IJPAM: Volume 66, No. 2 (2011)

INVESTIGATION OF THE FLUID LIMITS FOR
MULTIPHASE QUEUES IN HEAVY TRAFFIC

Saulius Minkevicius$^1$, Vladimiras Dolgopolovas$^2$
$^1$VU Institute of Mathematics and Informatics
4, Akademijos, Vilnius, 08663, LITHUANIA
$^{1,2}$Vilnius University
24, Naugarduko, Vilnius, 03225, LITHUANIA
$^1$e-mail: minkevicius.saulius@gmail.com


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: October 28, 2010

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

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

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 2