Model of a queue with almost self-similar or fractal-like traffic

Traditional modeling of queues is done assuming Poisson arrival rates. However several different types of input processes have been found to exhibit self-similar or fractal-like behavior. This phenomenon has been observed in Ethernet local area networks (LAN), variable bit rate (VBR) compressed video traffic, and wide area network (WAN) traffic. We analytically model the performance of a single server queue with almost self-similar traffic with exponentially distributed service times. The packet interarrival times of almost self-similar traffic have very large yet finite variance. It is assumed that the packet interarrival times have a gamma distribution with a specific range of parameter values. Using Lagrange series expansion, we analytically evaluate the performance of a single server queue with this input traffic.