Approximations in performance analysis of a controllable queueing system with heterogeneous servers

The paper studies a controllable multi-server heterogeneous queueing system where servers operate at different service rates without preemption, i.e., the service times are uninterrupted. The optimal control policy allocates the customers between the servers in such a way that the mean number of customers in the system reaches its minimal value. The Markov decision model and the policy-iteration algorithm are used to calculate the optimal allocation policy and corresponding mean performance characteristics. The optimal policy, when neglecting the weak influence of slow servers, is of threshold type defined as a sequence of threshold levels which specifies the queue lengths for the usage of any slower server. To avoid time-consuming calculations for systems with a large number of servers, we focus here on a heuristic evaluation of the optimal thresholds and compare this solution with the real values. We develop also the simple lower and upper bound methods based on approximation by an equivalent heterogeneous queueing system with a preemption to measure the mean number of customers in the system operating under the optimal policy. Finally, the simulation technique is used to provide sensitivity analysis of the heuristic solution to changes in the form of inter-arrival and service time distributions. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.

Авторы
Efrosinin D. 1, 2 , Stepanova N.3 , Sztrik J. 4 , Plank A.1
Журнал
Издательство
MDPI AG
Номер выпуска
10
Язык
Английский
Страницы
1-18
Статус
Опубликовано
Номер
1803
Том
8
Год
2020
Организации
  • 1 Insitute for Stochastics, Johannes Kepler University, 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 N17, Trapeznikov Institute of Control Sciences of RAS, Moscow, 117997, Russian Federation
  • 4 Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, Debrecen, 4032, Hungary
Ключевые слова
Decomposable semi-regenerative process; Heterogeneous servers; Markov decision process; Mean number of customers; Policy-iteration algorithm
Дата создания
02.11.2020
Дата изменения
02.11.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/64356/
Поделиться

Другие записи