The potentials method for a closed queueing system with hysteretic strategy of the service time change
Treść / Zawartość
We propose a method for determining the characteristics of a single-channel closed queueing system with an exponential distribution of the time generation of service requests and arbitrary distributions of the service times. In order to increase the system capacity, two service modes (the main mode and overload mode), with the service time distribution functions F ( x ) and F ( x ) respectively, are used. The overload mode starts functioning if at the beginning of service of the next customer the number of customers in the system ξ(t ) satisfies the condition ξ (t ) > h2. The return to the main mode carried out at the beginning of service of the customer, for which ξ (t ) = h1, where 1 ≤ h1 < h2. 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.
Bibliogr. 13 poz., tab.
-  Nesterov Yu.G., Analysis of characteristics of a closed queuing system with relative priorities, Nauka i Obrazovanie, MGTU im. N. Baumana 2014, 3, 242-254 (in Russian).
-  Bocharov P.P., Pechinkin A.V., Queueing Theory, RUDN, Moscow 1995 (in Russian).
-  Zhernovyi Yu.V., Markov Queueing Models, Vydavnychyi Tsentr LNU im. Ivana Franka, Lviv 2004 (in Ukrainian).
-  Zhernovyi Yu., Stationary probability distribution of states for a single-channel closed queuing system, Visnyk Lviv. Univer. Series Mech.-Math. 2007, 67, 130-136 (in Ukrainian).
-  Zhernovyi Yu.V., Zhernovyi K. Yu., Potentials method for a closed system with service times dependent on the queue length, Informatsionnye Protsessy 2015, 15, 1, 40-50.
-  Zhernovyi K.Yu., Zhernovyi Yu.V., M /G/1/m θ and M /G/1 θ systems with the service time dependent on the queue length, J. of Communicat. Technology and Electronics 2013, 58, 12, 1267-1275.
-  Zhernovyi Yu., Zhernovyi K., Potentials Method for Threshold Strategies of Queueing, LAP Lambert Academic Publishing, Saarbrűcken 2015 (in Russian).
-  Zhernovyi K.Yu., Stationary characteristics of the M /G/1/m θ system with the threshold functioning strategy, J. of Communicat. Technology and Electronics 2011, 56, 12, 1585-1596.
-  Zhernovyi Yu., Insensitivity of the Queueing Systems Characteristics, LAP Lambert Academic Publishing, Saarbrűcken 2015.
-  Zhernovyi Yu.V., Zhernovyi K.Yu., Probabilistic characteristics of an M /G/1/m 2 θ queue with two-loop hysteretic control of the service time and arrival rate, J. of Communicat. Technology and Electronics 2014, 59, 12, 1465-1474.
-  Korolyuk V.S., The Boundary Problem for the Compound Poisson Processes, Naukova Dumka, Kyiv 1975.
-  Bratiychuk M., Borowska B., Explicit formulae and convergence rate for the system M /G/1/N α as N → ∞, Stochastic Models 2002, 18, 1, 71-84.
-  Zhernovyi Yu., Creating Models of Queueing Systems in the Environment GPSS World, Palmarium Academic Publishing, Saarbrűcken 2014 (in Russian).