Informatics and Applications
2016, Volume 10, Issue 2, pp 123-131
STATIONARY CHARACTERISTICS OF THE FINITE CAPACITY QUEUEING SYSTEM WITH INVERSE SERVICE ORDER AND GENERALIZED PROBABILISTIC PRIORITY
Abstract
Consideration is given to the M/G/1/(r - 1) queueing system with LIFO (last in, first out) preemptive generalized probabilistic priority policy. It is assumed that customer's service time becomes known upon its arrival at the system and at any time instant remaining service times of all customers present in the system are available. On arrival of a customer at a nonempty system, its service time is compared to the (remaining) service time of the customer in service and one of the following events occurs: both customers leave the system at once, one of the customers leaves the system (the other occupies the server), or both customers stay in the system (one occupies the server, the other - one place in the queue). Those customers which stay in the system acquire new service time according to a known distribution, which can depend on their initial service times. Arriving customers which find the queue full, leave the system and have no influence on it. Analytical expressions forthe computation of the joint stationary distribution of the number of customers in the system and the remaining service time of the customer in the server, of the busy period and the stationary sojourn time (in terms of Laplace-Stieltjes transform) are proposed.
[+] References (8)
- Meykhanadzhyan, L. A., T. A. Milovanova, A. V. Pechinkin, and R. V. Razumchik. 2014. Statsionarnye veroyatnosti so- stoyaniy v sisteme obsluzhivaniya s inversionnym poryad- kom obsluzhivaniya i obobshchennym veroyatnostnym pri- oritetom [Stationary distribution in a queueing system with inverse service order and generalized probabilistic priority]. Informatika i ee Primeneniya - Inform.Appl. 8(3):16-26.
- Meykhanadzhyan, L.A., TA. Milovanova, and R. V. Ra- zumchik. 2015. Vremya ozhidaniya v sisteme obslu- zhivaniya s inversionnym poryadkom obsluzhivaniya
i obobshchennym veroyatnostnym prioritetom [Stationary waiting time in a queueing system with inverse service order and generalized probabilistic priority]. Informatika i ee Primeneniya - Inform.Appl. 9(2):14-22.
- Sevastyanov, B. A. 1957. Ergodicheskaya teorema dlya markovskikh protsessov i ee prilozhenie k telefonnym sis- temam s otkazami [An ergodic theorem for markov processes and its application to telephone systems with refusals].
Teor. Veroyatnost. i Primenen. [Probability Theory and Its Applications] 2(1):106-116.
- Bocharov, P P, and A. V. Pechinkin. 1995. Teoriya massovo- go obsluzhivaniya [Queueing theory]. Moscow: RUDN. 529 p.
- Meykhanadzhyan, L., and R. Razumchik. 2016. New scheduling policy for estimation of stationary performance characteristics in single server queues with inaccurate job size information. 30th European Conference on Modelling and Simulation Proceedings. Dudweiler, Germany: Digital- druck Pirrot GmbHP 710-716.
- Jerri, A. 1999. Introduction to integral equations with appli-cations. New York, NY: John Wiley & Sons. 272 p.
- Press, W. H., S. A. Teukolsky, W. T Vetterling, and
B. P Flannery. 2007. Numerical recipes: The art of Scientific computing. 3rded. 1256 p.
- Polyanin, A. D., and A. V. Manzhirov. 2008. Handbook of integral equations. Boca Raton - London: Chapman & Hall, CRC Press. 1108 p.
[+] About this article
Title
STATIONARY CHARACTERISTICS OF THE FINITE CAPACITY QUEUEING SYSTEM WITH INVERSE SERVICE ORDER AND GENERALIZED PROBABILISTIC PRIORITY
Journal
Informatics and Applications
2016, Volume 10, Issue 2, pp 123-131
Cover Date
2016-05-30
DOI
10.14357/19922264160214
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queueing system; special discipline; LIFO; probabilistic priority
Authors
L. A. Meykhanadzhyan
Author Affiliations
Peoples' Friendship University of Russia, 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
|