Modelling Packet Departure Times using a Known PDF

Abstract

This paper deals with IPTV traffic source modelling and describes a packet generator based on a known probability density function which is measured and formed from a histogram. Histogram based probability density functions destroy an amount of information, because classes used to form the histogram often cover significantly more events than one. In this work, we propose an algorithm to generate far more output states of random variable X than the input probability distribution function is made from. In this generator is assumed that all IPTV packets of the same video stream are the same length. Therefore, only packet times are generated. These times are generated using the measured normalized histogram that is converted to a cumulative distribution function which acts as a finite number of states that can be addressed. To address these states we use an ON/OFF model that is driven by an uniform random number generator in (0, 1). When a state is chosen then the resulting value is equal to a histogram class. To raise the number of possible output states of the random variable X, we propose to use an uniform random number generator that generates numbers within the range of the chosen histogram class. This second uniform random number generator assures that the number of output states is far more larger than the number of histogram classes.