In this paper we present routing protocols that are universal in the sense that they route messages along arbitrary (simple or shortest) paths in arbitrary networks. We study these protocols under a stochastic model of continuous message generation. The performance of such protocols is characterized by three parameters: the maximum message generation rate for which the protocol is stable, the expected delay of a message from generation to service, and the time the protocol needs to recover from worst case scenarios. Our main results are a universal continuous store-and-forward routing protocol and a universal continuous wormhole routing protocol. Both protocols yield significant performance improvements over all previously known continuous routing protocols. In addition, we present adaptations of our main results to continuous routing in node-symmetric networks, butterflies, and meshes.

This paper analyzes the worst-case performance of randomized backoff on simple multiple-access channels. Most previous analysis of backoff has assumed a statistical arrival model. For batched arrivals, in which all n packets arrive at time 0, we show the following tight high-probability bounds. Randomized binary exponential backoff has makespan Θ(nlgn), and more generally, for any constant r, r-exponential backoff has makespan Θ(nlog lgr n). Quadratic backoff has makespan Θ((n/lg n) 3/2), and more generally, for r> 1, r-polynomial backoff has makespan Θ((n/lg n) 1+1/r). Thus, for batched inputs, both exponential and polynomial backoff are highly sensitive to backoff constants. We exhibit a monotone superpolynomial subexponential backoff algorithm, called loglog-iterated backoff, that achieves makespan Θ(nlg lgn/lg lglgn). We provide a matching lower bound showing that this strategy is optimal among all monotone backoff algorithms. Of independent interest is that this lower bound was proved with a delay sequence argument. In the adversarial-queuing model, we present the following stability and instability results for exponential backoff and loglogiterated backoff. Given a (λ,T)-stream, in which at most n = λT packets arrive in any interval of size T, exponential backoff is stable for arrival rates of λ = O(1/lgn) and unstable for arrival rates of λ = Ω(lglgn/lg n); loglog-iterated backoff is stable for arrival rates of λ = O(1/(lg lgnlgn)) and unstable for arrival rates of λ = Ω(1/lg n). Our instability results show that bursty input is close to being worst-case for exponential backoff and variants and that even small bursts can create instabilities in the channel.

We study contention resolution problem in a multiple-access channel such as the Ethernet...

Backoff protocols are probably the most widely used protocols for contention resolution in multiple access channels. In this paper, we analyze the stochastic behavior of backoff 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 specified 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 singleserver systems.) Our main result is that any superlinear polynomial backoff protocol is stable for any multiple-server system with a sub-unit client-server request rate. Our result is the first proof of stability for any backoff protocol fo...

In this paper we consider the problem of designing a medium access control (MAC) protocol for single-hop wireless networks that is provably robust against adaptive adversarial jamming. The wireless network consists of a set of honest and reliable nodes that are within the transmission range of each other. In addition to these nodes there is an adversary. The adversary may know the protocol and its entire history and use this knowledge to jam the wireless channel at will at any time. It is allowed to jam a (1 − ɛ)-fraction of the time steps, for an arbitrary constant ɛ> 0, but it has to make a jamming decision before it knows the actions of the nodes at the current step. The nodes cannot distinguish between the adversarial jamming or a collision of two or more messages that are sent at the same time. We demonstrate, for the first time, that there is a local-control MAC protocol requiring only very limited knowledge about the adversary and the network that achieves a constant throughput for the non-jammed time steps under any adversarial strategy above. We also show that our protocol is very energy efficient and that it can be extended to obtain a robust and efficient protocol for leader election and the fair use of the wireless channel.

Recently there has been an increasing interest in models of parallel computation that account for the bandwidth limitations in communication networks. Some models (e.g., bsp and logp) account for bandwidth limitations using a per-processor parameter g> 1, such that eachpro cessor can send/receive at most h messages in g h time. Other models (e.g., pram(m)) account for bandwidth limitations as an aggregate parameter m<p, such thatthe p processors can send at most m messages in total at each step. This paper provides the rst detailed study of the algorithmic implications of modeling parallel bandwidth as a per-processor (local) limitation versus an aggregate (global) limitation. We consider a number of basic problems

A communication network is called a radio network if its nodes exchange messages in the following restricted way. First, a send operation performed by a node delivers copies of the same message to all directly reachable nodes. Secondly, a node can successfully receive an incoming message only if exactly one of its neighbors sent a message in that step. It is this semantics of how ports at nodes send and receive messages that defines the networks rather than the fact that only radio waves are used as a medium of communication; but if that is the case then just a single frequency is used. We discuss algorithmic aspects of exchanging information in such networks, concentrating on distributed randomized protocols. Specific problems and solutions depend a lot on the topology of the underlying reachability graph and how much the nodes know about it. In single-hop networks each pair of nodes can communicate directly. This kind of networks is also known as the multiple access channel. Popular

We study contention-resolution protocols for multiple-access channels. We show that every backo protocol is transient if the arrival rate, , is at least 0.42 and that the capacity of every backo protocol is at most 0.42. Thus, we show that backo 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 acknowledgement-based protocol.

We consider broadcasting on the multiple-access channel when packets are injected continuously. Multiple-access channel is a synchronous system with the properties that a single transmission at a round delivers the message to all nodes, while multiple simultaneous transmissions result in a conflict which prevents delivering messages to any among the recipients. The traditional approach to dynamic broadcasting has been concerned with stability of protocols under suitable stochastic assumptions about injection rates. We study deterministic protocols competing against adversaries restricted by injection rate and burstiness of traffic. Stability means that the number of packets in queues is bounded by a constant in any execution, for a given number of stations, protocol, and adversary. Strong stability denotes the

Abstract. Various timing-based mutual exclusion algorithms have been proposed that guarantee mutual exclusion if certain timing assumptions hold. In this paper, we examine how these algorithms behave when the time for the basic operations is governed by probability distributions. In particular, we are concerned withhow often suchalgorithms succeed in allowing a processor to obtain a critical region and how this success rate depends on the random variables involved. We explore this question in the case where operation times are governed by exponential and gamma distributions, using both theoretical analysis and simulations.