UDC 519.21
POTENTIALS METHOD
FOR THE Mn /Gn /1/ r
AND Mn /Gn /1/ ∞ QUEUEING SYSTEMS
WITH TYPICAL DEPENDENCES OF THE INPUT FLOW INTENSITY ON THE NUMBER
OF CUSTOMERS
Abstract. The application of the potential method to finding the stationary distribution of the number of customers
in the Mn /Gn /1/ r
and Mn /Gn /1/ ∞ queueing systems with threshold operation strateges is proposed.
The dependences of the input flow intensity on the number of customers are considered,
which are characteristic both for closed systems, which are models of the reliability theory,
and for queueing systems with random rarefaction of the input flow.
Service intensity control strategies are constructed on the assumption that the intensity
can vary at the time a customer starts servicing.
Formulas to determine Laplace transforms of the distribution of the number of customers
in the system during the busy period and for calculating the average duration of the busy period are obtained.
Keywords: single-channel queueing system, Poisson input stream of the second kind, dependence of the service time on the state of the system, method of potentials.
FULL TEXT
REFERENCES
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