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62
Adversarial Queuing Theory
, 2001
"... We consider packet routing when packets are injected continuously into a network. We develop an adversarial theory of queuing aimed at addressing some of the restrictions inherent in probabilistic analysis and queuing theory based on timeinvariant stochastic generation. We examine the stability of ..."
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Cited by 93 (0 self)
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We consider packet routing when packets are injected continuously into a network. We develop an adversarial theory of queuing aimed at addressing some of the restrictions inherent in probabilistic analysis and queuing theory based on timeinvariant stochastic generation. We examine the stability of queuing networks and policies when the arrival process is adversarial, and provide some preliminary results in this direction. Our approach sheds light on various queuing policies in simple networks, and paves the way for a systematic study of queuing with few or no probabilistic assumptions.
Stability of Adaptive and NonAdaptive Packet Routing Policies in Adversarial Queueing Networks
 In Proc. of the 31st STOC
, 2000
"... We investigate stability of packet routing policies in adversarial queueing networks. We provide a simple classification of networks which are stable under any greedy scheduling policy  network is stable if and only if the underlying undirected connected graph contains at most two edges. We also ..."
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Cited by 45 (3 self)
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We investigate stability of packet routing policies in adversarial queueing networks. We provide a simple classification of networks which are stable under any greedy scheduling policy  network is stable if and only if the underlying undirected connected graph contains at most two edges. We also propose a simple and distributed policy which is stable in an arbitrary adversarial queueing network even for the critical value of the arrival rate r = 1. Finally, a simple and checkable network flow type load condition is formulated for adaptive adversarial queueing networks and a policy is proposed which achieves stability under this new load condition. This load condition is a relaxation of the integral network flow type condition considered previously in the literature.
UniversalStability Results and Performance Bounds for Greedy ContentionResolution Protocols
"... In this paper, we analyze the behavior of packetswitched 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 timeaveraged arriva ..."
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Cited by 44 (2 self)
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In this paper, we analyze the behavior of packetswitched 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 timeaveraged arrival rate of packets requiring the use of any edge is limited to be less than 1. This model can reflect the behavior of connectionoriented networks with transient connections (such as ATM networks) as well as connectionless networks (such as the Internet). We concentrate on
Simple Routing Strategies for Adversarial Systems
, 2001
"... In this paper we consider the problem of delivering dynamically changing input streams in dynamically changing networks where both the topology and the input streams can change in an unpredictable way. In particular, we present two simple distributed balancing algorithms (one for packet injections ..."
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Cited by 43 (4 self)
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In this paper we consider the problem of delivering dynamically changing input streams in dynamically changing networks where both the topology and the input streams can change in an unpredictable way. In particular, we present two simple distributed balancing algorithms (one for packet injections and one for flow injections) and show that for the case of a single receiver these algorithms will always ensure that the number of packets in the system is bounded at any time step, even for an injection process that completely saturates the capacities of the available edges, and even if the network topology changes in a completely unpredictable way. We also show that the maximum number of packets or flow that can be in the system at any time is best possible by providing an (essentially) matching lower bound that holds for any online algorithm, whether distributed or not. Interestingly, our balancing algorithms do not only behave well in a completely adversarial setting. We show that also in the other extreme of a static network and a static injection pattern the algorithms will converge to a point in which they achieve an average routing time that is close to the best possible average routing time that can be achieved by any strategy. This demonstrates that there are simple algorithms that can be efficient at the same time for very different communication scenarios. To have such algorithms will be of particular importance for communication in wireless mobile ad hoc networks (or short MANETs), in which at some time the connections between mobile nodes and/or the rates of input streams may change quickly and unpredictably and at some other time may be quasi static. Supported by DARPA grant F306020020550 "A Cost Benefit Approach to Fault Tolerant Communicati...
On Local Algorithms for Topology Control and Routing in Ad Hoc Networks
 In Proc. SPAA
, 2003
"... An ad hoc network is a collection of wireless mobile hosts forming a temporary network without the aid of any fixed infrastructure. Indeed, an important task of an ad hoc network is to determine an appropriate topology over which highlevel routing protocols are implemented. Furthermore, since the u ..."
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Cited by 35 (2 self)
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An ad hoc network is a collection of wireless mobile hosts forming a temporary network without the aid of any fixed infrastructure. Indeed, an important task of an ad hoc network is to determine an appropriate topology over which highlevel routing protocols are implemented. Furthermore, since the underlying topology may change with time, we need to design routing algorithms that effectively react to dynamically changing network conditions. This paper studies algorithms...
Instability of FIFO at Arbitrarily Low Rates in the Adversarial Queueing Model
 SIAM Journal on Computing
, 2002
"... We study the stability of the commonly used packet forwarding protocol, FIFO (First In First Out), in the adversarial queueing model. We prove that FIFO can become unstable, i.e., lead to unbounded bufferoccupancies and queueing delays, at arbitrarily low injection rates. In order to demonstrate in ..."
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Cited by 30 (0 self)
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We study the stability of the commonly used packet forwarding protocol, FIFO (First In First Out), in the adversarial queueing model. We prove that FIFO can become unstable, i.e., lead to unbounded bufferoccupancies and queueing delays, at arbitrarily low injection rates. In order to demonstrate instability at rate r, we use a network of size polynomial in 1=r.
Models and Techniques for Communication in Dynamic Networks Christian
 In Proc. of the 19th Symp. on Theoretical Aspects of Computer Science (STACS
, 2001
"... In this paper we will present various models and techniques for communication in dynamic networks. Dynamic networks are networks of dynamically changing bandwidth or topology. Situations in which dynamic networks occur are, for example: faulty networks (links go up and down), the Internet (the bandw ..."
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Cited by 23 (2 self)
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In this paper we will present various models and techniques for communication in dynamic networks. Dynamic networks are networks of dynamically changing bandwidth or topology. Situations in which dynamic networks occur are, for example: faulty networks (links go up and down), the Internet (the bandwidth of connections may vary), and wireless networks (mobile units move around). We investigate the problem of how to ensure connectivity, how to route, and how to perform admission control in these networks. Some of these problems have already been partly solved, but many problems are still wide open. The aim of this paper is to give an overview of recent results in this area, to identify some of the most interesting open problems and to suggest models and techniques that allow us to study them.
Stability of load balancing algorithms in dynamic adversarial systems
 In Proc. of the 34th ACM Symp. on Theory of Computing (STOC
, 2002
"... Abstract. In the dynamic load balancing problem, we seek to keep the job load roughly evenly distributed among the processors of a given network. The arrival and departure of jobs is modeled by an adversary restricted in its power. Muthukrishnan and Rajaraman (1998) gave a clean characterization of ..."
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Cited by 23 (2 self)
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Abstract. In the dynamic load balancing problem, we seek to keep the job load roughly evenly distributed among the processors of a given network. The arrival and departure of jobs is modeled by an adversary restricted in its power. Muthukrishnan and Rajaraman (1998) gave a clean characterization of a restriction on the adversary that can be considered the natural analogue of a cut condition. They proved that a simple local balancing algorithm proposed by Aiello et. al. (1993) is stable against such an adversary if the insertion rate is restricted to a (1 − ε) fraction of the cut size. They left as an open question whether the algorithm is stable at rate 1. In this paper, we resolve this question positively, by proving stability of the local algorithm at rate 1. Our proof techniques are very different from the ones used by Muthukrishnan and Rajaraman, and yield a simpler proof and tighter bounds on the difference in loads. In addition, we introduce a multicommodity version of this load balancing model, and show how to extend the result to the case of balancing two different kinds of loads at once (obtaining as a corollary a new proof of the 2commodity MaxFlow MinCut Theorem). We also show how to apply the proof techniques to the problem of routing packets in adversarial systems. Awerbuch et. al. (2001) showed that the same load balancing algorithm is stable against an adversary inserting
Source Routing and Scheduling in Packet Networks
, 2001
"... We study routing and scheduling in packetswitched networks. We assume an adversary that controls the injection time, source, and destination for each packet injected. A set of paths for these packets is admissible if no link in the network is overloaded. We present the first online routing algorit ..."
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Cited by 22 (5 self)
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We study routing and scheduling in packetswitched networks. We assume an adversary that controls the injection time, source, and destination for each packet injected. A set of paths for these packets is admissible if no link in the network is overloaded. We present the first online routing algorithm that finds a set of admissible paths whenever this is feasible. Our algorithm calculates a path for each packet as soon as it is injected at its source using a simple shortest path computation. The length of a link reflects its current congestion. We also show how our algorithm can be implemented under today's Internet routing paradigms.