Informatics and Applications
2020, Volume 14, Issue 2, pp 72-79
OPTIMIZATION OF THE CAPACITY OF THE MAIN STORAGE IN G/M/1/K QUEUEING SYSTEM WITH AN ADDITIONAL STORAGE DEVICE
Abstract
The problem of optimizing the capacity of the main storage device of a queuing system of the type G/M/l/K with an additional storage device with the cost objective function is formulated taking into account the costs of the system associated with the loss of requests, storage of requests, maintenance of storage devices, and device downtime. A request arriving to the system is accepted into the main storage device if there is a free space; otherwise, according to the given probability distribution, it goes to the additional device if there is a free space.
A request leaves the system (is lost) if both storage devices are full. If space is freed up in the main storage device, then one of the requests from the queue in the additional device immediately enters the queue in the main device.
The unimodality of the objective function is proved and the procedure for finding the optimal capacity of the main storage device is proposed.
[+] References (10)
- Bocharov, P.P., and A.V. Pechinkin. 1995. Teoriya massovogo obsluzhivaniya [Queueing theory]. Moscow: RUDN. 529 p.
- Ata, B., and S. Shneorson. 2006. Dynamic control of an M/M/1 service system with adjustable arrival and service rates. Manage. Sci. 52(11):1778-1791.
- Ghosh, A. P, and A. P. Weerasinghe. 2007. Optimal buffer size for a stochastic processing network in heavy traffic. Queueing Syst. 55(3):1572-9443.
- Ward, A., and S. Kumar. 2008. Asymptotically optimal admission control of a queue with impatient customers. Math. Oper. Res. 33(1):167-202.
- Kocaga, Y. L., and A. R. Ward. 2010. Admission control for a multi-server queue with abandonment. Queueing Syst. 65(3):275-323.
- Ghosh, A. P, and A. P. Weerasinghe. 2010. Optimal buffer size and dynamic rate control for a queueing system with impatient customers in heavy traffic. Stoch. Proc. Appl. 120(11):2103-2141.
- Agalarov, Ya. M., M. Ya. Agalarov, and V. S. Shorgin. 2016. Ob optimal'nom porogovom znachenii dliny ocheredi v odnoy zadache maksimizatsii dokhoda sistemy massovogo obsluzhivaniya tipa M/G/1 [About the optimal threshold of queue length in particular problem of profit maximization in M/G/1 queueing system]. Informatika i ee Primeneniya - Inform. Appl. 10(2):70-79.
- Atar, R., and A. Lev-Ari. 2018. Optimizing buffer size for the retrial queue: Two state space collapse results in heavy traffic. Queueing Syst. 90(3-4):225-255.
- Agalarov, Ya. M., and M.G. Konovalov. 2019. Dokazatel'stvo unimodal'nosti tselevoy funktsii v zadache porogovogo upravleniya nagruzkoy na server [Proof of the unimodality of the objective function in M/M/N queue with threshold-based congestion control]. Informatika i ee primeneniya - Inform. Appl. 13(2):2-6.
- 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 Applied and Industrial Mathematics] 26(1):65-66.
[+] About this article
Title
OPTIMIZATION OF THE CAPACITY OF THE MAIN STORAGE IN G/M/1/K QUEUEING SYSTEM WITH AN ADDITIONAL STORAGE DEVICE
Journal
Informatics and Applications
2020, Volume 14, Issue 2, pp 72-79
Cover Date
2020-06-30
DOI
10.14357/19922264200210
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queueing system; optimization; storage device; storage capacity
Authors
Ya. M. Agalarov 
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
|