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Calculating steady-state probabilities of single-channel queueing systems with changes of service times depending on the queue length

Zhernovyi Yuriy, Kopytko Bohdan

Journal of Applied Mathematics and Computational Mechanics

2019

Vol. 18, nr 3

107--117

In this paper, we propose a method for calculating steady-state probabilities of the G/G/1/m and M/G/1/m queueing systems with service times changes depending of the number of customers in the system. The method is based on the use of fictitious phases and hyperexponential approximations with parameters of the paradoxical and complex type. A change in the service mode can only occur at the moment the service is started. We verified the obtained numerical results using the potential method and simulation models, constructed by means of GPSS World.

The potentials method for the M/G/1/m queue with customer dropping and hysteretic strategy of the service time change

Zhernovyi Y., Kopytko B.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 1

197--210

We propose a method for determining the probabilistic characteristics of the M/G/1/m queueing system with the random dropping of arrivals and distribution of the service time depending on the queue length. Two sets of service modes, with the service time distribution functions Fn (x) and Fn (x) respectively, are used according to the twothreshold hysteretic strategy. The Laplace transforms for the distribution of the number of customers in the system during the busy period and for the distribution function of the length of the busy period are found. The developed algorithm for calculating the stationary characteristics of the system is tested with the help of a simulation model constructed with the assistance of GPSS World tools.