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New Policy for Routing Jobs to Unobservable Parallel Queues with FIFO Scheduling

  • MATHEMATICAL MODELS AND COMPUTATIONAL METHODS
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Abstract

In this paper, we present the first results of an experimental study of a new dispatching strategy in unobservable queuing systems with parallel service. The main distinguishing feature of the considered system is the impossibility of observing its dynamic characteristics. A set of numerical examples covering various options for the input job stream, various length distributions of jobs, as well as a various number of heterogeneous servers is considered. All examples used the FIFO discipline. The new dispatching strategy was compared with the best algorithms known to the authors. In most examples, the new algorithm detects comparable (often better) values ​​of the mean and variance of the dwell time and requires significantly fewer parameters to be determined for its tuning.

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Notes

  1. Also sometimes referred to as job allocation strategies, routing strategies, or resource allocation strategies.

  2. Note that this assumption is essential when applying the obtained in voluntary computing systems, which are characterized by the unreliability of computing nodes. The demonstrated effectiveness of the proposed strategy implies that it is applied to a subset of nodes with at least high availability.

  3. In foreign literature—PAP (Probabilistic Allocation Policy) or RND (Random), or BS (Bernoulli Splitting). We recall that the RND strategy is described by set (p1, …, pN) of N numbers, i.e., probabilities pn of choice for the next job of server n.

  4. These are strategies parameterized by infinite sequences {a1, a2, …, ai – 1, ai, …}, where an means that the nth job is sent to server an. In this paper, the SG algorithm from [6, p. 184] is used to generate an.

  5. It was also shown in [1] that efficient strategies can be developed for other stationary characteristics (such as the average waiting time) using the same general considerations. For example, on EPS, the discipline of uniform (fair) processor sharing (see, for example, [7, p. 55] and [2]).

  6. This means that the performances of the servers do not differ too much from each other, i.e., there are no servers that are so fast that it is profitable to send all jobs to them.

  7. It may seem that the best c is also optimal for a system of parallel systems M/D/1 (see, for example, [8]). However, numerical experiments show that this is not the case. This is also additional evidence that the c value in the auxiliary process depends (in an unknown way) on the G distribution.

  8. Another simple solution, which, however, does not guarantee optimality, is pn = \({{{{{v}}^{{(n)}}}} \mathord{\left/ {\vphantom {{{{{v}}^{{(n)}}}} {\sum\nolimits_{i = 1}^N {{{{v}}^{{(i)}}}} }}} \right. \kern-0em} {\sum\nolimits_{i = 1}^N {{{{v}}^{{(i)}}}} }}\).

  9. It should be noted here that in the case of a multiprocessor system, this approach is no longer practically feasible.

  10.  For non-Markov systems close to optimal.

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Funding

This study was supported by the Russian Foundation for Basic Research, grant 18-07-00692.

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Authors and Affiliations

  1. Institute of Informatics Problems, FRC CSC RAS, 119333, Moscow, Russia

    M. G. Konovalov & R. V. Razumchik

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  1. M. G. Konovalov
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  2. R. V. Razumchik
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Correspondence to M. G. Konovalov or R. V. Razumchik.

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Translated by A. Ivanov

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Konovalov, M.G., Razumchik, R.V. New Policy for Routing Jobs to Unobservable Parallel Queues with FIFO Scheduling . J. Commun. Technol. Electron. 66, 737–744 (2021). https://doi.org/10.1134/S1064226921060176

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  • DOI: https://doi.org/10.1134/S1064226921060176

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