Abstract:
The paper presents a study of a queueing network with an unlimited number of servers in the nodes and service abandonments. Using such a model, a subscriber access network can be described. In the considered network, a connected subscriber can move from one node of the network to another during the service process or leave the network, having completed or not completed its service. It is assumed that such transitions occur independently of the current state of the nodes. The study is carried out using the method of asymptotic analysis under the condition of high input flow intensity. It is found that in the specified asymptotic regime, the joint stationary probability distribution of the number of subscribers in the network nodes converges to a multi-dimensional Gaussian distribution. Explicit expressions for the parameters of this distribution, including the mean vector and the covariance matrix, are obtained. Numerical experiments are performed to evaluate the accuracy of the approximation, and the domain of applicability of the results is established depending on the model parameters. In addition, an example of solving an optimization problem for the studied queueing network is provided, demonstrating the potential practical application of the proposed model and analytical methods for the analysis and management of telecommunication systems.
Keywords:queueing network, unlimited number of servers, service abandonments, asymptotic analysis.
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