Optimal provision of distributed reserves under dynamic energy service preferences

We propose and solve a stochastic dynamic programming (DP) problem addressing the optimal provision of regulation service reserves (RSR) by controlling dynamic demand preferences in smart buildings. A major contribution over past dynamic pricing work is that we pioneer the relaxation of static, uniformly distributed utility of demand. In this paper we model explicitly the dynamics of energy service preferences leading to a non-uniform and time varying probability distribution of demand utility. More explicitly, we model active and idle duty cycle appliances in a smart building as a closed queuing system with price-controlled arrival rates into the active appliance queue. Focusing on cooling appliances, we model the utility associated with the transition from idle to active as a non-uniform time varying function. We (i) derive an analytic characterization of the optimal policy and the differential cost function, and (ii) prove optimal policy monotonicity and value function convexity. These properties enable us to propose and implement a smart assisted value iteration (AVI) algorithm and an approximate DP (ADP) that exploits related functional approximations. Numerical results demonstrate the validity of the solution techniques and the computational advantage of the proposed ADP on realistic, large-state-space problems

A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets

Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net model and several translations to networks of timed automata have been proposed for this model. We present a direct, DBM-based algorithm for forward reachability analysis of bounded TAPNs extended with transport arcs, inhibitor arcs and age invariants. We also give a complete proof of its correctness, including reduction techniques based on symmetries and extrapolation. Finally, we augment the algorithm with a novel state-space reduction technique introducing a monotonic ordering on markings and prove its soundness even in the presence of monotonicity-breaking features like age invariants and inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and the experimental results document an encouraging performance compared to verification approaches that translate TAPN models to UPPAAL timed automata.Comment: In Proceedings SSV 2012, arXiv:1211.587

Adaptive Network Coding for Scheduling Real-time Traffic with Hard Deadlines

We study adaptive network coding (NC) for scheduling real-time traffic over a single-hop wireless network. To meet the hard deadlines of real-time traffic, it is critical to strike a balance between maximizing the throughput and minimizing the risk that the entire block of coded packets may not be decodable by the deadline. Thus motivated, we explore adaptive NC, where the block size is adapted based on the remaining time to the deadline, by casting this sequential block size adaptation problem as a finite-horizon Markov decision process. One interesting finding is that the optimal block size and its corresponding action space monotonically decrease as the deadline approaches, and the optimal block size is bounded by the "greedy" block size. These unique structures make it possible to narrow down the search space of dynamic programming, building on which we develop a monotonicity-based backward induction algorithm (MBIA) that can solve for the optimal block size in polynomial time. Since channel erasure probabilities would be time-varying in a mobile network, we further develop a joint real-time scheduling and channel learning scheme with adaptive NC that can adapt to channel dynamics. We also generalize the analysis to multiple flows with hard deadlines and long-term delivery ratio constraints, devise a low-complexity online scheduling algorithm integrated with the MBIA, and then establish its asymptotical throughput-optimality. In addition to analysis and simulation results, we perform high fidelity wireless emulation tests with real radio transmissions to demonstrate the feasibility of the MBIA in finding the optimal block size in real time.Comment: 11 pages, 13 figure

Energy Harvesting Networks with General Utility Functions: Near Optimal Online Policies

We consider online scheduling policies for single-user energy harvesting communication systems, where the goal is to characterize online policies that maximize the long term average utility, for some general concave and monotonically increasing utility function. In our setting, the transmitter relies on energy harvested from nature to send its messages to the receiver, and is equipped with a finite-sized battery to store its energy. Energy packets are independent and identically distributed (i.i.d.) over time slots, and are revealed causally to the transmitter. Only the average arrival rate is known a priori. We first characterize the optimal solution for the case of Bernoulli arrivals. Then, for general i.i.d. arrivals, we first show that fixed fraction policies [Shaviv-Ozgur] are within a constant multiplicative gap from the optimal solution for all energy arrivals and battery sizes. We then derive a set of sufficient conditions on the utility function to guarantee that fixed fraction policies are within a constant additive gap as well from the optimal solution.Comment: To appear in the 2017 IEEE International Symposium on Information Theory. arXiv admin note: text overlap with arXiv:1705.1030

Bounds on entanglement distillation and secret key agreement for quantum broadcast channels

The squashed entanglement of a quantum channel is an additive function of quantum channels, which finds application as an upper bound on the rate at which secret key and entanglement can be generated when using a quantum channel a large number of times in addition to unlimited classical communication. This quantity has led to an upper bound of $\log((1+\eta)/(1-\eta))$ on the capacity of a pure-loss bosonic channel for such a task, where $\eta$ is the average fraction of photons that make it from the input to the output of the channel. The purpose of the present paper is to extend these results beyond the single-sender single-receiver setting to the more general case of a single sender and multiple receivers (a quantum broadcast channel). We employ multipartite generalizations of the squashed entanglement to constrain the rates at which secret key and entanglement can be generated between any subset of the users of such a channel, along the way developing several new properties of these measures. We apply our results to the case of a pure-loss broadcast channel with one sender and two receivers.Comment: 35 pages, 1 figure, accepted for publication in IEEE Transactions on Information Theor

Monotonic Prefix Consistency in Distributed Systems

We study the issue of data consistency in distributed systems. Specifically, we consider a distributed system that replicates its data at multiple sites, which is prone to partitions, and which is assumed to be available (in the sense that queries are always eventually answered). In such a setting, strong consistency, where all replicas of the system apply synchronously every operation, is not possible to implement. However, many weaker consistency criteria that allow a greater number of behaviors than strong consistency, are implementable in available distributed systems. We focus on determining the strongest consistency criterion that can be implemented in a convergent and available distributed system that tolerates partitions. We focus on objects where the set of operations can be split into updates and queries. We show that no criterion stronger than Monotonic Prefix Consistency (MPC) can be implemented.Comment: Submitted pape

Broadcasting with an Energy Harvesting Rechargeable Transmitter

In this paper, we investigate the transmission completion time minimization problem in a two-user additive white Gaussian noise (AWGN) broadcast channel, where the transmitter is able to harvest energy from the nature, using a rechargeable battery. The harvested energy is modeled to arrive at the transmitter randomly during the course of transmissions. The transmitter has a fixed number of packets to be delivered to each receiver. Our goal is to minimize the time by which all of the packets for both users are delivered to their respective destinations. To this end, we optimize the transmit powers and transmission rates intended for both users. We first analyze the structural properties of the optimal transmission policy. We prove that the optimal total transmit power has the same structure as the optimal single-user transmit power. We also prove that there exists a cut-off power level for the stronger user. If the optimal total transmit power is lower than this cut-off level, all transmit power is allocated to the stronger user, and when the optimal total transmit power is larger than this cut-off level, all transmit power above this level is allocated to the weaker user. Based on these structural properties of the optimal policy, we propose an algorithm that yields the globally optimal off-line scheduling policy. Our algorithm is based on the idea of reducing the two-user broadcast channel problem into a single-user problem as much as possible.Comment: Submitted to IEEE Transactions on Wireless Communications, October 201