Fast Simulation of Steady-State Call Blocking Probability in a Two-Channel System with Threshold Service Strategies

• Published in: Cybernetics and systems analysis Vol. 59; no. 5; pp. 794 - 802
• Main Authors: Kuznetsov, M. Yu, Shumska, A. A.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2023; Springer; Springer Nature B.V
• Subjects: Analysis; Artificial Intelligence; Control; Mathematics; Mathematics and Statistics; Monte Carlo method; Monte Carlo simulation; Processor Architectures; Queuing theory; Simulation methods; Software Engineering/Programming and Operating Systems; Steady state; Systems Theory; Monte Carlo method; fast simulation; blocking state; resource; queueing system; stationary probability; stratified sampling; variance of estimate
• ISSN: 1060-0396; 1573-8337
• DOI: 10.1007/s10559-023-00615-w

The authors analyze the model of a queueing system consisting of two service channels. Each channel receives calls from several Poisson flows of different types. A call of each flow requires certain resource for its service. Threshold service strategies are defined that make it possible to redirect a call from one channel to the other. Blocking of calls of a certain flow occurs if each channel does not have sufficient service resources. All calls coming in the system-blocking state are lost. To evaluate the stationary probability of blocking calls of a certain flow, the fast simulation method is proposed. The accuracy of the estimates is illustrated by numerical examples. The possibility of the insensitivity of the steady-state blocking probabilities with respect to the form of service time distributions by fixed means is investigated.