Abstract
The paper deals with a multi-server controllable queueing system M(t)/M/K with time-dependent and, in particular, with periodic arrival rates. The models with homogeneous and heterogeneous servers are of interest. In latter case the fastest free server allocation mechanism is assumed and the preemption is allowed. The control problem consists in evaluation of the optimal number of servers during some specified stages and is solved by finite horizon dynamic programming approach. To calculate the transient solutions we use a forth-order Runge-Kutta method for the system with a truncated queue length. The results are compared with corresponding queues operating in a stationary regime. It is shown that the optimal control policies are also time dependent and periodic as arrival rates and heterogeneous systems are superior in performance comparing to the homogeneous ones.
D. Efrosinin—This work was funded by the Russian Foundation for Basic Research, Project No. 16-37-60072 mol_a_dk. The reported study was funded within the Agreement No. 02.a03.21.0008 dated 24.11.2016 between the Ministry of Education and Science of the Russian Federation and RUDN University.
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Efrosinin, D., Feichtenschlager, M. (2016). Optimal Control of M(t)/M/K Queues with Homogeneous and Heterogeneous Servers. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2016. Communications in Computer and Information Science, vol 678. Springer, Cham. https://doi.org/10.1007/978-3-319-51917-3_13
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DOI: https://doi.org/10.1007/978-3-319-51917-3_13
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