Informatics and Applications
2023, Volume 17, Issue 1, pp 89-95
OPTIMIZATION OF A QUEUE-LENGTH DEPENDENT ADDITIONAL SERVER IN THE MULTISERVER QUEUE
Abstract
The problem of optimal control of an additional server in a stationary G/M/s queue is considered.
The additional server can be turned on and off at instants when the queue length is changed. It is formulated as the nonlinear optimization problem, in which the objective function accounts for amounts for service, losses due to the waiting of customers, maintenance, and downtime of the additional server. The functioning of the system is described as a controlled Markov chain. Only stationary control policies are considered. For Poisson arrivals, necessary and sufficient conditions are given for the existence of the optimal decision point (threshold) and it is proved that the objective function is unimodal. A simple algorithm for the computation of the threshold is provided.
[+] References (8)
- Gortsev, A. M. 1978. A queueing system with an arbitrary number of stand-by channels and hysteresis control of their connection and disconnection. Automat. Rem. Contr. 38(10):1451-1457.
- Krylova, D. S., N. I. Golovko, andT. A. Zhuk. 2017. Analiz SMO s rezervnym priborom i skachkoobraznoy intensivnost'yu vkhodnogo potoka [Analysis of SMObackup device and the abrupt intensity of the input stream]. Vestnik VGU. Ser. Fizika. Matematika [Proceedings of Voronezh State University. Ser. Physics. Mathematics] 4:109-123.
- Klimenok, V. I. 2019. Mnogolineynaya sistema massovogo obsluzhivaniya s rezervnymi priborami [Multi-server queueing system with reserve servers]. J. Belarusian State University. Mathematics Informatics 3:57-70.
- Dudin, A. N. 1981. On optimal control of a multi-rate service system. Automat. Rem. Contr. 41(9):1221-1228.
- Samochernova, E. S., and L. I. Petrov. 2010. Optimizatsiya sistemy massovogo obsluzhivaniya s odnotipnym rezervnym priborom [Optimization of the queuing system with the same type of backup device]. Bulletin Tomsk Polytechnic University 317(5):28-31.
- Agalarov, Ya. M. 2022. Optimizatsiya porogovogo upravleniya pereklyucheniem skorosti obsluzhivaniya v sisteme massovogo obsluzhivaniya G/M/l [Optimization of the threshold service speed control in the G/M/l queue].
Informatika i ee Primeneniya - Inform. Appl. 16(1): 73-81.
- Agalarov Ya. M. 2022. Optimal'noe upravlenie podklyucheniem rezervnogo pribora v sisteme massovogo obsluzhivaniya G/M/l [Optimal control of a queue-length dependent additional server in GI/M/l queue]. Informatika i ee Primeneniya - Inform. Appl. 16(4):34-41.
- Agalarov, Ya. M. 2019. Priznak unimodal'nosti tselochislennoy funktsii odnoy peremennoy [A sign of unimodality of an integer function of one variable]. Obozrenie prikladnoy i promyshlennoy matematiki [Surveys on Applied and Industrial Mathematics] 26(1):65-66.
[+] About this article
Title
OPTIMIZATION OF A QUEUE-LENGTH DEPENDENT ADDITIONAL SERVER IN THE MULTISERVER QUEUE
Journal
Informatics and Applications
2023, Volume 17, Issue 1, pp 89-95
Cover Date
2023-04-10
DOI
10.14357/19922264230112
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
multiserver queuing system; optimization; additional server
Authors
Ya. M. Agalarov 
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
|