Informatics and Applications
2014, Volume 8, Issue 3, pp 28-38STATIONARY DISTRIBUTION IN A QUEUEING SYSTEM WITH INVERSE SERVICE ORDER AND GENERALIZED PROBABILISTIC PRIORITY
- L. A. Meykhanadzhyan
- T. A. Milovanova
- A. V. Pechinkin
- R. V. Razumchik
Abstract
Consideration is given to M|G|1 type queueing system. Inverse service order with generalized probabilistic priority is implemented in the system. It is assumed that at any instant, the remaining service time of each customer residing in the system is known. Upon arrival of a new customer, the system finds out its service time and compares it with the remaining service time of the currently served customer. The result of this comparison leads to one of the cases: one of them enters the server and another occupies the first place in the queue; one of them leaves the system and another enters the server; or both leave the system. In each case when customer remains in the system, its remaining service time may be updated. An analytical method that allows computing stationary performance characteristics related to the number of customers in the system is presented. Numerical examples based on the developed mathematical relations are provided.[+] References (12)
- Schrage, L. 1968. A proof of the optimality of the shortest remaining processing time discipline. Oper. Res. 16:687- 690.
- Nagonenko, V. A. 1981. O kharakteristikakh odnoy ne- standartnoy sistemy massovogo obsluzhivaniya [On the characteristics of one nonstandard queuing system]. I, II. Izv. ANSSSR. Tekhnich. kibernet. [Technical Cybernetics] 1:187-195; 3:91-99.
- Nagonenko, V. A., andA.V. Pechinkin. 1982. Obol'shoy zagruzke v sisteme s inversionnym obsluzhivaniem i vero- yatnostnym prioritetom [On high load in the system with an inversion procedure service and probabilistic priority]. Izv. AN SSSR. Tekhnich. kibernet. [Technical Cybernetics] (1):86-94.
- Pechinkin, A.V. 1983. Ob odnoy invariantnoy sisteme massovogo obsluzhivaniya [On an invariant queuing system]. Math. Operationsforsch. und Statist. Ser. Optimization 14(3):433-444.
- Nagonenko, V. A., and A.V Pechinkin. 1984. O ma- loy zagruzke v sisteme s inversionnym poryadkom ob- sluzhivaniya i veroyatnostnym prioritetom [On low load in the system with an inversion procedure service and probabilistic priority]. Izv. AN SSSR. Tekhnich. kibernet [Technical Cybernetics] (6):82-89.
- Pechinkin, A. V., and I. V. Stalchenko. 2010. Sistema MAP/G/1/infinity s inversionnym poryadkom obsluzhivaniya i veroyatnostnym prioritetom, funktsioniruyushchaya v diskretnom vremeni [The MAP/G/1/infinity discrete-time queueing system with inversive service order and probabilistic priority]. Vestnik Rossiyskogo Un-ta druzhby narodov. Ser. Matematika. Informatika. Fizika. [Bulletin of Peoples' Friendship University of Russia. Ser. Mathematics. Information Sciences. Physics] (2):26-36.
- Cascone, A., R. Manzo, A.V. Pechinkin, and S. Salerno. 2010. Sistema MAP/G/1/infinity v diskretnom vremeni s inversionnoy veroyatnostnoy distsiplinoy obsluzhivaniya [Discrete-time MAP/G/1/infinity system with inversive probabilistic servicing discipline]. Avtomat. i Telemekh. [Automation Remote Control] (12):57-69.
- Milovanova, T.A,, and A.V. Pechinkin. 2013. Statsio- narnye kharakteristiki sistemy obsluzhivaniya s inversion- nym poryadkom obsluzhivaniya, veroyatnostnym prior- itetom i gisterezisnoy politikoy [Stationary characteristics of queueing system with an inversion procedure service Contributors probabilistic priority and hysteresis policy] Informatika i ee Primeneniya - Inform. Appl. 7(1):22-35.
- Bocharov, P.P., and A.V. Pechinkin. 1995. Teoriya massovogo obsluzhivaniya [Queueing theory]. Moscow: RUDN. 529 p.
- Jerri, A. 1999. Introduction to integral equations with appli-cations. John Wiley & Sons. 433 p.
- Press, WH., S. A. Teukolsky, W.T. Vetterling, and B. P. Flannery. 2007. Numerical recipes: The art of scientific computing. 3rded. New York: Cambridge University Press. 1235 p.
- Polyanin, A. D., and A. V. Manzhirov. 2008. Handbook of integral equations. 2nd ed. Boca Raton - London: Chapman & Hall/ CRC Press. 1144 p.
[+] About this article
Title
STATIONARY DISTRIBUTION IN A QUEUEING SYSTEM WITH INVERSE SERVICE ORDER AND GENERALIZED PROBABILISTIC PRIORITYJournal
Informatics and Applications2014, Volume 8, Issue 3, pp 28-38
Cover Date
2014-03-31DOI
10.14357/19922264140304Print ISSN
1992-2264Publisher
Institute of Informatics Problems, Russian Academy of SciencesAdditional Links
Key words
queueing system; special discipline; LIFO; probabilistic priority; general service timeAuthors
L. A. Meykhanadzhyan
, T. A. Milovanova,
A. V. Pechinkin
, and R. V. Razumchik,
Author Affiliations
Peoples' Friendship University of Russia, 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
Institute of Informatics Problems, Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian
Federation