Прискорене моделювання ймовірності втрати вимоги у системі обслуговування з двічі стохастичними пуассонівськими вхідними потоками

• Date: 2024
• Main Authors: Kuznetsov, Mykola, Kuznetsov, Igor, Shumska, Alla
• Format: Article
• Language: Ukrainian
• Published: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2024
• Subjects: канал; лінія; ймовірність блокування; метод Монте-Карло; прискорене моделювання; розшарована вибірка; оцінка; відносна похибка
• Online Access: https://jais.net.ua/index.php/files/article/view/426
• Journal Title: Problems of Control and Informatics

A multichannel queueing system with several double stochastic input flows of customers is considered. Each service channel contains a fixed number of lines. The customers of different flows require a certain number of lines to be serviced (the corresponding distribution is given). Not every channel is accessible for the customers of different flows. Channel accessibility is determined by some distribution depending on both the flow and the number of lines that the customer needs to be served. If a customer arrives on a channel with an insufficient number of free lines, it is allowed to be redirected to another available channel. If there are no available channels with a sufficient number of free lines, the system is in the state of blocking with respect to customers of this flow with a request for a certain number of lines. The service time has a distribution function of a general form depending both on flow the customer came from and on the number of lines required for servicing. A fast simulation method aimed to evaluate the blocking probability of customers of a certain flow demanding a given number of service lines is proposed. A comparison with the Monte Carlo method is carried out on a numerical example, and the advantages and disadvantages of the proposed method are illustrated, in particular, how the relative error of estimates changes with a decrease in the probability of blocking.