Informatics and Applications
2017, Volume 11, Issue 3, pp 106-112
REVISITING JOINT STATIONARY DISTRIBUTION IN TWO FINITE CAPACITY QUEUES OPERATING IN PARALLEL
- L. Meykhanadzhyan
- S. Matyushenko
- D. Pyatkina
- R. Razumchik
Abstract
The paper revisits the problem of the computation of the joint stationary probability distribution pij in a queueing system consisting of two single-server queues, each of capacity N ≥ 3, operating in parallel, and a single Poisson flow. Upon each arrival instant, one customer is put simultaneously into each system. When a customer sees a full system, it is lost. The service times are exponentially distributed with different parameters. Using the approach based on generating functions, the authors obtain a new system of equations of a smaller size than the size of the original system of equilibrium equations (3N — 2 compared to (N + 1)2). Given the solution of the new system, the whole joint stationary distribution can be computed recursively. The new system gives some insights into the interdependence of pij and pnm. If relations between pi-1,N and pi,N for i = 3, 5, 7,... are known, then the blocking probability can be computed recursively. Using the known results for the asymptotic behavior of pij as i, j → ∞, the authors illustrate this idea by a simple numerical example.
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[+] About this article
Title
REVISITING JOINT STATIONARY DISTRIBUTION IN TWO FINITE CAPACITY QUEUES OPERATING IN PARALLEL
Journal
Informatics and Applications
2017, Volume 11, Issue 3, pp 106-112
Cover Date
2017-09-30
DOI
10.14357/19922264170312
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
two queues; generating function; stationary distribution; paired
Authors
L. Meykhanadzhyan  , S. Matyushenko  , D. Pyatkina , and R. Razumchik , 
Author Affiliations
School No. 281 of Moscow, 7 Raduzhnaya Str. Moscow 129344, Russian Federation
Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences; 44-2 Vavilova Str., Moscow 119333, Russian Federation
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