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

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

Theory and Applications of Robust Optimization

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.Comment: 50 page

Predictable Real-Time Wireless Networking For Sensing And Control

Towards the end goal of providing predictable real-time wireless networking for sensing and control, we have developed a real-time routing protocol MTA that predictably delivers data by their deadlines, and a scheduling protocol PRKS to ensure a certain link reliability based on the Physical-ratio-K (PRK) model, which is both realistic and amenable for distributed implementation, and a greedy scheduling algorithm to deliver as many packets as possible to the sink by a deadline in lossy multi-hop wireless sensor networks. Real-time routing is a basic element of closed-loop, real-time sensing and control, but it is challenging due to dynamic, uncertain link/path delays. The probabilistic nature of link/path delays makes the basic problem of computing the probabilistic distribution of path delays NP-hard, yet quantifying probabilistic path delays is a basic element of real-time routing and may well have to be executed by resource-constrained devices in a distributed manner; the highly-varying nature of link/path delays makes it necessary to adapt to in-situ delay conditions in real-time routing, but it has been observed that delay-based routing can lead to instability, estimation error, and low data delivery performance in general. To address these challenges, we propose the Multi-Timescale Estimation (MTE) method; by accurately estimating the mean and variance of per-packet transmission time and by adapting to fast-varying queueing in an accurate, agile manner, MTE enables accurate, agile, and efficient estimation of probabilistic path delay bounds in a distributed manner. Based on MTE, we propose the Multi-Timescale Adaptation (MTA) routing protocol; MTA integrates the stability of an ETX-based directed-acyclic-graph (DAG) with the agility of spatiotemporal data flow control within the DAG to ensure real-time data delivery in the presence of dynamics and uncertainties. We also address the challenges of implementing MTE and MTA in resource-constrained devices such as TelosB motes. We evaluate the performance of MTA using the NetEye and Indriya sensor network testbeds. We find that MTA significantly outperforms existing protocols, e.g., improving deadline success ratio by 89% and reducing transmission cost by a factor of 9.7. Predictable wireless communication is another basic enabler for networked sensing and control in many cyber-physical systems, yet co-channel interference remains a major source of uncertainty in wireless communication. Integrating the protocol model\u27s locality and the physical model\u27s high fidelity, the physical-ratio-K (PRK) interference model bridges the gap between the suitability for distributed implementation and the enabled scheduling performance, and it is expected to serve as a foundation for distributed, predictable interference control. To realize the potential of the PRK model and to address the challenges of distributed PRK-based scheduling, we design protocol PRKS. PRKS uses a control-theoretic approach to instantiating the PRK model according to in-situ network and environmental conditions, and, through purely local coordination, the distributed controllers converge to a state where the desired link reliability is guaranteed. PRKS uses local signal maps to address the challenges of anisotropic, asymmetric wireless communication and large interference range, and PRKS leverages the different timescales of PRK model adaptation and data transmission to decouple protocol signaling from data transmission. Through sensor network testbed-based measurement study, we observe that, unlike existing scheduling protocols where link reliability is unpredictable and the reliability requirement satisfaction ratio can be as low as 0%, PRKS enables predictably high link reliability (e.g., 95%) in different network and environmental conditions without a priori knowledge of these conditions, and, through local distributed coordination, PRKS achieves a channel spatial reuse very close to what is enabled by the state-of-the-art centralized scheduler while ensuring the required link reliability. Ensuring the required link reliability in PRKS also reduces communication delay and improves network throughput. We study the problem of scheduling packet transmissions to maximize the expected number of packets collected at the sink by a deadline in a multi-hop wireless sensor network with lossy links. Most existing work assumes error-free transmissions when interference constraints are complied, yet links can be unreliable due to external interference, shadow- ing, and fading in harsh environments in practice. We formulate the problem as a Markov decision process, yielding an optimal solution. However, the problem is computationally in- tractable due to the curse of dimensionality. Thus, we propose the efficient and greedy Best Link First Scheduling (BLF) protocol. We prove it is optimal for the single-hop case and provide an approach for distributed implementation. Extensive simulations show it greatly enhances real-time data delivery performance, increasing deadline catch ratio by up to 50%, compared with existing scheduling protocols in a wide range of network and traffic settings

Real-Time Guarantees For Wireless Networked Sensing And Control

Wireless networks are increasingly being explored for mission-critical sensing and control in emerging domains such as connected and automated vehicles, Industrial 4.0, and smart city. In wireless networked sensing and control (WSC) systems, reliable and real- time delivery of sensed data plays a crucial role for the control decision since out-of-date information will often be irrelevant and even leads to negative effects to the system. Since WSC differs dramatically from the traditional real-time (RT) systems due to its wireless nature, new design objective and perspective are necessary to achieve real-time guarantees. First, we proposed Optimal Node Activation Multiple Access (ONAMA) scheduling protocol that activates as many nodes as possible while ensuring transmission reliability (in terms of packets delivery ratio). We implemented and tested ONAMA on two testbeds both with 120+ sensor nodes. Second, we proposed algorithms to address the problem of clustering heterogeneous reliability requirements into a limit set of service levels. Our solutions are optimal, and they also provide guaranteed reliability, which is critical for wireless sensing and control. Third, we proposed a probabilistic real-time wireless communication framework that effectively integrates real-time scheduling theory with wireless communication. The per- packet probabilistic real-time QoS was formally modeled. By R3 mapping, the upper-layer requirement and the lower-layer link reliability are translated into the number of trans- mission opportunities needed. By optimal real-time communication scheduling as well as admission test and traffic period optimization, the system utilization is maximized while the schedulability is maintained. Finally, we further investigated the problem of how to minimize delay variation (i.e., jitter) while ensuring that packets are delivered by their deadlines