Abstract
A controllable tandem queueing system consists of two nodes in tandem of the type \(M/M/n_i\) and a controller. Customers arrive to the controller, who allocates them between the nodes. After service completion at node 2 the controller can allocate the customer waiting at node 1 to node 2. With probability \(p\) after a service completion at node 1 a failure occurs. In this case the customer from node 1 joins node 2. With complement probability \(1-p\) the service completion at node 1 is successful. For the given cost structure we formulate an optimal allocation problem to minimize the long-run average cost per unit of time. Using dynamic-programming approach we show the existence of thresholds which divides the state-space into two contiguous regions where the optimal decision is to allocate the customers to node 1 or to node 2. Some monotonicity properties of the dynamic-programming value function are established.
This work was funded by the COMET K2 Center “Austrian Center of Competence in Mechatronics (ACCM)”, funded by the Austrian federal government, the federal state Upper Austria, and the scientific partners of the ACCM.
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Efrosinin, D., Farhadov, M., Kudubaeva, S. (2014). Performance Analysis and Monotone Control of a Tandem Queueing System. In: Vishnevsky, V., Kozyrev, D., Larionov, A. (eds) Distributed Computer and Communication Networks. DCCN 2013. Communications in Computer and Information Science, vol 279. Springer, Cham. https://doi.org/10.1007/978-3-319-05209-0_21
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DOI: https://doi.org/10.1007/978-3-319-05209-0_21
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