ISSN 0032-9460, Problems of Information Transmission, 2007, Vol. 43, No. 2, pp. 143–166.
Pleiades Publishing, Inc., 2007.
Original Russian Text
A.Yu. Privalov, K. Sohraby, 2007, published in Problemy Peredachi Informatsii, 2007, Vol. 43, No. 2, pp. 85–111.
COMMUNICATION NETWORK THEORY
Playout in Slotted CBR Networks:
Single and Multiple Nodes
A. Yu. Privalov
and K. Sohraby
Computer Science Department, Samara State Aerospace University
Department of Computer Science and Electrical Engineering,
University of Missouri, Kansas City, USA
Received March 3, 2006; in ﬁnal form, January 16, 2007
Abstract—We consider playout of a constant bit-rate (CBR) traﬃc after one or several mul-
tiplexors in a network with a playout buﬀer. Probabilistic characteristics of the playout process
are found, depending on the traﬃc characteristics and parameters of the buﬀer. We present
conditions on the buﬀer parameters that guarantee no jitter (complete playout).
Consider a packet switching network, where all packets (cells) are of the same length (e.g., ATM
network). We assume that all communication links have the same rate, so that transmission of a
cell through any communication link takes one time unit. Time in the system is discrete, slotted,
and divided into unit time intervals (slots) [t, t+1), t ∈ I
. It is assumed that transmission of a cell
starts at the beginning of a slot (and ends just before the beginning of the next slot). We assume
that a constant bit-rate source produces a deterministic (periodic) ﬂow of cells, one cell every T slots
(T ∈ I
). We refer to cells from this source as tagged cells. After entering the network, the tagged
cells pass through several network nodes that are statistical multiplexors. At a multiplexor, the
tagged cells compete for transmission with cells from other sources, referred to as background cells.
After leaving the last multiplexor in their route in the network, the tagged cells are stored in
a playout buﬀer. The goal is to play out the tagged ﬂow periodically. Operation of the playout
buﬀer is speciﬁed by two parameters: initial delay D of the tagged ﬂow and size B of the buﬀer.
The very ﬁrst cell of the tagged ﬂow arrived at the buﬀer (referred to as the 0th cell) is delayed
by D slots; if the buﬀer operates normally, the nth cell is transmitted D + nT slots after the 0th
cell had arrived at the buﬀer. If at the playout time of a cell, the cell has not departed from the
node yet, i.e., has not arrived at the playout buﬀer, disturbance of periodicity of the buﬀer output
ﬂow occurs, referred to as underﬂow. In this case, the departing cell is immediately available for
playout as soon as it arrives at the buﬀer. If at the arrival of a cell at the buﬀer, there are already
B cells in the buﬀer, a cell with the smallest number immediately leaves the buﬀer, which also may
cause periodicity disturbance of the buﬀer output ﬂow, referred to as overﬂow.
Our goal is the analysis of probabilities of various disturbances of periodicity of the buﬀer output
ﬂow for a certain background ﬂow model. For the case of a single multiplexing of the tagged ﬂow,
Supported in part by the Cooperative Grant Program of Civilian Research and Development Founda-
tion (CRDF), Grant no. RU-M1-2590-SA-04. A conference version of this paper was presented at the
International Teletraﬃc Congress (ITC’19, Beijing, 2005).