Optimal open-loop routing and threshold-based allocation in two parallel queueing systems with heterogeneous servers

In this paper, we study the problem of optimal routing for the pair of two-server heterogeneous queues operating in parallel and subsequent optimal allocation of customers between the servers in each queue. Heterogeneity implies different servers in terms of speed of service. An open-loop control assumes the static resource allocation when a router has no information about the state of the system. We discuss here the algorithm to calculate the optimal routing policy based on specially constructed Markov-modulated Poisson processes. As an alternative static policy, we consider an optimal Bernoulli splitting which prescribes the optimal allocation probabilities. Then, we show that the optimal allocation policy between the servers within each queue is of threshold type with threshold levels depending on the queue length and phase of an arrival process. This dependence can be neglected by using a heuristic threshold policy. A number of illustrative exam-ples show interesting properties of the systems operating under the introduced policies and their performance characteristics. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Authors
Efrosinin D. 1, 2 , Stepanova N.3
Journal
Publisher
MDPI AG
Number of issue
21
Language
English
Status
Published
Number
2766
Volume
9
Year
2021
Organizations
  • 1 Institute for Stochastics, Johannes Kepler University Linz, Linz, 4040, Austria
  • 2 Department of Information Technologies, Faculty of Mathematics and Natural Sciences, Peoples’ Friendship, University of Russia (RUDN University), Moscow, 117198, Russian Federation
  • 3 Laboratory 17, V.A. Trapeznikov Institute of Control Sciences of RAS, Moscow, 117997, Russian Federation
Keywords
Difference equations; Markov decision process; Matrix-analytic approach; Open-loop policy; Parallel queues; Threshold policy
Date of creation
16.12.2021
Date of change
16.12.2021
Short link
https://repository.rudn.ru/en/records/article/record/76528/
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