A Risk-Sensitive Approach for Packet Inter-Delivery Time Optimization in Networked Cyber-Physical Systems
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1993-2012 IEEE. In networked cyber-physical systems, the inter-delivery time of data packets becomes an important quantity of interest. However, providing a guarantee that the inter-delivery times of the packets are 'small enough' becomes a difficult task in such systems due to the unreliable communication medium and limited network resources. We design scheduling policies that meet the inter-delivery time requirements of multiple clients connected over wireless channels. We formulate the problem as an infinite-state risk-sensitive Markov decision process, where large exceedances of inter-delivery times for different clients over their design thresholds are severely penalized. We reduce the infinite-state problem to an equivalent finite-state problem and establish the existence of a stationary optimal policy and an algorithm for computing it in a finite number of steps. However, its computational complexity makes it intractable when the number of clients is of the order of 100 or so that is found in applications such as in-vehicle networks. To design computationally efficient optimal policies, we, therefore, develop a theory based on the high reliability asymptotic scenario, in which the channel reliability probabilities are close to one. We thereby obtain an algorithm of relatively low computational complexity for determining an asymptotically optimal policy. To address the remaining case when the channels are not relatively reliable, we design index-based policies for the risk sensitive case, which extends key ideas for index policies in risk-neutral multi-armed bandit problems. Simulation results are provided to show the effectiveness of our policies.
