An Exact Method for a Class of Self-Similar M/Ga/1/K Queueing System of Internet Stream

Abstract

In Internet stream monitoring, computing the expected parameters and distributions for the stream process under self-similarity and long-range dependency requires appropriate and exact methods queueing analyses to obtain performance of the Internet. Our method avoids fitting a non-heavy tailed distribution to Internet stream data by specifically fitting Gamma distribution to its service time process, which enhances the features of correlated events that explain self-similarity and long-range dependency compared to the classical memoryless assumptions of standard Poisson arrival and Exponential service. We propose the specific expectations of the parameters for a class of M/Ga/1/k queueing system (‘M’ represents a Markovian arrival process that follows Poisson distribution, ‘Ga’ represents a Gamma distribution service process, ‘1’ represents a single server, ‘k’ represents the buffer size) in an exact closed-form derivations using the Pollaczek Khintchine formulae alongside the Laplace transform to obtain the performance of   queue. The adequacy of the proposed model was confirmed using simulated data of Internet traffic.