Non-Stationary Single-Channel Queuing System Features Research in Context of Number of Served Queries
Sergey Porshnev,Ivan A. Korelin +1 more
- Vol. 10, pp 03006
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TLDR
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 and the maximum value of the arrival rate function λ(t).Abstract:
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 and the maximum value of the arrival rate function λ(t).read more
Citations
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Rationale choosing interval of a piecewise-constant approximation of input rate of non-stationary queue system
Ivan A. Korelin,Sergey Porshnev +1 more
Journal ArticleDOI
Computational approach for researching visitor flow dynamics at public venues and mass gathering events
Ivan A. Korelin,Sergey Porshnev +1 more
Proceedings ArticleDOI
Performance Analysis of Priority Queueing Systems Using Timed Petri Nets
TL;DR: Research results and performance analysis of Priority Queuing System (PQS) that are supporting the Quality of Service (QoS) and it was shown that temporal models of Petri nets can be effectively used in modeling and analysis of the performance of priority queuing systems.
References
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Journal ArticleDOI
Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov Chain
TL;DR: In this paper, it was shown that the equilibrium distribution of a queue is a geometric series mixed with a concentration at 0, and that for a queue of size s = 1, 2 and 3, the equilibrium is a negative-exponential distribution mixed with concentration at n = 0.
Journal ArticleDOI
Markov-modulated queueing systems
N. U. Prabhu,Yixin Zhu +1 more
TL;DR: A model in which the workload process and the secondary process together constitute a Markov compound Poisson process is analyzed, which derives the properties of the waiting time, idle time and busy period, using techniques based on infinitesimal generators.