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A multichannel non-stationary queuing system model of stadium checkpoint system studied. Input flow of model is based on statistical information of visitors flows from football matches in the Russian Federation. An algorithm choosing the shortest queue for implementing a policy of choosing a non-random queue presented. Result of comparing different policies described for input rate like real ones. The result is substantiated by comparing the functioning of the stationary QS with different queue selection policies in 3 modes: underload, load, overload.

Visitor flow dynamics at public venues has been studied by using mathematical models of the non-stationary queuing system and discrete-event modelling. Computational approach for research visitor flows quantitative characteristics is described. The dependence of input rate from time in non-stationary queuing system model is like the dependencies of rate of visitors to football matches. Quantitative characteristics are waiting line length and waiting time (time spend in queue) from time for different parameters of the input rate and the service rate device. It is proven that the maximum values of the studied characteristics and the corresponding time values are described by deterministic functions that depend on the maximum intensity of visitor flow and the average service speed. The form of these functions is well described. © Published under licence by IOP Publishing Ltd. The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0006

Access control systems (ACS) are widely used to provide safe and comfortable passing for public events. The input rate of the flows of visitors passing through the ACS varies in the time. That is why ACS can be considered as non-stationary queuing system (NQS). The study of the features of the functioning of such systems is of great interest from a practical point of view. The obtained results could be used as a scientific justification for the design decisions that are accepted at the design and modernization stage of NQS. In addition, an objective assessment of the features of the functioning of these systems in moment of incident on an object for carrying out mass events (terrorist act, fire, etc.) need to be done. In simulation the input rate is similar to the function approximating the dependence λ = λ(t), fixed during the football matches. The results of simulation NQS, which receives on the input flow of requests with the rate λ = λ(t), changing in time are some of NQS characteristics. The dependence of the queue length, the waiting time in service queue and the number of visitors entered from time were calculated. The averaged dependencies of the NQS characteristics on time should be considered as functions. These functions have significant values that can be useful for engineers, designers and also appropriate security services: the number of entered visitors at the beginning of the event, the maximum length of the queue of visitors, the maximum waiting time in the queue and the corresponding time points. We propose to call them macroscopic characteristics of NQS. Taking into account that the dependencies recorded during the football matches contain both deterministic and random components, a priori, we can expect that the random part will influence the macroscopic characteristics listed above. The results of the conducted statistical modeling showed that in the studied range of variations in the input rate of requests, this component does not have a significant effect on the selected macroscopic indicators of NQS. © 2019 Tomsk State University. All rights reserved.

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. © Published under licence by IOP Publishing Ltd.

This work devoted to researching of mathematical model of non-stationary queuing system (NQS). Arrival rate in studied NQS λ(t) is similar to rate which observed in practice in a real access control system of objects of mass events. Dependence of number of serviced requests from time was calculated. It is proven that the ratio value of served requests at the beginning of event to all served requests described by a deterministic function, depending on the average service rate μ¯$\bar \mu $ and the maximum value of the arrival rate function λ(t).