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 as...

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Autores principales:	Dmitry Efrosinin, Natalia Stepanova
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	parallel queues open-loop policy Markov decision process threshold policy matrix-analytic approach difference equations Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/aa1ec983460b441f87ea29df02b703dd
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spelling	oai:doaj.org-article:aa1ec983460b441f87ea29df02b703dd2021-11-11T18:18:32ZOptimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers10.3390/math92127662227-7390https://doaj.org/article/aa1ec983460b441f87ea29df02b703dd2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2766https://doaj.org/toc/2227-7390In 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 examples show interesting properties of the systems operating under the introduced policies and their performance characteristics.Dmitry EfrosininNatalia StepanovaMDPI AGarticleparallel queuesopen-loop policyMarkov decision processthreshold policymatrix-analytic approachdifference equationsMathematicsQA1-939ENMathematics, Vol 9, Iss 2766, p 2766 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	parallel queues open-loop policy Markov decision process threshold policy matrix-analytic approach difference equations Mathematics QA1-939
spellingShingle	parallel queues open-loop policy Markov decision process threshold policy matrix-analytic approach difference equations Mathematics QA1-939 Dmitry Efrosinin Natalia Stepanova Optimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers
description	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 examples show interesting properties of the systems operating under the introduced policies and their performance characteristics.
format	article
author	Dmitry Efrosinin Natalia Stepanova
author_facet	Dmitry Efrosinin Natalia Stepanova
author_sort	Dmitry Efrosinin
title	Optimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers
title_short	Optimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers
title_full	Optimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers
title_fullStr	Optimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers
title_full_unstemmed	Optimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers
title_sort	optimal open-loop routing and threshold-based allocation in two parallel queueing systems with heterogeneous servers
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/aa1ec983460b441f87ea29df02b703dd
work_keys_str_mv	AT dmitryefrosinin optimalopenlooproutingandthresholdbasedallocationintwoparallelqueueingsystemswithheterogeneousservers AT nataliastepanova optimalopenlooproutingandthresholdbasedallocationintwoparallelqueueingsystemswithheterogeneousservers
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Optimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers

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