Analysis of a semi-open queueing network with adaptation of service rates to the rates of arriving requests

Abstract

Objectives. The problem of computation of the main probabilistic characteristics of operation of a semi-open queueing network, in which the intensity of the input flow to the nodes has several possible levels, is considered. When the changing the level of flow intensity occurs, it is possible to change the rate of requests service in the nodes in order to optimize the network functioning.
Methods. The solution is based on the apparatus of multidimensional Markov chains with continuous time and a special block structure of the infinitesimal generator.
Results. The generator blocks of this chain are calculated using algorithms and formulas, which allows the invariant probability distribution to be determined. Formulas for calculating the main characteristics of network performance using the known invariant probability distribution of the states of the Markov chain are derived. A numerical example is provided to illustrate how the dependence of the main characteristics of network performance depend on the throughput of its nodes. Using the selected economic criterion for network performance quality, it is demonstrated that the redistribution of network resources between its nodes can be optimised with the change of the arrival flow level.
Conclusion. The obtained results can be used to optimize the functioning of various real objects described by semi-open queueing networks, for example, telecommunication and logistic systems, mobile robotic fulfillment systems, by adapting the distribution of network resources between its nodes to the changing rate of incoming requests