Scheduling in Cyber-Physical Systems

Cyber-physical systems (CPS) refer to a promising class of systems featuring intimate coupling between the ‘cyber’ intelligence and the ‘physical’ world. Enabled by the ubiquitous availability of computation and communication capabilities, such systems are widely envisioned to redefine the way that people interact with the physical world, similar to the revolutionary role of internet in transforming how people interact with each other. As the whole society becomes increasingly dependent on such systems, it is crucial to develop a theory to understand and optimize the CPS in a systematic manner.

This thesis contributes to the foundations of CPS by identifying and addressing a general class of scheduling-type applications for a vital class of CPS, the physical networks (PhyNets). Different from the abstract CPS, a PhyNet has a graph-type physical part, which represents the local interactions among users in the system, as specified by certain well-known physical laws. Thus, it is very promising to develop efficient distributed algorithms in PhyNets with proper communication infrastructure and protocols, due to the physical graph structure. The ‘scheduling’ refers to the applications where joint actions of all users are coordinated, in order to allocate system resources to satisfy certain long term and uncertain demands. Important applications of the scheduling in PhyNets include packet scheduling in wireless networks, coordinated charging of electric vehicles (EV) in electric power grids, and workload scheduling in data centers. In this thesis, we assume very mild assumptions on the stochastic processes, and provide probabilistic scheduling performance guarantees using the technique of fluid limits.

In this thesis, we will investigate a broad range of scheduling algorithms and discuss their performance and distributed implementation. We first investigate the class of optimal scheduling algorithms in the dynamic regime, where the system modes change randomly with time. We focus on augmented max-weight scheduling schemes, which choose a max-weight schedule, where the weight is specified by queue lengths. Two scenarios are considered in this case. For the first scenario, we assume the scheduler has asymptotic knowledge about the optimal cost, and propose virtual cost queue based max-weight scheduling schemes. We prove cost optimality and rate stability results using fluid limits. For the second scenario, we assume no knowledge on optimal cost, and adopt a Lyapunov optimization based approach. We demonstrate the asymptotic optimality and provide bounds on the average queue lengths. Finally, we apply the augmented max-weight algorithms to the important application of coordinated EV charging in power systems.

We next consider the class of optimal scheduling algorithms in the quasi-static regime, where the system modes remain constant for the scheduling application. The quasi-static property is promising for efficient scheduling design by allowing the system to ‘memorize’ good schedules. We propose a simplex algorithm based scheduling scheme, and prove that it is asymptotically throughput optimal. For the important application of packet scheduling in wireless networks, we show that the simplex scheduling can be implemented in a distributed manner with average consensus and carrier sensing multiple access (CSMA) mechanisms. We also demonstrate that it achieves significant steady-state delay reduction compared to the popular throughput optimal distributed adaptive CSMA schemes, by successfully avoiding the random walk behavior associated with the distributed CSMA.

Finally, we investigate the performance of suboptimal scheduling schemes. We will discuss the performance of a class of interesting scheduling schemes, maximal scheduling. A maximal scheduling algorithm only involves simple and local coordination among users, and therefore has low complexity and is easy for distributed implementation. We propose a tight lower bound throughput region for maximal scheduling algorithms, and show that it can achieve a certain fraction of the optimal region. We also investigate the performance improvement on maximal scheduling. In particular, for packet scheduling in wireless networks, we propose a static priority assisted maximal scheduling scheme. We show that the optimal static priority assignment can be computed with low complexity in an online manner, and that the combined priority assignment and maximal scheduling achieve dramatic throughput improvement over the conventional maximal scheduling