IJPAM: Volume 95, No. 2 (2014)

FLUID LIMIT FOR CUMULATIVE IDLE TIME
IN MULTIPHASE QUEUES

Saulius Minkevičius$^1$, Vladimiras Dolgopolovas$^2$
$^{1,2}$VU Institute of Mathematics and Informatics
Akademijos 4, LT-08663, Vilnius, LITHUANIA
$^{1,2}$Vilnius University
Naugarduko 24, LT-03225, Vilnius, LITHUANIA


Abstract. The object of this research in the queueing theory is the Functional-Strong-Law-of- Large-Numbers (FSLLN) under the conditions of heavy traffic in Multiphase Queueing Systems (MQS). A FSLLN is known as fluid limit or fluid approximation. In this paper, the FSLLN is proved for values of important probabilistic characteristics of the MQS investigated as well as the summary queue length of customers and the queue length of customers.

Received: December 29, 2013

AMS Subject Classification: 60K25, 60G70, 60F17

Key Words and Phrases: queueing systems, multiphase queueing systems, heavy traffic, a law of the iterated logarithm, summary queue length of customers, queue length of customers

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DOI: 10.12732/ijpam.v95i2.1 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 95
Issue: 2
Pages: 123 - 129


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