Transmission of messages using parallel servers: asymptotic approach

Vvedenskaya, N. D.

doi:10.1109/isit.1997.612947

Cited by 1 publication

(5 citation statements)

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“…A more complete analysis was given by Azar et al [4]. In the dynamic setting, this work was extended to a queuing theoretic model in [18], [19]; similar results were independently reported in [29].…”

Section: Related Previous Workmentioning

confidence: 63%

“…While the queuing process is random, however, these differential equations are deterministic, yielding a fixed trajectory once the initial conditions are given. In fact, these equations describe the limiting behavior of the process as n 3 I, as can be proven with standard (albeit complex) methods [8], [14], [19], [20], [22], [28], [29].…”

Section: Periodic Updatesmentioning

confidence: 94%

“…We often call this system the limiting system. This approach has successfully been applied previously to study load balancing problems in [1], [18], [19], [20], [22], [29] (see also [1] for more references or [21], [28] for the use of this approach in different settings), and it can be seen as a generalization of the previous Markov chain analysis. Using this technique, we examine several new models of load balancing in the presence of old information.…”

Section: Related Previous Workmentioning

confidence: 99%

“…The strategy of choosing a random server has several advantages: It is easy to implement, it has low overhead, it works naturally in a distributed setting, and it is known that the expected lengths of the queues remain finite over time. However, the strategy of choosing a small number of servers and queuing at the least loaded has been shown to perform significantly better in the case where the load information is up to date [6], [18], [19], [29]. It has also proven effective in other similar models [4], [11], [19].…”

Section: The Bulletin Board Modelmentioning

confidence: 99%

“…This corresponds to the exact behavior of the system as n 3 I. More information on this approach can be found in [8], [14], [18], [19], [20], [22], [28], [29]; we emphasize that here we will not detour into a theoretical justification for this limiting approach and, instead, refer the reader to these sources for more information. (We note, however, that this approach works only because the systems for finite n have an appropriate form as a Markov chain; indeed, we initially require exponential service times and Poisson arrivals to ensure this form.)…”

Section: The Bulletin Board Modelmentioning

confidence: 99%

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How useful is old information?

Mitzenmacher

2000

IEEE Trans. Parallel Distrib. Syst.

182

120

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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 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.

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