Abstract—Consideration is given to the dispatching problem in an almost nonobservable distributed processing system with M, M ≥ 2, single-server queues operating in parallel, each under the processor-sharing discipline. Jobs having the same job size distribution arrive one-by-one to the dispatcher, which immediately routes it to one of the queues. When making a routing decision, the dispatcher has no online information about the system (like current queues sizes, size of arriving job, etc.). The only information available to the dispatcher is job-size distribution, job-interarrival-time distribution, server speeds, time instants of previously arrived jobs, and previous routing decisions. Under these conditions, one is interested in the routing policies that minimize the job long-run mean response time. A new class of dispatching policies is proposed that, according to the numerical experiments, may significantly outperform all classical dispatching policies available for such system: (optimal) probabilistic policy and the round-robin policy.
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From the practical point of view, these systems find application in modeling systems of cloud computing, grid-systems, and volunteer computing systems.
That is, the dispatcher has no queue for storing incoming jobs which allows conducting deferred choice.
The solutions proposed in the paper are rather universal and allow constructing procedures for another optimality criteria, for instance, for the variance of response time and for the quantile of a prescribed level of response time.
As a main algorithm, we consider different algorithms well proven in observable systems of parallel processing of jobs.
For simplicity’s sake, we assume that a single stream of homogeneous jobs arrives in the system. However, there is no principal difficulty in applying the obtained results to the system with several input streams of heterogeneous jobs.
In the foreign literature, PAP (probabilistic allocation policy), RND (Random), or BS (Bernoulli Splitting).
This situation is related with the intuitive consideration that the input stream to each server is more regular (i.e., less random) in the deterministic strategy than in the probabilistic one, which may imply reduction in the mean response time.
Note that, for systems of servers with the FIFO policy, it is sometimes possible to construct such deterministic sequences that cannot be improved without using additional information about the system in dispatching. In these cases, they are apparently close to optimal (see details in [11–14]).
Perhaps, the most prominent variant of such strategy is the round robin (further, RR): nth arrived job is scheduled to the server with the number (n mod M) + 1.
Although the input stream to each server is more regular (less random) in the deterministic strategy, the cyclical strategy may lead to unlimited values of W (see, e.g., Table 2) even in weakly loaded systems. This is associated with the fact that the loading of one or several servers in this strategy becomes larger than unity.
At first glance, it is not clear if the account for additional information can lower the value W. There are intuitive suppositions about this, see [4, P. 61]. The numerical experiments, some results of which are presented in Sect. 4, justify them.
The prefix so- from English scant observation.
For an arbitrary recurrent input stream, for the RND strategy there is no analytical approach to compute the optimal values (p1, …, pM) (from the point of view of long-run mean response time), which are the probabilities pi that server i is selected for the next job. In this situation the probability pi was set equal to \({{{{{v}}^{{(i)}}}} \mathord{\left/ {\vphantom {{{{{v}}^{{(i)}}}} {\sum\limits_{j = 1}^M {{{{v}}^{{(j)}}}} }}} \right. \kern-0em} {\sum\limits_{j = 1}^M {{{{v}}^{{(j)}}}} }}\).
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Translated by E. Oborin
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Konovalov, M.G., Razumchik, R.V. Minimizing Mean Response Time in Nonobservable Distributed Processing Systems with Nodes Operating under Egalitarian Processor-Sharing Policy. J. Commun. Technol. Electron. 65, 677–689 (2020). https://doi.org/10.1134/S1064226920060182
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DOI: https://doi.org/10.1134/S1064226920060182