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Randomized Protocols for LowCongestion Circuit Routing in Multistage Interconnection Networks
"... In this paper we study randomized algorithms for circuit switching on multistage networks related to the butterfly. We devise algorithms that route messages by constructing circuits (or paths) for the messages with small congestion, dilation, and setup time. Our algorithms are based on the idea of h ..."
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Cited by 14 (5 self)
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In this paper we study randomized algorithms for circuit switching on multistage networks related to the butterfly. We devise algorithms that route messages by constructing circuits (or paths) for the messages with small congestion, dilation, and setup time. Our algorithms are based on the idea of having each message choose a route from two possibilities, a technique that has previously proven successful in simpler load balancing settings. As an application of our techniques, we propose a novel design for a data server.
Recovery time of dynamic allocation processes
 IN PROCEEDINGS OF THE 10TH ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES, PUERTO VALLARTA, MEXICO, 28 JUNE–2
, 1998
"... Many distributed protocols arising in applications in online load balancing and dynamic resource allocation can be modeled by dynamic allocation processes related to the “balls into bin” problems. Traditionally the main focus of the research on dynamic allocation processes is on verifying whether a ..."
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Cited by 13 (3 self)
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Many distributed protocols arising in applications in online load balancing and dynamic resource allocation can be modeled by dynamic allocation processes related to the “balls into bin” problems. Traditionally the main focus of the research on dynamic allocation processes is on verifying whether a given process is stable, and if so, on analyzing its behavior in the limit (i.e., after sufficiently many steps). Once we know that the process is stable and we know its behavior in the limit, it is natural to analyze its recovery time, which is the time needed by the process to recover from any arbitrarily bad situation and to arrive very closely to a stable (i.e., a typical) state. This investigation is important to provide assurance that even if at some stage the process has reached a highly undesirable state, we can predict with high confidence its behavior after the estimated recovery time. In this paper we present a genera / framework to study the recovery time of discretetime dynamic allocation processes. We model allocation processes by suitably chosen ergodic Markov chains. For a given Markov chain we apply path coupling arguments to bound its convergence rates to the stationary distribution, which directly yields the estimation of the recovery time of the corresponding allocation process. Our coupling approach provides in a relatively simple way an accurate prediction of the recovery time. In particular, we show that our method can be applied to significantly improve estimations of the recovery time for various allocation processes related to allocations of balls into bins, and for the edge orientation problem studied before by Ajtai et al.
Reducing network congestion and blocking probability through balanced allocation
 in: Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science, FOCS
, 1999
"... We compare the performance of a variant of the standard Dynamic Alternative Routing (DAR) technique commonly used in telephone and ATM networks to a path selection algorithm that is based on the balanced allocations principle [4, 18] the Balanced Dynamic Alternative Routing (BDAR) algorithm. While ..."
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Cited by 12 (3 self)
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We compare the performance of a variant of the standard Dynamic Alternative Routing (DAR) technique commonly used in telephone and ATM networks to a path selection algorithm that is based on the balanced allocations principle [4, 18] the Balanced Dynamic Alternative Routing (BDAR) algorithm. While the standard technique checks alternative routes sequentially until available bandwidth is found, the BDAR algorithm compares and chooses the best among a small number of alternatives. We show that, at the expense of a minor increase in routing overhead, the BDAR gives a substantial improvement in network performance in terms of both network congestion and blocking probabilities. 1
Load Profiling for Efficient Route Selection in MultiClass Networks
 IN PROC. IEEE ICNP
, 1997
"... Highspeed networks, such as ATM networks, are expected to support diverse Quality of Service (QoS) constraints, including realtime QoS guarantees. Realtime QoS is required by many applications such as those that involvevoice and video communication. To support such services, routing algorithms ..."
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Cited by 11 (2 self)
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Highspeed networks, such as ATM networks, are expected to support diverse Quality of Service (QoS) constraints, including realtime QoS guarantees. Realtime QoS is required by many applications such as those that involvevoice and video communication. To support such services, routing algorithms that allow applications to reserve the needed bandwidth over a Virtual Circuit (VC) have been proposed. Commonly, these bandwidthreservation algorithms assign VCs to routes using the leastloaded concept, and thus result in balancing the load over the set of all candidate routes.
Averagecase analyses of first fit and random fit bin packing
 In Proc. Ninth Annual ACMSIAM Symposium on Discrete Algorithms
, 1998
"... ABSTRACT: We prove that the First Fit bin packing algorithm is stable under the input distribution U�k − 2�k � for all k ≥ 3, settling an open question from the recent survey by Coffman, Garey, and Johnson [“Approximation algorithms for bin backing: A survey, ” Approximation algorithms for NPhard p ..."
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Cited by 9 (2 self)
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ABSTRACT: We prove that the First Fit bin packing algorithm is stable under the input distribution U�k − 2�k � for all k ≥ 3, settling an open question from the recent survey by Coffman, Garey, and Johnson [“Approximation algorithms for bin backing: A survey, ” Approximation algorithms for NPhard problems, D. Hochbaum (Editor), PWS, Boston, 1996]. Our proof generalizes the multidimensional Markov chain analysis used by Kenyon, Sinclair, and Rabani to prove that Best Fit is also stable under these distributions [Proc Seventh Annual ACMSIAM Symposium on Discrete Algorithms, 1995, pp. 351–358]. Our proof is motivated by an analysis of Random Fit, a new simple packing algorithm related to First Fit, that is interesting in its own right. We show that Random Fit is stable under the input distributions U�k − 2�k�, as well as present worst case bounds and some results on distributions
Load Balancing in Arbitrary Network Topologies with Stochastic Adversarial Input
 SIAM Journal on Computing
, 2005
"... We study the longterm (steady state) performance of a simple, randomized, local load balancing technique under a broad range of input conditions. We assume a system of n processors connected by an arbitrary network topology. Jobs are placed in the processors by a deterministic or randomized adversa ..."
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Cited by 9 (2 self)
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We study the longterm (steady state) performance of a simple, randomized, local load balancing technique under a broad range of input conditions. We assume a system of n processors connected by an arbitrary network topology. Jobs are placed in the processors by a deterministic or randomized adversary. The adversary knows the current and past load distribution in the network and can use this information to place the new tasks in the processors. A node can execute one job per step, and can also participate in one load balancing operation in which it can move tasks to a direct neighbor in the network. In the protocol we analyze here, a node equalizes its load with a random neighbor in the graph.
Parallel Continuous Randomized Load Balancing (Extended Abstract)
 In Proceedings of the Tenth ACM Symposium on Parallel Algorithms and Architectures
, 1998
"... ) Petra Berenbrink Department of Mathematics and Computer Science Paderborn University, Germany Email: pebe@unipaderborn.de Tom Friedetzky and Ernst W. Mayr y Institut fur Informatik Technische Universitat Munchen, Germany Email: (friedetzmayr)@informatik.tumuenchen.de Abstract Recently, ..."
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Cited by 8 (2 self)
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) Petra Berenbrink Department of Mathematics and Computer Science Paderborn University, Germany Email: pebe@unipaderborn.de Tom Friedetzky and Ernst W. Mayr y Institut fur Informatik Technische Universitat Munchen, Germany Email: (friedetzmayr)@informatik.tumuenchen.de Abstract Recently, the subject of allocating tasks to servers has attracted much attention. There are several ways of distinguishing load balancing problems. There are sequential and parallel strategies, that is, placing the tasks one after the other or all of them in parallel. Another approach divides load balancing problems into continuous and static ones. In the continuous case new tasks are generated and consumed as time proceeds, in the second case the number of tasks is fixed. We present and analyze a parallel randomized continuous load balancing algorithm in a scenario where n processors continuously generate and consume tasks according to some given probability distribution. Each processor initiates l...
On the maximum queue length in the supermarket model
, 2004
"... There are n queues, each with a single server. Customers arrive in a Poisson process at rate λn, where0<λ<1. Upon arrival each customer selects d ≥ 2 servers uniformly at random, and joins the queue at a leastloaded server among those chosen. Service times are independent exponentially distributed r ..."
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Cited by 8 (2 self)
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There are n queues, each with a single server. Customers arrive in a Poisson process at rate λn, where0<λ<1. Upon arrival each customer selects d ≥ 2 servers uniformly at random, and joins the queue at a leastloaded server among those chosen. Service times are independent exponentially distributed random variables with mean 1. We show that the system is rapidly mixing, and then investigate the maximum length of a queue in the equilibrium distribution. We prove that with probability tending to 1 as n →∞the maximum queue length takes at most two values, which are ln ln n / ln d + O(1). 1. Introduction. We
Balanced Allocations: The Weighted Case
, 2008
"... We investigate ballsandbins processes where m weighted balls are placed into n bins using the “power of two choices ” paradigm, whereby a ball is inserted into the less loaded of two randomly chosen bins. The case where each of the m balls has unit weight had been studied extensively. In a seminal ..."
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Cited by 7 (2 self)
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We investigate ballsandbins processes where m weighted balls are placed into n bins using the “power of two choices ” paradigm, whereby a ball is inserted into the less loaded of two randomly chosen bins. The case where each of the m balls has unit weight had been studied extensively. In a seminal paper Azar et al. [2] showed that when m = n the most loaded bin has Θ(log log n) balls with high probability. Surprisingly, the gap in load between the heaviest bin and the average bin does not increase with m and was shown by Berenbrink et al. [4] to be Θ(log log n) with high probability for arbitrarily large m. We generalize this result to the weighted case where balls have weights drawn from an arbitrary weight distribution. We show that as long as the weight distribution has finite second moment and satisfies a mild technical condition, the gap between the weight of the heaviest bin and the weight of the average bin is independent of the number balls thrown. This is especially striking when considering heavy tailed distributions such as PowerLaw and LogNormal distributions. In these cases, as more balls are thrown, heavier and heavier weights are encountered. Nevertheless with high probability, the imbalance in the load distribution does not increase. Furthermore, if the fourth moment of the weight distribution is finite, the expected value of the gap is shown to be independent of the number of balls. 1 1
Load Profiling Based Routing for Guaranteed Bandwidth Flows
, 1999
"... . To support the stringent Quality of Service (QoS) requirements of realtime (e.g. audio/video) applications in integrated services networks, several routing algorithms that allow for the reservation of the needed bandwidth over a Virtual Circuit (VC), established on one of several candidate routes ..."
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Cited by 6 (0 self)
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. To support the stringent Quality of Service (QoS) requirements of realtime (e.g. audio/video) applications in integrated services networks, several routing algorithms that allow for the reservation of the needed bandwidth over a Virtual Circuit (VC), established on one of several candidate routes, have been proposed. Traditionally, such routing is done using the leastloaded concept, and thus results in balancing the load across the set of candidate routes. In this paper, we propose the use of load profiling as an attractive alternative to load balancing for routing guaranteed bandwidth VCs (flows). Load profiling techniques allow the distribution of "available" bandwidth across a set of candidate routes to match the characteristics of incoming VC QoS requests. We thoroughly characterize the performance of VC routing using load profiling and contrast it to routing using load balancing and load packing. We do so both analytically and via extensive simulations of multiclass traffic r...