Transient Behavior of the MAP/M/1/N Queuing System

Transient Behavior of the MAP/M/1/N Queuing System

This paper investigates the characteristics of the MAP/M/1/N queuing system in the transient mode. The matrix method for solving the Kolmogorov equations is proposed. This method makes it possible, in general, to obtain the main characteristics of the considered queuing system in a non-stationary mo...

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Veröffentlicht in:Mathematics (Basel) 2021-10, Vol.9 (20), p.2559
Hauptverfasser: Vishnevsky, Vladimir, Vytovtov, Konstantin, Barabanova, Elizaveta, Semenova, Olga
Format: Artikel
Sprache:eng
Schlagworte:
Customer services
Kolmogorov equations
MAP flow
Markov analysis
Mathematics
matrix method
Numerical analysis
Probability
queuing system
Queuing theory
Research methodology
Servers
transient mode
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Zusammenfassung:This paper investigates the characteristics of the MAP/M/1/N queuing system in the transient mode. The matrix method for solving the Kolmogorov equations is proposed. This method makes it possible, in general, to obtain the main characteristics of the considered queuing system in a non-stationary mode: the probability of losses, the time of the transient mode, the throughput, and the number of customers in the system at time t. The developed method is illustrated by numerical calculations of the characteristics of the MAP/M/1/3 system in the transient mode.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9202559