About influence of input rate random part of nonstationary queue system on statistical estimates of its macroscopic indicators

• Published in: Journal of physics. Conference series 2018-05, Vol.1015 (3), p.32064
• Main Authors: Korelin, Ivan A, Porshnev, Sergey V
• Format: Article
• Language: English
• Subjects: Parameter identification; Physics; Queuing theory; Stadiums; Statistical models
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1015/3/032064

A model of the non-stationary queuing system (NQS) is described. The input of this model receives a flow of requests with input rate λ = λdet(t) + λrnd(t), where λdet(t) is a deterministic function depending on time; λrnd(t) is a random function. The parameters of functions λdet(t), λrnd(t) were identified on the basis of statistical information on visitor flows collected from various Russian football stadiums. The statistical modeling of NQS is carried out and the average statistical dependences are obtained: the length of the queue of requests waiting for service, the average wait time for the service, the number of visitors entered to the stadium on the time. It is shown that these dependencies can be characterized by the following parameters: the number of visitors who entered at the time of the match; time required to service all incoming visitors; the maximum value; the argument value when the studied dependence reaches its maximum value. The dependences of these parameters on the energy ratio of the deterministic and random component of the input rate are investigated.