Informatics and Applications
December 2013, Volume 7, Issue 4, pp 20-33
THE DISTRIBUTION OF THE RETURN TIME FROM THE SET
OF OVERLOAD STATES TO THE SET OF NORMAL LOAD STATES
IN A SYSTEM M | M | 1 | <L,H> | <H,R> WITH HYSTERETIC LOAD
CONTROL
- Yu. V. Gaidamaka
- A. V. Pechinkin
- R. V. Razumchik
- A.K. Samuylov
- K. E. Samouylov
- I.A. Sokolov
- E. S. Sopin
- S. Ya. Shorgin
Abstract
An analytical method for studying the parameters of the hysteretic control, which is implemented as one
of the effective solutions to the overload problem in the network of SIP-servers, is suggested. As a mathematical
model, the queuing system with two loops hysteretic control was developed, where H is the
overload onset threshold, L is the overload abatement threshold, and R is the discard threshold. Two methods of
calculating the Laplace–Stieltjes transform of the distribution function of the return time from the set of overload
system states to the set of normal load system states were obtained. The first method consists in solving a system of
equations with return times for each state of the set of overload system states as unknowns, the second deals with
the recurrence for the Laplace–Stieltjes transform of the distribution function of the return time for each state of
the set of overload system states as rational fractional expressions. Both methods allow the effective calculations
with standard software tools, as shown in the numerical example.
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[+] About this article
Title
THE DISTRIBUTION OF THE RETURN TIME FROM THE SET
OF OVERLOAD STATES TO THE SET OF NORMAL LOAD STATES
IN A SYSTEM WITH HYSTERETIC LOAD
CONTROL
Journal
Informatics and Applications
December 2013, Volume 7, Issue 4, pp 20-33
Cover Date
2013-12-31
DOI
10.14357/19922264130403
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
SIP-server overload; queueing system; hysteretic load control; return time to normal load states;
Laplace–Stieltjes transform; distribution function
Authors
Yu. V. Gaidamaka , A. V. Pechinkin , R. V. Razumchik , A.K. Samuylov , K. E. Samouylov ,
I.A. Sokolov , E. S. Sopin , and S. Ya. Shorgin
Author Affiliations
Peoples’ Friendship University of Russia, Moscow, Russia
Institute of Informatics Problems, Russian Academy of Sciences, Moscow, Russia
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