Research of impact input rate random variations on macroscopic characteristics of non-stationary queuing system

The results of research of input stream rate random variations influence on the macroscopic characteristics of a nonstationary queuing system (NQS) are discussed in this paper. Statistical information obtained during the football match between the football clubs "Krylia Sovetov" and "Dynamo" at the stadium "Metallurg" in Samara is available. The characteristics of the stochastic component of the variation in the input rate were chosen on the basis of this information. The probability density function and the cumulative distribution function of random variations in the input rate of applications were estimated using the Rosenblatt-Parzen approximation. NQ's characteristics was studied such as the maximum queue length, the maximum waiting time in the queue, the time point at which the maximum queue length is reached, and the time point at which waiting time in the queue the longest, the number of visitors who entered at the time of the match beginning, the time needed to service the entire queue. The results of the statistical simulation shown that taking into account the random component of the variation input rate does not affect this macroscopic characteristics. (paper)