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

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 This work was supported by Army grant DAAH 04-95-1-0607 and ARPA contract N00014-95-1-1246.A preliminary version of this work appeared in 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 networks (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-toend 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.

Guaranteeing Stability and Delay in Dynamic Networks Based on Infinite Games

“…We show that f is in fact an MCF with throughput λ j for each commodity j, i.e., it satisfies the constraints (1) to (5). The play at ρ = r ·s i and ρ = r ·s i+1 is at position s l which means the number of packets of commodity j received at each node u during s 1 , ... , s l is equal to the number of packets sent, i.e.,…”

“…One of the first contributions in this line was provided by Borodin et al in [3] where network stability of backpressure routing was investigated for adversarial conditions. Since then, several contributions have extended the original models and results [4], [5], [6]. Most recently, two contributions from Andrews et al [7], [8] addressed the stability of backpressure routing for dynamic networks (i.e., networks with varying link capacities) where an adversary injects multi-commodity traffic into the network.…”

Effective Routing and Scheduling in Adversarial Queueing Networks

“…Adversarial networks have received a lot of attention in recent years. They were first introduced by Borodin et al [9], and further elaborated by Andrews et al [3,4]. Later, these were seen to be non-trivial generalizations of earlier models of Cruz [10].…”

Packet Forwarding Algorithms in a Line Network

“…In general this depends on the protocol studied, on the size and topology of the network and on the maximum rate at which the adversary is allowed to inject packets into the network. We refer to [2][3][4][5][6][7][8][9][10][11][12][13] for some representative papers under this model. In the second model, a subset of the packets has to be dropped, due to some restriction.…”