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13
The Power of Two Choices in Randomized Load Balancing
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 1996
"... Suppose that n balls are placed into n bins, each ball being placed into a bin chosen independently and uniformly at random. Then, with high probability, the maximum load in any bin is approximately log n log log n . Suppose instead that each ball is placed sequentially into the least full of d ..."
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Cited by 208 (22 self)
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Suppose that n balls are placed into n bins, each ball being placed into a bin chosen independently and uniformly at random. Then, with high probability, the maximum load in any bin is approximately log n log log n . Suppose instead that each ball is placed sequentially into the least full of d bins chosen independently and uniformly at random. It has recently been shown that the maximum load is then only log log n log d +O(1) with high probability. Thus giving each ball two choices instead of just one leads to an exponential improvement in the maximum load. This result demonstrates the power of two choices, and it has several applications to load balancing in distributed systems. In this thesis, we expand upon this result by examining related models and by developing techniques for stu...
Parallel Randomized Load Balancing
 In Symposium on Theory of Computing. ACM
, 1995
"... It is well known that after placing n balls independently and uniformly at random into n bins, the fullest bin holds \Theta(log n= log log n) balls with high probability. Recently, Azar et al. analyzed the following: randomly choose d bins for each ball, and then sequentially place each ball in the ..."
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Cited by 57 (8 self)
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It is well known that after placing n balls independently and uniformly at random into n bins, the fullest bin holds \Theta(log n= log log n) balls with high probability. Recently, Azar et al. analyzed the following: randomly choose d bins for each ball, and then sequentially place each ball in the least full of its chosen bins [2]. They show that the fullest bin contains only log log n= log d + \Theta(1) balls with high probability. We explore extensions of this result to parallel and distributed settings. Our results focus on the tradeoff between the amount of communication and the final load. Given r rounds of communication, we provide lower bounds on the maximum load of \Omega\Gamma r p log n= log log n) for a wide class of strategies. Our results extend to the case where the number of rounds is allowed to grow with n. We then demonstrate parallelizations of the sequential strategy presented in Azar et al. that achieve loads within a constant factor of the lower bound for two ...
On the Analysis of Randomized Load Balancing Schemes
 IN PROCEEDINGS OF THE 9TH ANNUAL ACM SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 1998
"... It is well known that simple randomized load balancing schemes can balance load effectively while incurring only a small overhead, making such schemes appealing for practical systems. In this paper, we provide new analyses for several such dynamic randomized load balancing schemes. Our work extends ..."
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Cited by 56 (7 self)
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It is well known that simple randomized load balancing schemes can balance load effectively while incurring only a small overhead, making such schemes appealing for practical systems. In this paper, we provide new analyses for several such dynamic randomized load balancing schemes. Our work extends a previous analysis of the supermarket model, a model that abstracts a simple, efficient load balancing scheme in the setting where jobs arrive at a large system of parallel processors. In this model, customers arrive at a system of n servers as a Poisson stream of rate #n, # < 1, with service requirements exponentially distributed with mean 1. Each customer chooses d servers independently and uniformly at random from the n servers, and is served according to the First In First Out (FIFO) protocol at the choice with the fewest customers. For the supermarket model, it has been shown that using d = 2 choices yields an exponential improvement in the expected time a customer spends in the syst...
The natural workstealing algorithm is stable
 In Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science (FOCS
, 2001
"... In this paper we analyse a very simple dynamic workstealing algorithm. In the workgeneration model, there are n (work) generators. A generatorallocation function is simply a function from the n generators to the n processors. We consider a fixed, but arbitrary, distribution D over generatoralloca ..."
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Cited by 28 (1 self)
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In this paper we analyse a very simple dynamic workstealing algorithm. In the workgeneration model, there are n (work) generators. A generatorallocation function is simply a function from the n generators to the n processors. We consider a fixed, but arbitrary, distribution D over generatorallocation functions. During each timestep of our process, a generatorallocation function h is chosen from D, and the generators are allocated to the processors according to h. Each generator may then generate a unittime task which it inserts into the queue of its host processor. It generates such a task independently with probability λ. After the new tasks are generated, each processor removes one task from its queue and services it. For many choices of D, the workgeneration model allows the load to become arbitrarily imbalanced, even when λ < 1. For example, D could be the point distribution containing a single function h which allocates all of the generators to just one processor. For this choice of D, the chosen processor receives around λn units of work at each step and services one. The natural workstealing algorithm that we analyse is widely used in practical applications and works as follows. During each time step, each empty
On Balls and Bins with Deletions
 In Proc. of the RANDOM'98
, 1998
"... Microsystems. The views and conclusions contained here are those of the authors and should not be interpreted as necessarily representing the official policies or ..."
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Cited by 20 (1 self)
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Microsystems. The views and conclusions contained here are those of the authors and should not be interpreted as necessarily representing the official policies or
Allocating Weighted Jobs in Parallel
, 1997
"... It is well known that after placing m n balls independently and uniformly at random (i.u.r.) into n bins, the fullest bin contains \Theta(log n= log log n+ m n ) balls, with high probability. It is also known (see [Ste96]) that a maximum load of O \Gamma m n \Delta can be obtained for all m n ..."
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Cited by 15 (4 self)
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It is well known that after placing m n balls independently and uniformly at random (i.u.r.) into n bins, the fullest bin contains \Theta(log n= log log n+ m n ) balls, with high probability. It is also known (see [Ste96]) that a maximum load of O \Gamma m n \Delta can be obtained for all m n if a ball is allocated in one (suitably chosen) of two (i.u.r.) bins. Stemann ([Ste96]) shows that r communication rounds suffice to guarantee a maximum load of maxf r p log n; O \Gamma m n \Delta g, with high probability. Adler et al. have shown in [ACMR95] that Stemanns protocol is optimal for constant r. In this paper we extend the above results in two directions: We generalize the lower bound to arbitrary r log log n. This implies that the result of Stemanns protocol is optimal for all r. Our main result is a generalization of Stemanns upper bound to weighted jobs: Let W A (W M ) denote the average (maximum) weight of the balls. Further let \Delta = W A =W M . Note that...
SIMLAB  A Simulation Environment for Storage Area Networks
 In Workshop on Parallel and Distributed Processing (PDP
, 2001
"... In this paper, we present a simulation environment for storage area networks called SIMLAB. SIMLAB is a part of the PRESTO project, which is a joint project of the Electrical Engineering Department and the Computer Science Department of the Paderborn University. The aim of the PRESTO project is to c ..."
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Cited by 5 (1 self)
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In this paper, we present a simulation environment for storage area networks called SIMLAB. SIMLAB is a part of the PRESTO project, which is a joint project of the Electrical Engineering Department and the Computer Science Department of the Paderborn University. The aim of the PRESTO project is to construct a scalable and resourceefficient storage network that can support the realtime delivery of data. SIMLAB has been implemented to aid the development and verification of distributed algorithms for this storage network. However, it has been designed in such a way that it can also be used for the simulation of many other types of networking problems. SIMLAB is based on C++ and common libraries and input/output formats, which ensures that SIMLAB can be used on many different platforms. We therefore expect SIMLAB to be useful also for other people working on similar problems. 1 Introduction In the last couple of years, a dramatic increase in the need of storing huge amounts of data can...
Design of the PRESTO Multimedia Storage Network
, 1999
"... In this paper, we present concepts and simulation results for the design of the Paderborn realtime storage network, short PRESTO, which is currently developed at the Paderborn University in a joint project of the Electrical Engineering Department and the Computer Science Department. In this proj ..."
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Cited by 2 (0 self)
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In this paper, we present concepts and simulation results for the design of the Paderborn realtime storage network, short PRESTO, which is currently developed at the Paderborn University in a joint project of the Electrical Engineering Department and the Computer Science Department. In this project, we aim at constructing a scalable and faulttolerant storage network that manages a set of parallel disks in a resource ecient way and that can support the realtime delivery of data. We discuss in this paper the principal concepts of the PRESTO storage network, concentrating on data placement and load balancing strategies. Furthermore, we present simulation results that demonstrate that our techniques achieve a high disk utilization together with a low latency with a very high degree of reliability.
Simple Competitive Request Scheduling Strategies
 in 11th ACM Symposium on Parallel Architectures and Algorithms
, 1999
"... In this paper we study the problem of scheduling realtime requests in distributed data servers. We assume the time to be divided into time steps of equal length called rounds. During every round a set of requests arrives at the system, and every resource is able to fulfill one request per round. Ev ..."
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Cited by 2 (0 self)
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In this paper we study the problem of scheduling realtime requests in distributed data servers. We assume the time to be divided into time steps of equal length called rounds. During every round a set of requests arrives at the system, and every resource is able to fulfill one request per round. Every request specifies two (distinct) resources and requires to get access to one of them. Furthermore, every request has a deadline of d, i.e. a request that arrives in round t has to be fulfilled during round t +d 1 at the latest. The number of requests which arrive during some round and the two alternative resources of every request are selected by an adversary. The goal is to maximize the number of requests that are fulfilled before their deadlines expire. We examine the scheduling problem in an online setting, i.e. new requests continuously arrive at the system, and we have to determine online an assignment of the requests to the resources in such a way that every resource has to fulfil...
Simplified witness tree arguments
 PROCEEDINGS OF THE 27TH ANNUAL CONFERENCE ON CURRENT TRENDS IN THEORY AND PRACTICE OF INFORMATICS, IN: LNCS
, 2000
"... In this paper we survey some results concerning ballsintobinsgames and the power of two choices. We present a unified and rather elementary analysis for models in the parallel as well as in the sequential setting which is based on witness trees. ..."
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Cited by 1 (0 self)
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In this paper we survey some results concerning ballsintobinsgames and the power of two choices. We present a unified and rather elementary analysis for models in the parallel as well as in the sequential setting which is based on witness trees.