Universal-stability results and performance bounds for greedy contention-resolution protocols

  • Authors:

  • Matthew Andrews;Baruch Awerbuch;Antonio Fernández;Tom Leighton;Zhiyong Liu;Jon Kleinberg

  • Affiliations:

  • Bell Labs, Lucent Technologies, Murray Hill, NJ;Johns Hopkins Univ., Baltimore, MD;Massachusetts Institute of Technology, Cambridge;Massachusetts Institute of Technology, Cambridge;Massachusetts Institute of Technology, Cambridge;Cornell Univ., Ithaca, NY

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 2001

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Abstract

In this paper, we analyze the behavior of packet-switched communication networks in which packets arrive dynamically at the nodes and are routed in discrete time steps across the edges. We focus on a basic adversarial model of packet arrival and path determination for which the time-averaged arrival rate of packets requiring the use of any edge is limited to be less than 1. This model can reflect the behavior of connection-oriented networks with transient connections (such as ATM networks) as well as connectionless networks (such as the Internet). We concentrate on greedy (also known as work-conserving) contention-resolution protocols. A crucial issue that arises in such a setting is that of stability—will the number of packets in the system remain bounded, as the system runs for an arbitrarily long period of time? We study the universal stability of network (i.e., stability under all greedy protocols) and universal stability of protocols (i.e., stability in all networks). Once the stability of a system is granted, we focus on the two main parameters that characterize its performance: maximum queue size required and maximum end-to-end delay experienced by any packet. Among other things, we show: (i) There exist simple greedy protocols that are stable for all networks.(ii) There exist other commonly used protocols (such as FIFO) and networks (such as arrays and hypercubes) that are not stable.(iii) The n-node ring is stable for all greedy routing protocols (with maximum queue-size and packet delay that is linear in n).(iv) There exists a simple distributed randomized greedy protocol that is stable for all networks and requires only polynomial queue size and polynomial delay.Our results resolve several questions posed by Borodin et al., and provide the first examples of (i) a protocol that is stable for all networks, and (ii) a protocol that is not stable for all networks.