T2-3 - Sedma Nacionalna Konferencija so Me|unarodno U~estvo...

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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 time-division multiplexing, where asynchronous and synchronous time-division 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 fixed-size 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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T2-3 - Sedma Nacionalna Konferencija so Me|unarodno U~estvo...

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