Bivariate gamma distribution: A plausible solution for joint distribution of packet arrival and their sizes

Network traffic has been studied extensively since new findings by Taqqu et. al. (1994), which has shown that network traffic is not memoryless. Such traffic has been called self similar with Long Range Dependence (LRD) and their distribution is commonly known as heavy-tailed. It is very hard to estimate buffer size to protect against overflow in presence of such traffic as packet sizes and their arrival count is positively correlated. Queuing analysis of network devices consider only arriving packets irrespective of their sizes, but existing network protocols allow for variable packet sizes. This can lead to higher overflow probability. This paper examines network traffic heavy-tailedness assumption via number of experimentation on connectionless service traffic. Number of arrival per second and number of bytes transferred per second are found to be highly correlated across lags. Based on these findings, this work proposes bivariate gamma distribution for joint probability distribution of these parameters.