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On approximation with truncations for the nonstationary queuing model
Ya. A. Satin Department of Applied Mathematics, Vologda State University, 15 Lenin Str., Vologda 160000, Russian Federation
Abstract:
The author deals with a nonstationary queuing model $M_t/M_t/1$ with one server. It is assumed here that the customers arrive with the intensity $\lambda(t)$ but are served in pairs (that is, in this case, $\mu(t)$ is the service rate of a group of two customers). For the considered model, the limiting characteristics are constructed using the method of truncating the state space of the system. A numerical example with exact given values of intensities showing the application of the studied approach is constructed and corresponding graphic illustrations are provided. The author uses the general algorithm to build graphs, it is associated with solving the Cauchy problem for the forward Kolmogorov system on the corresponding interval which has already been used by the author in previous papers.
Keywords:
queuing systems, $M_t/M_t/1$ queue, nonstationary queuing model, approximation, limiting characteristics, rate of convergence, truncation of the state space.
Received: 22.01.2021
Citation:
Ya. A. Satin, “On approximation with truncations for the nonstationary queuing model”, Sistemy i Sredstva Inform., 31:1 (2021), 28–36
Linking options:
https://www.mathnet.ru/eng/ssi747 https://www.mathnet.ru/eng/ssi/v31/i1/p28
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