity of every backoff protocol is at most 0.42. Thus, we show that backoff protocols have (provably) smaller capacity than full-sensing protocols. Finally, we show that the corresponding results, with the larger arrival bound of 0.531, also hold for every acknowledgment-based protocol.

[1]  Raphael Rom,et al.  Multiple Access Protocols: Performance and Analysis , 1990, SIGMETRICS Perform. Evaluation Rev..

[2]  R. A. Doney,et al.  4. Probability and Random Processes , 1993 .

[3]  Leslie Ann Goldberg,et al.  Analysis of practical backoff protocols for contention resolution with multiple servers , 1996, SODA '96.

[4]  Peter March,et al.  Stability of binary exponential backoff , 1988, JACM.

[5]  Frank Kelly,et al.  Stochastic Models of Computer Communication Systems , 1985 .

[6]  Eli Upfal,et al.  Stochastic Contention Resolution With Short Delays , 1998, SIAM J. Comput..

[7]  Anthony Ephremides,et al.  Information Theory and Communication Networks: An Unconsummated Union , 1998, IEEE Trans. Inf. Theory.

[8]  Pierre A. Humblet,et al.  A Class of Efficient Contention Resolution Algorithms for Multiple Access Channels , 1985, IEEE Trans. Commun..

[9]  Aravind Srinivasan,et al.  Contention resolution with constant expected delay , 2000, JACM.

[10]  George C. Polyzos,et al.  Conflict Resolution Algorithms and their Performance Analysis , 1993 .

[11]  U. Loher.  Efficiency of first-come first-served algorithms , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[12]  John Capetanakis,et al.  Tree algorithms for packet broadcast channels , 1979, IEEE Trans. Inf. Theory.

[13]  I. MacPhee,et al.  The Number of Packets Transmitted by Collision Detect Random Access Schemes , 1987 .

[14]  Leslie Ann Goldberg,et al.  An Improved Stability Bound for Binary Exponential Backoff , 2001, Theory of Computing Systems.

[15]  Aravind Srinivasan,et al.  Contention resolution with bounded delay , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[16]  G. Grimmett,et al.  Probability and random processes , 2002 .

[17]  Philippe Flajolet,et al.  Estimating the multiplicities of conflicts to speed their resolution in multiple access channels , 1987, JACM.

[18]  Leslie Ann Goldberg,et al.  Binary Exponential Backoff Is Stable for High Arrival Rates , 2000, STACS.

[19]  G. Fayolle,et al.  Topics in the Constructive Theory of Countable Markov Chains , 1995 .

[20]  Rajeev Motwani,et al.  Randomized Algorithms , 1995, SIGA.

[21]  Frank Thomson Leighton,et al.  Analysis of Backoff Protocols for Multiple Access Channels , 1996, SIAM J. Comput..

[22]  David J. Aldous.  Ultimate instability of exponential back-off protocol for acknowledgment-based transmission control of random access communication channels , 1987, IEEE Trans. Inf. Theory.

[23]  Gordon Bell,et al.  Ethernet: Distributed Packet Switching for Local Computer Networks , 1976 .

[24]  Raphael Rom,et al.  Multiple Access Protocols: Performance and Analysis , 1990, SIGMETRICS Perform. Evaluation Rev..

[25]  S. Verdu.  Computation of the efficiency of the Mosely-Humblet contention resolution algorithm: A simple method , 1986, Proceedings of the IEEE.

[26]  Urs Loher.  Information-theoretic and genie-aided analyses of random-acess algorithms , 1998 .

[27]  F. G. Foster.  On the Stochastic Matrices Associated with Certain Queuing Processes , 1953 .