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79
Adaptive Packet Routing for Bursty Adversarial Traffic
, 1998
"... One of the central tasks of networking is packetrouting when edge bandwidth is limited. Tremendous progress has been achieved by separating the issue of routing into two conceptual subproblems: path selection and congestion resolution along the selected paths. However, this conceptual separatio ..."
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Cited by 59 (7 self)
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One of the central tasks of networking is packetrouting when edge bandwidth is limited. Tremendous progress has been achieved by separating the issue of routing into two conceptual subproblems: path selection and congestion resolution along the selected paths. However, this conceptual separation has a serious drawback: each packet's path is fixed at the source and cannot be modified adaptively enroute. The problem is especially severe when packet injections are modeled by an adversary, whose goal is to cause "trafficjams".
Recursive Markov decision processes and recursive stochastic games
 In Proc. of 32nd Int. Coll. on Automata, Languages, and Programming (ICALP’05
, 2005
"... Abstract. We introduce Recursive Markov Decision Processes (RMDPs) and Recursive Simple Stochastic Games (RSSGs), and study the decidability and complexity of algorithms for their analysis and verification. These models extend Recursive Markov Chains (RMCs), introduced in [EY05a,EY05b] as a natural ..."
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Cited by 39 (10 self)
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Abstract. We introduce Recursive Markov Decision Processes (RMDPs) and Recursive Simple Stochastic Games (RSSGs), and study the decidability and complexity of algorithms for their analysis and verification. These models extend Recursive Markov Chains (RMCs), introduced in [EY05a,EY05b] as a natural model for verification of probabilistic procedural programs and related systems involving both recursion and probabilistic behavior. RMCs define a class of denumerable Markov chains with a rich theory generalizing that of stochastic contextfree grammars and multitype branching processes, and they are also intimately related to probabilistic pushdown systems. RMDPs & RSSGs extend RMCs with one controller or two adversarial players, respectively. Such extensions are useful for modeling nondeterministic and concurrent behavior, as well as modeling a system’s interactions with an environment. We provide a number of upper and lower bounds for deciding, given an RMDP (or RSSG) A and probability p, whether player 1 has a strategy to force termination at a desired exit with probability at least p. We also address “qualitative ” termination questions, where p = 1, and model checking questions. 1
Adversarial contention resolution for simple channels
 In: 17th Annual Symposium on Parallelism in Algorithms and Architectures
, 2005
"... This paper analyzes the worstcase performance of randomized backoff on simple multipleaccess 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 highprobability bounds. Rand ..."
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Cited by 36 (1 self)
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This paper analyzes the worstcase performance of randomized backoff on simple multipleaccess 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 highprobability bounds. Randomized binary exponential backoff has makespan Θ(nlgn), and more generally, for any constant r, rexponential backoff has makespan Θ(nlog lgr n). Quadratic backoff has makespan Θ((n/lg n) 3/2), and more generally, for r> 1, rpolynomial 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 loglogiterated 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 adversarialqueuing 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); loglogiterated 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 worstcase for exponential backoff and variants and that even small bursts can create instabilities in the channel.
Further improvements in competitive guarantees for QoS buffering
 In Proc. 31st International Colloquium on Automata, Languages, and Programming (ICALP
, 2004
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Statistical PerFlow Service Bounds in a Network with Aggregate Provisioning
 In Proceedings of IEEE Infocom 2003
, 2003
"... Scalability concerns of QoS implementations have stipulated service architectures where QoS is not provisioned separately to each flow, but instead to aggregates of flows. This paper determines stochastic bounds for the service experienced by a single flow when resources are managed for aggregates o ..."
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Cited by 23 (4 self)
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Scalability concerns of QoS implementations have stipulated service architectures where QoS is not provisioned separately to each flow, but instead to aggregates of flows. This paper determines stochastic bounds for the service experienced by a single flow when resources are managed for aggregates of flows and when the scheduling algorithms used in the network are not known. Using a recently developed statistical network calculus, perflow bounds can be calculated for backlog, delay, and the burstiness of output traffic.
Scheduling TimeConstrained Communication in Linear Networks
 IN PROC. 10TH ANN. ACM SYMP. ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 1998
"... We study the problem of centrally scheduling multiple messages in a linear network, when each message has both a release time and a deadline. We show that the problem of transmitting optimally many messages is NPhard, both when messages may be buffered in transit and when they may not be; for eithe ..."
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Cited by 23 (1 self)
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We study the problem of centrally scheduling multiple messages in a linear network, when each message has both a release time and a deadline. We show that the problem of transmitting optimally many messages is NPhard, both when messages may be buffered in transit and when they may not be; for either case, we present efficient algorithms that produce approximately optimal schedules. In particular, our bufferless scheduling algorithm achieves throughput that is within a factor of two of optimal. We show that buffering can improve throughput in general by a logarithmic factor (but no more), but that in several significant special cases, such as when all messages can be released immediately, buffering can help by only a small constant factor. Finally, we show how to convert our centralized, offline bufferless schedules to equally productive fully...
Dynamic Routing on Networks with FixedSize Buffers
 In Proc. of the 14th ann. ACMSIAM Symposium on Discrete Algorithms
, 2003
"... William Aiello Rafail Ostrovsky Eyal Kushilevitz Adi Ros'en Abstract The combination of the buffer size of routers deployed in the Internet and the Internet traffic itself leads routinely to routers dropping packets. Motivated by this, we initiate the rigorous study of dynamic storean ..."
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Cited by 22 (2 self)
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William Aiello Rafail Ostrovsky Eyal Kushilevitz Adi Ros'en Abstract The combination of the buffer size of routers deployed in the Internet and the Internet traffic itself leads routinely to routers dropping packets. Motivated by this, we initiate the rigorous study of dynamic storeand forward routing on arbitrary networks in a model in which dropped packets must explicitly be taken into account. To avoid the uncertainties of traffic modeling, we consider arbitrary traffic on the network. We analyze and compare the effectiveness of several greedy, online, localcontrol protocols using a competitive analysis of the throughput. One goal of our approach is for the competitive results to continue to hold as a network grows without requiring the memory in the nodes to increase with the size of the network. Thus, in our model, we have link buffers of fixed size, B, which is independent of the size of the network, and B becomes a parameter of the model.
A General Approach to Dynamic Packet Routing with Bounded Buffers
"... We prove a sufficient condition for the stability of dynamic packet routing algorithms. Our approach reduces the problem of steady state analysis to the easier and better understood question of static routing. We show that certain high probability and worst case bounds on the quasistatic (finite ..."
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Cited by 21 (2 self)
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We prove a sufficient condition for the stability of dynamic packet routing algorithms. Our approach reduces the problem of steady state analysis to the easier and better understood question of static routing. We show that certain high probability and worst case bounds on the quasistatic (finite past) performance of a routing algorithm imply bounds on the performance of the dynamic version of that algorithm. Our technique is particularly useful in analyzing routing on networks with bounded buffers where complicated dependencies make standard queuing techniques inapplicable. We present
Multihop local pooling for distributed throughput maximization in wireless networks
 in IEEE INFOCOM
, 2008
"... Abstract—Efficient operation of wireless networks requires distributed routing and scheduling algorithms that take into account interference constraints. Recently, a few algorithms for networks with primary or secondaryinterference constraints have been developed. Due to their distributed operatio ..."
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Cited by 19 (4 self)
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Abstract—Efficient operation of wireless networks requires distributed routing and scheduling algorithms that take into account interference constraints. Recently, a few algorithms for networks with primary or secondaryinterference constraints have been developed. Due to their distributed operation, these algorithms can achieve only a guaranteed fraction of the maximum possible throughput. It was also recently shown that if a set of conditions (known as Local Pooling) is satisfied, simple distributed scheduling algorithms achieve 100 % throughput. However, previous work conditions and on networks with singlehop interference or singlehop traffic. In this paper, we identify several graph classes that satisfy the Local Pooling conditions, thereby enabling the use of such graphs in network design algorithms. Then, we study the multihop implications of Local Pooling. We show that in many cases, as the interference degree increases, the Local Pooling conditions are more likely to hold. Consequently, although increased interference reduces the maximum achievable throughput of the network, it tends to enable distributed algorithms to achieve 100 % of this throughput. Regarding multihop traffic, we show that if the network satisfies only the singlehop Local Pooling conditions, distributed joint routing and scheduling algorithms are not guaranteed to achieve maximum throughput. Therefore, we present new conditions for Multihop Local Pooling, under which distributed algorithms achieve 100 % throughout. Finally, we identify network topologies in which the conditions hold and discuss the algorithmic implications of the results.
Adversarial queuing on the multipleaccess channel
 In Proc. of PODC ’06
, 2006
"... We consider broadcasting on the multipleaccess channel when packets are injected continuously. Multipleaccess 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 ..."
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Cited by 17 (8 self)
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We consider broadcasting on the multipleaccess channel when packets are injected continuously. Multipleaccess 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