Delay Constrained Scheduling over Fading Channels: Optimal Policies for Monomial Energy-Cost Functions

A point-to-point discrete-time scheduling problem of transmitting $B$ information bits within $T$ hard delay deadline slots is considered assuming that the underlying energy-bit cost function is a convex monomial. The scheduling objective is to minimize the expected energy expenditure while satisfying the deadline constraint based on information about the unserved bits, channel state/statistics, and the remaining time slots to the deadline. At each time slot, the scheduling decision is made without knowledge of future channel state, and thus there is a tension between serving many bits when the current channel is good versus leaving too many bits for the deadline. Under the assumption that no other packet is scheduled concurrently and no outage is allowed, we derive the optimal scheduling policy. Furthermore, we also investigate the dual problem of maximizing the number of transmitted bits over $T$ time slots when subject to an energy constraint.Comment: submitted to the IEEE ICC 200

A Dynamic Boundary Guarding Problem with Translating Targets

We introduce a problem in which a service vehicle seeks to guard a deadline (boundary) from dynamically arriving mobile targets. The environment is a rectangle and the deadline is one of its edges. Targets arrive continuously over time on the edge opposite the deadline, and move towards the deadline at a fixed speed. The goal for the vehicle is to maximize the fraction of targets that are captured before reaching the deadline. We consider two cases; when the service vehicle is faster than the targets, and; when the service vehicle is slower than the targets. In the first case we develop a novel vehicle policy based on computing longest paths in a directed acyclic graph. We give a lower bound on the capture fraction of the policy and show that the policy is optimal when the distance between the target arrival edge and deadline becomes very large. We present numerical results which suggest near optimal performance away from this limiting regime. In the second case, when the targets are slower than the vehicle, we propose a policy based on servicing fractions of the translational minimum Hamiltonian path. In the limit of low target speed and high arrival rate, the capture fraction of this policy is within a small constant factor of the optimal.Comment: Extended version of paper for the joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conferenc

Energy Optimal Transmission Scheduling in Wireless Sensor Networks

One of the main issues in the design of sensor networks is energy efficient communication of time-critical data. Energy wastage can be caused by failed packet transmission attempts at each node due to channel dynamics and interference. Therefore transmission control techniques that are unaware of the channel dynamics can lead to suboptimal channel use patterns. In this paper we propose a transmission controller that utilizes different "grades" of channel side information to schedule packet transmissions in an optimal way, while meeting a deadline constraint for all packets waiting in the transmission queue. The wireless channel is modeled as a finite-state Markov channel. We are specifically interested in the case where the transmitter has low-grade channel side information that can be obtained based solely on the ACK/NAK sequence for the previous transmissions. Our scheduler is readily implementable and it is based on the dynamic programming solution to the finite-horizon transmission control problem. We also calculate the information theoretic capacity of the finite state Markov channel with feedback containing different grades of channel side information including that, obtained through the ACK/NAK sequence. We illustrate that our scheduler achieves a given throughput at a power level that is fairly close to the fundamental limit achievable over the channel.Comment: Accepted for publication in the IEEE Transactions on Wireless Communication

Timely-Throughput Optimal Scheduling with Prediction

Motivated by the increasing importance of providing delay-guaranteed services in general computing and communication systems, and the recent wide adoption of learning and prediction in network control, in this work, we consider a general stochastic single-server multi-user system and investigate the fundamental benefit of predictive scheduling in improving timely-throughput, being the rate of packets that are delivered to destinations before their deadlines. By adopting an error rate-based prediction model, we first derive a Markov decision process (MDP) solution to optimize the timely-throughput objective subject to an average resource consumption constraint. Based on a packet-level decomposition of the MDP, we explicitly characterize the optimal scheduling policy and rigorously quantify the timely-throughput improvement due to predictive-service, which scales as $\Theta(p\left[C_{1}\frac{(a-a_{\max}q)}{p-q}\rho^{\tau}+C_{2}(1-\frac{1}{p})\right](1-\rho^{D}))$, where $a, a_{\max}, \rho\in(0, 1), C_1>0, C_2\ge0$ are constants, $p$ is the true-positive rate in prediction, $q$ is the false-negative rate, $\tau$ is the packet deadline and $D$ is the prediction window size. We also conduct extensive simulations to validate our theoretical findings. Our results provide novel insights into how prediction and system parameters impact performance and provide useful guidelines for designing predictive low-latency control algorithms.Comment: 14 pages, 7 figure

Proactive Location-Based Scheduling of Delay-Constrained Traffic Over Fading Channels

In this paper, proactive resource allocation based on user location for point-to-point communication over fading channels is introduced, whereby the source must transmit a packet when the user requests it within a deadline of a single time slot. We introduce a prediction model in which the source predicts the request arrival $T_p$ slots ahead, where $T_p$ denotes the prediction window (PW) size. The source allocates energy to transmit some bits proactively for each time slot of the PW with the objective of reducing the transmission energy over the non-predictive case. The requests are predicted based on the user location utilizing the prior statistics about the user requests at each location. We also assume that the prediction is not perfect. We propose proactive scheduling policies to minimize the expected energy consumption required to transmit the requested packets under two different assumptions on the channel state information at the source. In the first scenario, offline scheduling, we assume the channel states are known a-priori at the source at the beginning of the PW. In the second scenario, online scheduling, it is assumed that the source has causal knowledge of the channel state. Numerical results are presented showing the gains achieved by using proactive scheduling policies compared with classical (reactive) networks. Simulation results also show that increasing the PW size leads to a significant reduction in the consumed transmission energy even with imperfect prediction.Comment: Conference: VTC2016-Fall, At Montreal-Canad

Finite Horizon Throughput Maximization for a Wirelessly Powered Device over a Time Varying Channel

In this work, we consider an energy harvesting device (EHD) served by an access point with a single antenna that is used for both wireless power transfer (WPT) and data transfer. The objective is to maximize the expected throughput of the EHD over a finite horizon when the channel state information is only available causally. The EHD is energized by WPT for a certain duration, which is subject to optimization, and then, EHD transmits its information bits to the AP until the end of the time horizon by employing optimal dynamic power allocation. The joint optimization problem is modeled as a dynamic programming problem. Based on the characteristic of the problem, we prove that a time dependent threshold type structure exists for the optimal WPT duration, and we obtain closed form solution to the dynamic power allocation in the uplink period.Comment: arXiv admin note: substantial text overlap with arXiv:1804.0183

Optimal Energy Allocation For Delay-Constrained Traffic Over Fading Multiple Access Channels

In this paper, we consider a multiple-access fading channel where $N$ users transmit to a single base station (BS) within a limited number of time slots. We assume that each user has a fixed amount of energy available to be consumed over the transmission window. We derive the optimal energy allocation policy for each user that maximizes the total system throughput under two different assumptions on the channel state information. First, we consider the offline allocation problem where the channel states are known a priori before transmission. We solve a convex optimization problem to maximize the sum-throughput under energy and delay constraints. Next, we consider the online allocation problem, where the channels are causally known to the BS and obtain the optimal energy allocation via dynamic programming when the number of users is small. We also develop a suboptimal resource allocation algorithm whose performance is close to the optimal one. Numerical results are presented showing the superiority of the proposed algorithms over baseline algorithms in various scenarios.Comment: IEEE Global Communications Conference: Wireless Communications (Globecom2016 WC