Dmitry Efrosinin, Natalia Stepanova,
"Average Cost Minimization in a Multi-server Retrial Queueing System with a Controllable Reserve Group of Servers"
, in Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V.: Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2022. Lecture Notes in Computer Science, Serie Lecture Notes in Computer Science, Vol. 13766, Springer, 2023, ISBN: 978-3-031-23206-0
Average Cost Minimization in a Multi-server Retrial Queueing System with a Controllable Reserve Group of Servers
Sprache des Titels:
Distributed Computer and Communication Networks: Control, Computation, Communications. DCCN 2022. Lecture Notes in Computer Science
The paper deals with a dynamic optimal activation and deactivation of a reserve group of servers in a multi-server retrial queueing system. The repeated attempts to occupy the server from the orbit occur due to a classical retrial discipline, and the activation of reserves requires a random set-up time. The optimal policy minimizes the average cost per unit of time which consists of the holding and usage cost components. The optimal control policy belongs to a class of hysteretic control policies defined by two threshold levels for the orbit size and prescribes the necessity to activate and deactivate a standby reserve group of servers. A dynamic-programming approach for the Markov decision process is used to show that the optimal thresholds depend on the number of busy servers as well. In order to provide a less computationally expensive method for calculating optimal thresholds, explicit heuristic expressions are proposed to guarantee at least a quasi-optimal solution to the optimization problem. Numerical examples confirm the efficiency of the proposed approach.