A dynamic distributed load balancing algorithm with provable good performance

Lüling, Reinhard; Monien, Burkhard

doi:10.1145/165231.165252

Cited by 48 publications

(21 citation statements)

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“…Several existing models [AA+93,LM93] underestimate available parallelism in link capacity by assuming that only one load unit can be transferred across a link at a time. This assumption overlooks a significant point.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Load Balancing by Random Matchings

Ghosh

Muthukrishnan

1996

Journal of Computer and System Sciences

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The fundamental problems in dynamic load balancing and job scheduling in parallel and distributed networks involve moving load between processors. In this paper we consider a new model for load movement in synchronous machines. In each step of our model, load can be moved across only a matching set of communication links but across each link any amount of load can be moved. We present an efficient local algorithm for the dynamic load balancing problem under our model of load movement. Our algorithm works on networks of arbitrary topology under possible failure of links. The running time of our algorithm is related to the eigenstructure of the underlying graph. We also present experimental results analyzing issues in load balancing related to our algorithms. ]

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Section: Introductionmentioning

confidence: 99%

Dynamic Load Balancing by Random Matchings

Ghosh

Muthukrishnan

1996

Journal of Computer and System Sciences

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“…They show that the expected load of any processor at any point of time is within a constant factor of the average load. In [LM93], Lüling and Monien use a similar work-generation model. They show that the expected load difference between any two processors is bounded by a constant factor.…”

Section: Known Resultsmentioning

confidence: 99%

The natural work-stealing algorithm is stable

Berenbrink

Friedetzky

2001

Proceedings 42nd IEEE Symposium on Foundations of Computer Science

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In this paper we analyse a very simple dynamic work-stealing algorithm. In the work-generation model, there are Ò generators which are arbitrarily distributed among a set of Ò processors. The distribution of generators is arbitrary -generators may even move at the beginning of each time step. During each time-step, each generator may generate a unit-time task which it inserts into the queue of its host processor. It generates such a task independently with probability . After the new tasks are generated, each processor removes one task from its queue and services it. Clearly, the work-generation model allows the load to grow more and more imbalanced, so, even when ½, the system load can be unbounded. The natural work-stealing algorithm that we analyse is widely used in practical applications and works as follows. During each time step, each empty processor (with no work to do) sends a request to a randomly selected other processor. Any non-empty processor having received at least one such request in turn decides (again randomly) in favour of one of the requests. The number of tasks which are transferred from the non-empty processor to the empty one is determined by the so-called work-stealing function . In particular, if a processor that accepts a request has tasks stored in its queue, then ´ µ tasks are transferred to the currently empty one. A popular work-stealing function is ´ µ ¾, which transfers (roughly) half of the tasks. We analyse the long-term behaviour of the system as a function of and . We show that the system is stable for any constant generation rate ½ and for a wide class of functions . Most intuitively sensible functions are included in this class (for example, every function ´ µ which is ´½µ as a function of is included). We give a quantitative description of the functions which lead to stable systems. Furthermore, we give upper bounds on the average system load (as a function of and Ò). Our proof techniques combine Lyapunov function arguments with domination arguments, which are needed to cope with dependency.

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“…In many applications it is possible that some of the existing tasks (balls) may be reassigned. As it turns out, the performance of many load balancing algorithms may be significantly improved if we allow reallocations of the balls (see, e.g., [5,24,39]). If the number of reallocations is not limited, it is trivial to maintain the ideally balanced load.…”

Section: Reassignmentsmentioning

confidence: 99%

“…It has been observed that the performance of many allocation processes may be significantly improved if the process can reassign some of the balls (see e.g., [5,24,39]). Notice that if the number of reallocations is not limited, it is trivial to maintain the ideally balanced load.…”

Section: Introductionmentioning

confidence: 99%

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Randomized allocation processes

Czumaj

Stemann

2001

Random Struct Algorithms

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Many dynamic resource allocation and on-line load balancing problems can be modeled by processes that sequentially allocate balls into bins. The balls arrive one by one and are to be placed into bins on-line without using a centralized controller. If n balls are sequentially placed into n bins by placing each ball in a randomly chosen bin, then it is widely known that the maximum load in bins is ln n/ ln ln n · 1 + o 1 with high probability. Azar, Broder, Karlin, and Upfal extended this scheme, so that each ball is placed sequentially into the least full of d randomly chosen bins. They showed that the maximum load of the bins reduces exponentially and is ln ln n/ ln d + 1 with high probability, provided d ≥ 2. In this paper we investigate various extensions of these schemes that arise in applications in dynamic resource allocation and on-line load balancing. Traditionally, the main aim of allocation processes is to place balls into bins to minimize the maximum load in bins. However, in many applications it is equally important to minimize the number of choices performed (the allocation time). We study adaptive allocation schemes that achieve optimal tradeoffs between the maximum load, the maximum allocation time, and the average allocation time. We also investigate allocation processes that may reallocate the balls. We provide a tight analysis of a natural class of processes that each time a ball is placed in one of d randomly chosen bins may move balls among these d bins arbitrarily. Finally, we provide a tight analysis of the maximum load of the off-line process in which each ball may be placed into one of d randomly chosen bins. We apply this result to competitive analysis of on-line load balancing processes.

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A dynamic distributed load balancing algorithm with provable good performance

Cited by 48 publications

References 1 publication

Dynamic Load Balancing by Random Matchings

Dynamic Load Balancing by Random Matchings

The natural work-stealing algorithm is stable

Randomized allocation processes

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