Problems of Information Transmission, Vol. 37, No. 3, 2001, pp. 262–275. Translated from Problemy Peredachi Informatsii, No. 3, 2001, pp. 82–95.
Original Russian Text Copyright
2001 by Stepanov, Iversen.
COMMUNICATION NETWORK THEORY
Methods for Reducing the Amount of Computation
in Modeling Lossy Communication Systems
Based on Ignoring Low-Probability States
S. N. Stepanov and V. B. Iversen
Received May 17, 2001
Abstract—Ways for reducing the amount of computation when estimating capacity charac-
teristics of models of lossy communication systems with product form representation of the
stationary probability vector are considered. The algorithm of convolution is applied to the
computation of the characteristics. The reduction in computation is due to both decreasing
the number of convolutions required for the estimation of service characteristics of all the ﬂows
and decreasing the number of operations in performing a single convolution, which is achieved
by ignoring low-probability states in the process of computation.
In the theory of teletraﬃc, much attention is paid to the class of communication system models
with explicit losses of calls and the product form of representing the stationary probability vector.
For computation of the characteristics of the corresponding models, a variety of algorithms based on
the product property has been proposed [1–4]. The main problem in their realization is determining
the normalization constant. Its computation is often complicated by an enormous number of states
of the corresponding models. The goal of the present investigation is to state the opportunities
that make it possible in a number of cases to cope with the problems concerned. The essence
of the approach lies in ignoring low-probability states of a model in the process of computation.
For a well-founded realization of the idea, we need the following: to modify the computational
algorithms so that they allow for the peculiarities introduced by employing truncated state spaces;
to develop means for a priori determination of bounds of a truncated state space that makes it
possible to ﬁnd the characteristics with a given precision; to obtain formulas for estimating the
error introduced into the value of a computed characteristic by removing a part of states. The
solution of the corresponding problems for some models was found by the author in [5, 6]. In the
present paper, these problems are solved for the model of a fully accessible system with an arbitrary
number of Poisson traﬃc ﬂows, restricted access, and dependence of the size of engaged resources
on the ﬂow type. The analysis presented is a generalization of . For estimating the parameters
of joint traﬃc, we propose to apply the convolution algorithm [4, 7]. We show that the amount of
computation can be reduced by organizing the procedure of performing the convolution algorithm
in a more eﬃcient way.
2. SCHEME OF THE MODEL FUNCTIONING
Let v be the transmission rate of a digital communication line expressed in standard transmission
units. As such a unit, we take the greatest common divisor of the number of units of the line resource
used for transmission of each message. The digital line is fed by n Poisson ﬂows with intensities
Supported in pat by the Russian Foundation for Basic Research, project no. 99-01-00386, and Technical
University of Denmark.
2001 MAIK “Nauka/Interperiodica”