Abstract
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.
Highlights
It turns out to be relevant to find a solution for the problem associated with the estimation of the characteristics of a nonstationary queuing system (NQS)
The article discusses the results of statistical modeling of NQS, whose λ(t) function properties are similar to real dependencies λ(t) registered during football matches at various stadiums in the Russian Federation
The parameters of functions λdet(t), λrnd(t) are analogous to the actual dependencies registered during football matches at various Russian stadiums
Summary
It turns out to be relevant to find a solution for the problem associated with the estimation of the characteristics of a nonstationary queuing system (NQS). NQS input rate of requests is λ(t) = λdet(t) + λrnd(t), where λdet(t) is a time-dependent deterministic function; λrnd(t) is a random function. It is clear that the estimations of the NQS characteristics calculated from random component λrnd(t) will differ from the corresponding characteristics given in [6, 7]. That is why it is relevant to study characteristics of the NQS with the input rate of the flow of requests λ(t) = λdet(t) + λrnd(t). The article discusses the results of statistical modeling of NQS, whose λ(t) function properties are similar to real dependencies λ(t) registered during football matches at various stadiums in the Russian Federation
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