# Delay constrained scheduling in wireless networks and smart grids

#### Abstract

Delay constrained scheduling is a decision making process that allocates resources among a variety of tasks with delay constraints. It has extensive applications in real systems such as wireless networks and smart grids. In wireless networks, the resources are the wireless channels including time, frequency, etc., and the tasks are the transmissions of packets from different users. An ideal scheduling algorithm should properly schedule the transmissions of packets to achieve both high throughput and low delay. In smart grids, the resources are the traditional energy generated by electric generators plus the renewable energy, and the tasks are the non-deferrable background demand that needs to be served immediately plus the deferrable demand that needs to be served within a time window. An ideal scheduling algorithm should properly arrange the service of the deferrable demand to minimize the energy generating cost and improve the stability of the grid. This thesis contains two parts. In the first part, we study the problem of link scheduling for wireless networks with stringent delay constraints. We first study how to optimize delay performance under stochastic arrivals. Specifically, we are interested in algorithms that maximize the asymptotic decay-rate of the probability with which the maximum end-to-end backlog among all flows exceeds a threshold, as the threshold becomes large. We provide both positive and negative results in this direction. By minimizing the drift of the maximum end-to-end backlog in the converge-cast on a tree, we design an algorithm, called Largest-Weight-First(LWF), that achieves the optimal asymptotic decay-rate for the overflow probability of the maximum end-to-end backlog as the threshold becomes large. However, such a drift minimization algorithm may not exist for general networks. We provide an example in which no algorithm can minimize the drift of the maximum end-to-end backlog. We then study how to deal with hard deadlines for wireless applications like video streaming, video conferencing, etc. Our objective here is to develop deadline-aware algorithms that can optimize the total system reward obtained from packets meeting their deadlines. Motivated by a heuristic utility-based approach, we propose a class of threshold-based rate-control and wireless scheduling policies that can respect the deadline constraints and approach the optimal system reward asymptotically as the system size increases. We also propose a distributed realization of our threshold-based policies that can be easily implemented in practical scenarios. In the second part, we study the scheduling problem in Electrical Vehicle (EV) charging for an aggregator with its own background demand, renewable energy and EV-charging jobs. EV-charging jobs represent a large class of deferrable demand. Specifically, each EV requests a certain amount of energy that needs to be charged before a deadline. The goal of the aggregator is to control the charging rates of electric vehicles to reduce its peak demand over the decision horizon subject to the uncertainty of the renewable energy. A key challenge that the aggregator faces in this scheduling problem is that there exists significant uncertainty in the future background demand, the future renewable energy supply, and the future arrivals of EV charging jobs. In contrast to existing approaches that either require precise future knowledge or do not make use of any future information at all, we consider a more practical scenario where the aggregator can obtain a limited amount of future knowledge. Specifically, we propose two different uncertainty models to capture partial future knowledge and study how limited future knowledge can improve the performance of the online algorithms. We provide a general and systematic framework for determining the optimal competitive ratios for arbitrary parameter settings under different uncertainty models. Such competitive ratios can be used to measure the price of uncertainty in this EV-charging decision-making problem. We are also interested in online algorithms that attain these optimal competitive ratios. We first propose an EPS algorithm that has optimal competitive ratio. However, this online algorithm's average performance is very poor. In fact, there is a fundament disadvantage of general competitive-online-algorithm design, i.e., the design of most competitive online algorithms focuses only on the worst-case performance, and an algorithm with good competitive ratio could have very poor average-case performance. We then design an algorithm-robustification procedure that can convert an algorithm with good average-case performance to an algorithm with both good average-case performance and optimal worst-case guarantee. Our numerical results compare the price of uncertainty under different uncertainty models with different parameter settings, and also demonstrate the effectiveness of the algorithm-robustification procedure in online algorithm design.

#### Degree

Ph.D.

#### Advisors

Lin, Purdue University.

#### Subject Area

Electrical engineering|Energy

Off-Campus Purdue Users:

To access this dissertation, please **log in to our
proxy server**.