UDC 519.872
1 V.M. Glushkov Institute of Cybernetics,
National Academy of Sciences of Ukraine, Kyiv, Ukraine, and National Aviation University, Kyiv, Ukraine
 ekoba2056@gmail.com
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2 V.M. Glushkov Institute of Cybernetics,
National Academy of Sciences of Ukraine, Kyiv, Ukraine, and National Aviation University, Kyiv, Ukraine
svitlaspv@gmail.com
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GI/G/1 LAKATOS-TYPE QUEUEING SYSTEM WITH Т-RETRIALS
Abstract. Authors consider the Lakatosh-type GI/G/1 queueing system with T-retrials, i.e.,
the system with the FCFS service discipline and a constant cycle time T of the orbit.
Here we construct the Markov chain for the system, prove its ergodicity condition,
solve the system of equations for the stationary distribution of the system state probabilities,
and derive formulas for the average number of requests and the average number of the orbit cycles
at a specific ratio of service time and orbit time. Also, we develop an algorithm for statistical modeling
of the considered system. Results of analytical and statistical modeling show consistency between them.
Authors indicate an essential property of the Lakatos-type system, namely, that we can use it to evaluate
a system in which the FCFS service order is not necessary.
Keywords: retrial queues, Lakatos-type queueung system, cyclic queueing systems,
queueing system with T-retrials, orbit, orbit cycle, Markov chain, queueing system ergodicity.
FULL TEXT
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