Geodesic
Method for analysis of closed queueing networks with discrete time, batch movements of customers and dynamic control of service rates
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 17 (2017) no. 1, pp. 96-108

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The closed queueing networks with single class of customers, discrete time and batch movements of customers are considered. Queues include multiple identical servers with geometric distribution of service times. A method for dynamic control of service rates in queues is proposed. The control is realized by use of different service rates during fixed time intervals in process of networks operation. When this method is used in queueing networks of considered type, close to given customer allocation among queueing systems is provided. Models for evolution and methods for analysis of closed queueing networks with single class of customers, discrete time and batch movements of customers without control and with dynamic control of service rates are proposed. These methods provide possibility of computing basic steady-state characteristics of considered classes queueing networks. An example of queueing network with control of service rates is presented. Results of analysis of this network have shown efficiency of method for control of service rates and acceptable for practical applications accuracy of method for analysis. 
@article{ISU_2017_17_1_a8,
     author = {Yu. I. Mitrophanov and V. I. Dolgov and E. S. Rogachko and E. P. Stankevich},
     title = {Method for analysis of closed queueing networks with discrete time, batch movements of customers and dynamic control of service rates},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {96--108},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2017_17_1_a8/}
}
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Yu. I. Mitrophanov; V. I. Dolgov; E. S. Rogachko; E. P. Stankevich. Method for analysis of closed queueing networks with discrete time, batch movements of customers and dynamic control of service rates. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 17 (2017) no. 1, pp. 96-108. http://geodesic.mathdoc.fr/item/ISU_2017_17_1_a8/