DOI
10.34229/KCA2522-9664.24.6.7
UDC 519.872
1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 kuznetsov2016@icloud.com
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2 Physical and Technical Institute of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine
sea_hawk@icloud.com
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3 Physical and Technical Institute of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine
shumska-aa@ukr.net
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FAST SIMULATION OF CUSTOMERS BLOCKING PROBABILITY
IN A QUEUEING SYSTEM WITH POISSON INPUT FLOW CONTROLLED
BY A SEMI-MARKOV PROCESS
Abstract. A multichannel queueing system with a Poisson input flow is considered.
The input flow rate depends on the current state of a semi-Markov process. This state also determines the type of the customer.
Each channel contains several service lines. To be serviced, the customer requires several lines with the distribution dependent on the customer’s type.
Not each channel is accessible for customers of a given type.
The accessibility is determined by some distribution depending both on the customer’s type and on the required number of lines.
If the channel does not have sufficient service lines, it is possible to reorient this customer to another channel.
The service time has a general distribution function depending on the customer’s type and the number of lines required for servicing.
A fast simulation method is proposed to evaluate the blocking probability of customers of a certain type demanding a given number of service lines. A comparison with the Monte Carlo method is made using a numerical example, and the change in the relative error of the estimate for decreasing blocking probability is analyzed.
Keywords: queueing system, semi-Markov process, channel, line, blocking probability, Monte Carlo method, fast simulation, estimate, relative error.
full text
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