The study of influence of random variations of input rate to macroscopic indicators of a non-stationary queuing system

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 X = X(t), fixed during the football matches. The results of simulation NQS, which receives on the input flow of requests with the rate X = X(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.

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