Jindřiška Šedová

Multichannel Queueing Systems and Their Simulation

This paper is concerned with multichannel queueing systems showing how to derive their characteristics if the requirement arrivals correspond to a Poisson process and the service times have the exponential distribution. However, the requirements of stationarity, regularity, and independence of increases needed to model these processes by Markov chains and to define the transition probabilities may not be satisfied, or no information may be available on such parameters. Using randomly generated data, we propose a strategy of processing the requirements in multichannel systems and a way of evaluating the probabilities necessary to express the characteristics of the systems comparing these results with the theoretical ones. It has been discovered that with, as the number of outputs increases, the simulation results converge to the theoretical ones.

Models and Simulations of Queueing Systems

In the queueing theory, it is assumed that requirement arrivals correspond to the Poisson process and the service time has the exponential distribution. Using these assumptions, the behaviour of the queueing system can be described by means of the Markov chains and it is possible to derive characteristics of the system. In the paper, these theoretical approaches are presented and focused on systems with several service lines and the FIFO queue when the number of requirements exceeds the number of lines. Finally, it is also shown how to compute the characteristics in a situation when these assumptions are not satisfied.