ON THE DISTRIBUTION OF TRANSMISSION AND ARRIVAL TIMES OF PACKET-SWITCHED NETWORK UNDER SELF-SIMILARITY AND LONG RANGE DEPENDENCY

It is widely known that the standard Markov process does not allow batch arrivals or batch transmission, which is prominent in the TCP/IP Internet network design. Another drawback of the standard Poisson/exponential processes is the stringent memoryless assumption which does not permit correlated events. When these assumptions are relaxed, they are referred to as self-similarity and long range dependency in internet data transmission. In this paper, an attempt was made to review some of the existing distributions used to model transmission and arrival times of internet packets in order to determine the most suitable ones other than the standard Poisson/exponential for modeling internet data transmission with self-similarity and long range dependency properties. Results from the Monte-Carlo simulation using log-likelihood, AIC, BIC and Kolmogorov Smirnov test criteria established the supremacy of Weibull distribution over the other five distributions considered. In addition, the steady state performance measures were also achieved via discrete event simulation. The performance measures also affirm the adequacy of the Weibull distribution with relatively close results to the analytical and the simulation outputs.