ISSN 0032-9460, Problems of Information Transmission, 2007, Vol. 43, No. 4, pp. 344–352.
Pleiades Publishing, Inc., 2007.
Original Russian Text
G.S. Evseev, A.M. Turlikov, 2007, published in Problemy Peredachi Informatsii, 2007, Vol. 43, No. 4, pp. 83–92.
COMMUNICATION NETWORK THEORY
Interrelation of Characteristics of Blocked
RMA Stack Algorithms
St. Petersburg State University of Aerospace Instrumentation
Received April 25, 2007
Abstract—A method to analyze the duration of collision resolution for blocked RMA stack
algorithms is proposed. Simple formulas are obtained that express the average length of a colli-
sion resolution interval for the modiﬁed (frugal) algorithm in a noisy and in a noiseless channel,
as well as for the basic algorithm in a noisy channel, through the corresponding parameters for
the basic algorithm in a noiseless channel. From estimates of the throughput of the basic algo-
rithm in a noiseless channel, estimates for the throughput in the other three cases are directly
In [1, 2] there was ﬁrst considered an algorithm using which inﬁnitely many users sharing a
communication channel can transmit data with a ﬁnite average delay provided that the arrival rate
is bounded. Using the terminology of , the supremum of arrival rates for which the average delay
is ﬁnite will be referred to as the throughput of an algorithm.
In what follows, we call the algorithm considered in [1, 2] the basic algorithm (in , the term
basic stack algorithm with blocked access was used). In [1, 2] it was also noted that from the basic
algorithm one can also obtain an algorithm with a higher throughput, which will be referred to
as the modiﬁed (or frugal) algorithm (in  it was called the frugal stack algorithm with blocked
access ). The analysis made in [1,2] has shown that for the throughputs R
the basic and modiﬁed (frugal) algorithms, we have
After the publication of [1, 2], investigation of algorithms was developed in two directions: re-
ﬁnement of estimates for throughputs and extending results to the case of noisy channels where
false collisions are possible.
In , results on ﬁnding estimates for the throughput in a noiseless channel were summed up
and the following reﬁned estimates were given:
< 0.34657397, (2)
< 0.3753698. (3)
In  there was introduced a model of a noisy channel where false collisions may occur, and
methods for computing estimates for the throughput in a noisy channel were described. In  it