Controlling queuing system characteristics through shifting the distribution laws
Keywords:
systems with shifted distributions, Laplace transform, Lindley integral equation, spectral solution, discrete-event modeling, GPSS World.Abstract
Introduction: The results of classical queuing theory are used to model computing systems and communication networks, with the average delay of claims in the queue and the average queue length used as the main characteristics. The ability to regulate characteristics such as queue time or queue length could bring a lot of new things to data communication systems. Purpose: To present a new class of queuing systems as systems with a time delay to expand the scope of application of queuing models. Methods: To obtain new queuing models based on classical systems a method of shifting the distribution laws in queuing systems is offered. Results: The research paper presents numerical and analytical solutions for two different systems in comparison with the solutions where discrete event simulation models are used. We demonstrate that shifting the distribution law to the right-hand side from the point of view of probability theory increases the mathematical expectation of the described random variable and thereby reduces the coefficient of variation. It is known that the average waiting time for requests is directly proportional to the squares of the coefficients of time interval variations of arrivals and service, and in the systems with shifted distributions it will decrease many times in comparison with conventional classical systems. The parameters of the distribution laws that form the queuing systems, as well as their numerical characteristics, become functionally dependent on the time shift. In this case the most important characteristics of the systems will also depend on the time shift and, therefore, it will be possible to control them through the shift parameter. The results obtained are confirmed by numerical calculations, as well as simulation experiments in the GPSS World discrete-event modeling system. Practical relevance: The results obtained can be applied in the theory and practice of data transmission, which makes it possible to regulate the queue waiting time and the queue length in the buffers in data transmission systems. Discussion: In the future, we need to evaluate the applied aspect of the proposed approach in relation to data transmission systems. To do this, it is necessary to develop an experimental software and hardware complex to confirm the results obtained.