Index Policies for Optimal Mean-Variance Trade-Off of Inter-delivery Times in Real-Time Sensor Networks

A problem of much current practical interest is the replacement of the wiring infrastructure connecting approximately 200 sensor and actuator nodes in automobiles by an access point. This is motivated by the considerable savings in automobile weight, simplification of manufacturability, and future upgradability. A key issue is how to schedule the nodes on the shared access point so as to provide regular packet delivery. In this and other similar applications, the mean of the inter-delivery times of packets, i.e., throughput, is not sufficient to guarantee service-regularity. The time-averaged variance of the inter-delivery times of packets is also an important metric. So motivated, we consider a wireless network where an Access Point schedules real-time generated packets to nodes over a fading wireless channel. We are interested in designing simple policies which achieve optimal mean-variance tradeoff in interdelivery times of packets by minimizing the sum of time-averaged means and variances over all clients. Our goal is to explore the full range of the Pareto frontier of all weighted linear combinations of mean and variance so that one can fully exploit the design possibilities. We transform this problem into a Markov decision process and show that the problem of choosing which node's packet to transmit in each slot can be formulated as a bandit problem. We establish that this problem is indexable and explicitly derive the Whittle indices. The resulting Index policy is optimal in certain cases. We also provide upper and lower bounds on the cost for any policy. Extensive simulations show that Index policies perform better than previously proposed policies

A High Reliability Asymptotic Approach for Packet Inter-Delivery Time Optimization in Cyber-Physical Systems

In cyber-physical systems such as automobiles, measurement data from sensor nodes should be delivered to other consumer nodes such as actuators in a regular fashion. But, in practical systems over unreliable media such as wireless, it is a significant challenge to guarantee small enough inter-delivery times for different clients with heterogeneous channel conditions and inter-delivery requirements. In this paper, we design scheduling policies aiming at satisfying the inter-delivery requirements of such clients. We formulate the problem as a risk-sensitive Markov Decision Process (MDP). Although the resulting problem involves an infinite state space, we first prove that there is an equivalent MDP involving only a finite number of states. Then we prove the existence of a stationary optimal policy and establish an algorithm to compute it in a finite number of steps. However, the bane of this and many similar problems is the resulting complexity, and, in an attempt to make fundamental progress, we further propose a new high reliability asymptotic approach. In essence, this approach considers the scenario when the channel failure probabilities for different clients are of the same order, and asymptotically approach zero. We thus proceed to determine the asymptotically optimal policy: in a two-client scenario, we show that the asymptotically optimal policy is a "modified least time-to-go" policy, which is intuitively appealing and easily implementable; in the general multi-client scenario, we are led to an SN policy, and we develop an algorithm of low computational complexity to obtain it. Simulation results show that the resulting policies perform well even in the pre-asymptotic regime with moderate failure probabilities