Queue Performance in Presence of Long-Range Dependencies – An Empirical Study

The queuing, as an inherent feature of each real system, plays a very important role in teletraffic networks as well. It is known that the queuing system consists of three basic components: the input stream of requests, the service processes and the queue discipline. The optimal performance of system can be achieved only in the case when all components are “matched” together. The teletraffic models that describe the early telephone services (e.g. Poisson and Markov) have been very successful. One of the main reasons for this success with models, which accurately resembles the real-world behavior, has been due to the highly static, low varying nature of early development phase of telephone voice traffic. This means that the whole environment of early telephone networks can be treated as a simple system. The main features of such systems can be described by: thermodynamic quasi-equilibrium, homogenous topologies, random graph theory, short-range dependencies, Poisson distribution, circuit switching, etc. However, the evolution of teletraffic from voice to new data traffic and integrated services inevitably leads to the vastly different statistical characteristics that are much more irregular and variable and as a result undermine the basis for the traditional traffic models. In this paper we show that taking into account the complex systems approach the existence of long-range dependencies (expressed by 1/f noise) influence queue performance. This is done basing on analytical approach with presentation of long-range dependent queue model and also by experimental study of traffic behavior in computer network during daily workload generated by computer user.