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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 288 (23 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...
The Power of Two Random Choices: A Survey of Techniques and Results
 in Handbook of Randomized Computing
, 2000
"... ITo motivate this survey, we begin with a simple problem that demonstrates a powerful fundamental idea. Suppose that n balls are thrown into n bins, with each ball choosing a bin independently and uniformly at random. Then the maximum load, or the largest number of balls in any bin, is approximately ..."
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Cited by 139 (6 self)
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ITo motivate this survey, we begin with a simple problem that demonstrates a powerful fundamental idea. Suppose that n balls are thrown into n bins, with each ball choosing a bin independently and uniformly at random. Then the maximum load, or the largest number of balls in any bin, is approximately log n= log log n with high probability. Now suppose instead that the balls are placed sequentially, and each ball is placed in the least loaded of d 2 bins chosen independently and uniformly at random. Azar, Broder, Karlin, and Upfal showed that in this case, the maximum load is log log n= log d + (1) with high probability [ABKU99]. The important implication of this result is that even a small amount of choice can lead to drastically different results in load balancing. Indeed, having just two random choices (i.e.,...
On Choosing a Task Assignment Policy for a Distributed Server System
, 1999
"... We consider a distributed server system model and ask which policy should be used for assigning tasks to hosts. In our model each host processes tasks in FirstComeFirstServe order and the task's service demand is known in advance. We consider four task assignment policies commonly proposed f ..."
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Cited by 136 (21 self)
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We consider a distributed server system model and ask which policy should be used for assigning tasks to hosts. In our model each host processes tasks in FirstComeFirstServe order and the task's service demand is known in advance. We consider four task assignment policies commonly proposed for such distributed server systems: RoundRobin, Random, SizeBased, in which all tasks within a give size range are assigned to a particular host, and DynamicLeastWorkRemaining, in which a task is assigned to the host with the least outstanding work. Our goal is to understand the influence of task size variability on the decision of which task assignment policy is best. We evaluate the above policies using both analysis and simulation. We find that no one of the above task assignment policies is best and that the answer depends critically on the variability in the task size distribution. In particular we find that when the task sizes are not highly variable, the Dynamic policy is preferable. ...
How Useful Is Old Information
 IEEE Transactions on Parallel and Distributed Systems
, 2000
"... AbstractÐWe consider the problem of load balancing in dynamic distributed systems in cases where new incoming tasks can make use of old information. For example, consider a multiprocessor system where incoming tasks with exponentially distributed service requirements arrive as a Poisson process, the ..."
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Cited by 107 (9 self)
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AbstractÐWe consider the problem of load balancing in dynamic distributed systems in cases where new incoming tasks can make use of old information. For example, consider a multiprocessor system where incoming tasks with exponentially distributed service requirements arrive as a Poisson process, the tasks must choose a processor for service, and a task knows when making this choice the processor queue lengths from T seconds ago. What is a good strategy for choosing a processor in order for tasks to minimize their expected time in the system? Such models can also be used to describe settings where there is a transfer delay between the time a task enters a system and the time it reaches a processor for service. Our models are based on considering the behavior of limiting systems where the number of processors goes to infinity. The limiting systems can be shown to accurately describe the behavior of sufficiently large systems and simulations demonstrate that they are reasonably accurate even for systems with a small number of processors. Our studies of specific models demonstrate the importance of using randomness to break symmetry in these systems and yield important rules of thumb for system design. The most significant result is that only small amounts of queue length information can be extremely useful in these settings; for example, having incoming tasks choose the least loaded of two randomly chosen processors is extremely effective over a large range of possible system parameters. In contrast, using global information can actually degrade performance unless used carefully; for example, unlike most settings where the load information is current, having tasks go to the apparently least loaded server can significantly hurt performance. Index TermsÐLoad balancing, stale information, old information, queuing theory, large deviations. æ 1
Task Assignment with Unknown Duration
 Journal of the ACM
, 2000
"... We consider a distributed server system and ask which policy should be used for assigning jobs (tasks) to hosts. In our server, jobs are ot preemptible. Also, the job's service demand is ot known a priori. We are particularly concerned with the case where the workload is heavytailed, as is ..."
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Cited by 84 (16 self)
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We consider a distributed server system and ask which policy should be used for assigning jobs (tasks) to hosts. In our server, jobs are ot preemptible. Also, the job's service demand is ot known a priori. We are particularly concerned with the case where the workload is heavytailed, as is characteristic of many empirically measured computer workloads. We analyze several natural task assignment policies and propose a new one T/IGS (Task Assignment based on Guessing Size). The T/IGS algorithm is counterintuitive in many respects, including load mbalancing, omworkconserving, and faithless. We find that under heavytailed workloads, T/IGS can outperform all task assignment policies known to us by several orders of magnitude with respect to both mean response time and mean slowdown, provided the system load is not too high.
Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling, Queueing Systems 13
, 1993
"... We present an introductory review of recent work on the control of open queueing networks. We assume that customers ofdifferent types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through th ..."
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Cited by 62 (4 self)
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We present an introductory review of recent work on the control of open queueing networks. We assume that customers ofdifferent types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through the network is an ordered set of service stations: a customer queues for service at each station on its route and then leaves the system. The two methods of control we consider are the routing of customers through the network, and the sequencing of service at the stations, and our aim is to minimize the number of customers in the system. We concentrate especially on the insights which can be obtained from heavy traffic analysis, and in particular from Harrison's Brownian etwork models. Our main conclusion is that in many respects dynamic routing simplifies the behaviour of networks, and that under good control policies itmay well be possible to model the aggregate b haviour of a network quite straightforwardly.
Adaptive Scheduling of Master/Worker Applications on Distributed Computational Resources
, 2001
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Analysis of jointheshortestqueue routing for web server farms
 In PERFORMANCE 2007. IFIP WG 7.3 International Symposium on Computer Modeling, Measurement and Evaluation
, 2007
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A New Ordering for Stochastic Majorization: Theory and Applications
 Advances in Applied Probability
, 1991
"... In this paper, we develop a unified approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings defined in Marshall and Olkin, by defining a new ordering based on the set of functions that are symmetric, Lsubadditive and convex in each variable. This ..."
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Cited by 23 (7 self)
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In this paper, we develop a unified approach for stochastic load balancing on various multiserver systems. We expand the four partial orderings defined in Marshall and Olkin, by defining a new ordering based on the set of functions that are symmetric, Lsubadditive and convex in each variable. This new partial ordering is shown to be equivalent to the previous four orderings for comparing deterministic vectors but differ for random vectors. Sample path criteria and a probability enumeration method for the new stochastic ordering are established and the ordering is applied to various forkjoin queues, routing and scheduling problems. Our results generalize previous work and can be extended to multivariate stochastic majorization which includes tandem queues and queues with finite buffers. Keywords: load balancing, stochastic convexity, majorization ordering, routing, scheduling, forkjoin queues 0 1 Introduction Recently, stochastic comparison has received a great deal of attention. ...