The Poisson Multiple-Access Conflict Resolution Problem

  • Toby berger
Part of the International Centre for Mechanical Sciences book series (CISM, volume 265)


The major thrust of system theory research in recent years has been directed at multiterminal, or decentralized, problems. These are characterized by the fact that system functions — such as coding, routing, control, decision, and estimation — are effected simultaneously at several physically distinct sites within the system. The information available differs, in general, from site to site. This necessitates the development of distributed algorithms aimed at cooperatively achieving optimum, or near-optimum, performance in the face of topologically complex information patterns. In previous lectures at CISM, several investigators including myself have treated multiterminal information theory problems involving distributed algorithms for encoding and decoding. In these lectures I concentrated instead on an intriguing problem in multiterminal communication theory, the conflict resolution problem in packet-switched communication networks. After stating the problem, we recast it as one of “fishing in a Poisson stream with a weak net”. The slotted ALOHA protocol is described ana analyzed. Gallager’s improvement on Capetanakis’s algorithm is then treated in considerable detail; a closed-form expression for its efficiency is derived. Recursive equations developed by the Russian and French schools are presented as an alternative means of analyzing this algorithm and others. Then we present Pippenger’s and Molle’s upper bounds to the maximum efficiency attainable. We conclude with what we feel to be a convincing case for our belief that Molle’s method can be improved upon to yield an upper bound of 0.5254 which is only 0.0377 above the efficiency of 0.4877 achieved by the optimized version of Gallager’s algorithm.


Slot Aloha Fishing Strategy Poisson Stream Poisson Limit Geneous Poisson Process 
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  1. 1.
    Gallager, R. G., Conflict resolution in random access broadcast networks, Proc. of the AFOSR Workshop in Communications Theory and Applications, Provincetown, MA, 17–20, 74, 17–20 September 1978.Google Scholar
  2. 2.
    Pippenger, Bounds on the performance of protocols for a multiple-access broadcast channel, Report RC-7742, Mathematical Sciences Department, IBM Thomas J. Watson Research Center, Yorktown Heights, NY, June 1979.Google Scholar
  3. 3.
    Molle, M. L., On the capacity of infinite population multiple access protocols, Computer Science Department, University of California, Los Angeles, CA, March 1980.Google Scholar
  4. 4.
    Roberts, L. G., Aloha packet system with and without slots and capture, ARPANET Satellite System Note 8, (NIC 11290), June 1972; reprinted in Computer Communication Review, Vol. 5, April 1975.Google Scholar
  5. 5.
    Mikhailov, V. A., On ergodicity of slotted ALOHA, Fifth International Symposium on Information Theory, Tbilisi, Georgia USSR, July 3–7, 1979.Google Scholar
  6. 6.
    Capetanakis, J. I., The multiple access broadcast channel: Protocol and capacity considerations, Technical Report ESL-R-806, MIT, Cambridge, MA, March 1978. (See also, Tree algorithm for Packet broadcast channels, IEEE Trans. on Information Theory, Vol. IT-25, No. 5,. 505, September 1979.Google Scholar
  7. 7.
    Ruget, G., Lectures delivered at CISM summer school, July 1979, Udine, Italy.Google Scholar
  8. 8.
    Tsybakov, B. S., Berkovskii, M. A. Vvedenskaja, N. D., Mikhailov, V. A. and Fedorzov, S. P., Methods of random multiple access, Fifth International Symposium on Information Theory, Tbilisi, Georgia USSR, July 3–7, 1979.Google Scholar
  9. 9.
    Gallager, R. G., Information Theory and Reliable Communication, Wiley, New York, 1968.MATHGoogle Scholar
  10. 10.
    Mehravari, N., The straddle algorithm for conflict resolution in multiple access channels, M.S. Thesis, Cornell University, School of Electrical Engineering, Ithaca, NY, May 1980.Google Scholar

Copyright information

© Springer-Verlag Wien 1981

Authors and Affiliations

  • Toby berger
    • 1
  1. 1.School of Electrical EngineeringCornell UniversityIthacaUSA

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