Systems and Means of Informatics
2016, Volume 26, Issue 4, pp 74-88
PROFIT MAXIMIZATION IN G/M/1 QUEUING SYSTEM ON A SET OF THRESHOLD STRATEGIES WITH TWO SWITCH POINTS
- Ya. M. Agalarov
- M. Ya. Agalarov
- V. S. Shorgin
Abstract
The problem of maximizing the average profit per time in G/M/1 queuing system is considered on a set of stationary access restriction threshold strategies with one "switch point." The objective function depends on the following measures: service fee, hardware maintenance fee, cost of service delay, fine for unhandled requests, and fine for system idle. The authors have formulated the necessary conditions of existence of finite problem solution on a subset of threshold strategies with fixed distance between the upper and lower thresholds and have got necessary and sufficient conditions for optimality of threshold strategy on this subset. The authors have also developed a method of finding the optimal strategy and algorithm for calculating the parameters of the optimal strategy and the corresponding value of the objective function.
[+] References (17)
- Floyd, S., and V. Jacobson. 1993. Random early detection gateways for congestion avoidance. IEEE ACM Trans. Network. 1:397-413.
- Kabra, M., S. Saha, and B. Lin. 2006. Fast buffer memory with deterministic packet departures. 14th IEEE Symposium on High-Performance Interconnects Proceedings. Stanford, CA. 67-72.
- Zheng, B., and M. Atiquzzaman. 2008. A framework to determine the optimal weight parameter of RED in next-generation Internet routers. Int. J. Commun. Syst. 21:9871008.
- Reddy, T.B., A. Ahammed, and R. Banu. 2009. Performance comparison of active queue management techniques. Int. J. Computer Sci. Network Security 9(2):405-408.
- Lin, D., and R. Morris. 1997. Dynamics of random early detection. ACM SIGCOMM'97 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication Proceedings. ACM. 127-137.
- Feng, W.-C., K. G. Shin, D. D. Kandlur, and D. Saha. 2002. The BLUE active queue management algorithms. IEEE ACM Trans. Network. 10(4):513-528.
- Feng, W.-C., D. D. Kandlur, D. Saha, and K. G. Shin. 2001. Stochastic Fair Blue: A queue management algorithm for enforcing fairness. INFOCOM 2001. 20th Annual Joint Conference of the IEEE Computer and Communications Societies. IEEE. 3:1520-1529.
- Parris, M., K. Jeffay, and F.D. Smith. 1999. Lightweight active router-queue management for multimedia networking. Multimedia computing and networking. Eds.
D. D. Kandlur, K. Jeffay, and T. Roscoe. Proc. SPIE ser. San Jose, CA: SPIE. 3654:162-174. doi: 10.1117/12.333807.
- Pan, R., B. Prabhakar, and K. Psounis. 2000. CHOKe: A stateless active queue management scheme for approximating fair bandwidth allocation. INFOCOM 2000: 19th Annual Joint Conference of the IEEE Computer and Communications Societies Proceedings. Piscataway, NJ: IEEE. 2:942-951.
- Zhernovyj, Ju.V. 2010. Reshenie zadach optimal'nogo sinteza dlya nekotorykh markovskikh modeley obsluzhivaniya [Solution of optimum synthesis problem for some Markov models of service]. Informatsionnye Processy [Information Processses] 10(3):257-274.
- Konovalov, M. G. 2013. Ob odnoy zadache optimal'nogo upravleniya nagruzkoy na server [About one task of overload control]. Informatika i ee Primeneniya - Inform. Appl. 7(4):34-43.
- Agalarov, Ya. M. 2015. Porogovaya strategiya ogranicheniya dostupa k resursam v sisteme massovogo obsluzhivaniya M/D/1 s funktsiey shtrafov za nesvoevremennoe obsluzhivanie zayavok [The threshold strategy for restricting access in the M/D/1 queueing system with penalty function for late service]. Informatika i ee Primeneniya - Inform. Appl. 9(3):55-64.
- Grishunina, Yu.B. 2015. Optimal'noe upravlenie ochered'yu v sisteme M/G/1/то s vozmozhnost'yu ogranicheniya priema zayavok [Optimal control of queue in the M/G/1/то system with possibility of customer admission restriction]. Avtomatika
i Telemekhanika [Automation and Remote Control] 3:79-93.
- 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 queuing system]. Informatika i ee Primeneniya - Inform. Appl. 10(2):70-79.
- Karlin, S. 1968. A first course in stochastic processes. New York-London: Academic Press. 502 p.
- Bocharov, P. P., and A. V. Pechinkin. 1995. Teoriya massovogo obsluzhivaniya [Queueing theory]. Moscow: RUDN. 529 p.
- Agalarov, Ya. M., M. Ya. Agalarov, and V. S. Shorgin. Appendix to the paper "Profit maximization in G/M/1 queuing system on the set of threshold strategies with two switch points." Available at: http://www.ipiran.ru/publications/Pril_Agalarov.docx (accessed August 29, 2016).
[+] About this article
Title
PROFIT MAXIMIZATION IN G/M/1 QUEUING SYSTEM ON A SET OF THRESHOLD STRATEGIES WITH TWO SWITCH POINTS
Journal
Systems and Means of Informatics
Volume 26, Issue 4, pp 74-88
Cover Date
2016-11-30
DOI
10.14357/08696527160407
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queuing system; threshold strategy; optimization
Authors
Ya. M. Agalarov  , M. Ya. Agalarov  , and V. S. Shorgin
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science
and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
PromsvyazBank OJSC, 10 Smirnovskaya Str., Moscow 109052, Russian Federation
|