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APPLICATION OF MARKOV CHAINS TO MULTIPLEXING
AND ACCESS IN TELECOMMUNICATION NETWORKS
Dimitar Radev
1
1
University of Ruse, Department of Communication Technique and Technologies, Assoc. Prof.,
Ph.D., 8 Studentska Str. 7017 Ruse, Bulgaria,
dradev@abv.bg
Abstract
– The paper presents results from a
number of investigations into the problems of
application of Markov chains to multiplexing and
access in communication networks. In this
research are investigated arrival process, arrival
distribution and timedivision multiplexing, where
asynchronous and synchronous timedivision
multiplexing is concerned. A technique for
message delay determination is suggested. With
this technique is determined average delay versus
message arrival rate.
Applications of suggested
methods in queuing networks are shown.
Index terms
– communication networks,
simulation. Markov chain models, random access
techniques
1.
INTRODUCTION
The simulation model helps to imitate the logical
trace of the cell translation and the interaction of the
elements of network with the help of structural
algorithms. The traffic, generated on a various
application is based on study of certain classes of
probability processes like time series analysis
(autoregressive models, moving average models,
autoregressive  moving average models), Long
Range Dependence (LRD) stochastic processes,
chaotic time series, state models (Markov Modulated
Poisson Process MMPP, Generally Modulated
Deterministic Process  GMDP) [1].
For simulation of the behavior of stochastic processes
the most popular methods are connected with
simulation of the behavior of time series and Markov
chains. Markov chains are members of the class of
random processes, which assume a countable set of
values and change state at regularly spaced intervals
[2]. Markov chains are characterized by certain
memorylessness in the state transitions; the
probability distribution of the state after the next
transition depends only on the present state and not
on the succession of states that led up to the present
state. They are used to model techniques for
multiplexing and access in telecommunications
networks.
2.
THE ARRIVAL PROCESS
For determining the arrival process, very important
are packetization and compound arrivals. In order for
a source to be multiplexed onto a slotted line, its
output must be segmented into fixedsize units,
generally called packets and in ATM, called cells. In
terms of the analysis of performance, packetization is
simply a transformation of random variables [3].
Suppose that the probability distribution of the
number of bits in a message is denoted by
B
(
i
)=
P
(message =
i
bits). If the number of
information bits in packet is denoted as
I
, the
probability distribution of the number of packets in a
message is given by (1), where
k
are packets in a
message.
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 Spring '10
 PopovskiBorislav

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