Optimal control with monotonicity constraints for a parallel-server loss channel serving multi-class jobs

Abstract

We study a parallel-server loss channel serving multi-class jobs, which appears in many real-world systems, e.g., cloud computing, multi-input multi-output (MIMO) orthogonal frequency division multiplexing (OFDM), and call centre. An -discounted optimal control with monotonicity constraints (OCMC) model over infinite time horizon is established by using the physical queueing model with linear revenue function. Existence of a solution to the OCMC model is proved, whose optimal value provides an upper bound of the corresponding values of the physical queueing model under Markovian decision rules. Algorithms with lower complexity in solving the OCMC model are proposed, which are further used to design an admission control policy for the loss channel. Furthermore, a simulation algorithm is proposed to implement the designed policy. Performance comparisons through numerical examples are conducted among our newly designed policy, the first-in first-out (FIFO) policy, an arbitrarily selected (AS) policy, and the Markov decision process (MDP) based threshold policy. Advantages and disadvantages of these policies are identified under different channel parameters and channel (e.g., Markovian and non-Markovian) conditions. Particularly, we find out that our designed policy outperforms the other three policies when the traffic intensity is relatively large, and the differences of the revenues per unit of time and the penalty costs among different classes of jobs are large.