Modelling Internet Traffic Streams with Ga/M/1/K Queuing Systems under Self-similarity

Abstract

High-intensity concurrent arrivals of request packets in Internet traffic can cause dependence of event-to-event-times of the requests being served, which causes non-memoryless, modelled with heavy-tail distributions unlike common known traffics. The performance of Internet traffic can be examined using analytical models for the purpose of optimizing the system to reduce its operating costs. Therefore, our study examined a Ga/M/1/K Internet queue class (Gamma arrival processes, Ga; with memoryless-Poisson service process, M; a single server, 1, and K waiting room) and proposed specific derivations of its performance indicators. Real-life data of a corporate organisation Internet server was monitored at both peak and off-peak periods of its usage for Internet traffic data analysis. The minimum ‘0’ in the arrival process indicates self-similarity and was assessed using Hurst parameter, H, and their (standard deviation). ‘H’ > 0.5 arrival process in the peak period only, indicates self-similarity. Performance of Ga/M/1/K was compared with various queuing Internet traffic models used in existing literatures. Results showed that the value of the waiting room size for Ga/M/1/K has closest ties with true self-similar model at peak-periods usage of the Internet, which indicates possible concurrent arrival of clients' requests leading to more usage of the waiting room, but with light-tailed queue model at the off-peak periods. Therefore, the proposed Ga/M/1/K model can assist in evaluating the performance of high-intensity self-similar Internet traffic.     

Keywords: Internet traffic; self-similarity; Ga/M/1/K model; gamma distribution