This tutorial provides a detailed account of mathematical models that utilize the ubiquitous linear-quadratic (LQ) dose-response framework to guide decisions in the fractionation and modality selection problems. The choice of a modality depends on its physical characteristics and its radiobiological power to damage cells. Radiotherapy can be administered using different modalities such as photons, protons, and carbon ions. This is called the optimal fractionation problem, and has been studied clinically for over a hundred years. The key challenge on this temporal side is to choose an optimal number of fractions and the corresponding dosing schedule. This gives the healthy tissue some time to recover between sessions, as it possesses better damage-repair capabilities than the tumor. The temporal component of the problem involves breaking the total planned dose into several treatment sessions called fractions, which are administered over multiple weeks. The radiation intensity profile is then optimized to meet this treatment protocol as closely as possible. The spatial component involves prescribing a high dose to the tumor and putting upper limits on the dose delivered to the healthy anatomies. This is attempted via spatial localization of radiation dose, temporal dispersion of radiation dose, and radiation modality selection. The goal in radiotherapy for cancer is to maximize tumor-kill while limiting toxic effects on nearby healthy anatomies. Response-guided Dosing in Cancer Radiotherapy He currently serves as an associate editor for Operations Research. Sevcik Outstanding Student Paper Award at ACM SIGMETRICS (2013), and the ACM SIGMETRICS Rising Star Research Award (2020). Nicholson Student Paper Competition (2011), Best Paper Award and Kenneth C. He is a first-place recipient of the INFORMS George E. His research focuses on understanding fundamental properties and design principles of large-scale stochastic systems using tools from probability theory and optimization, with applications in queueing networks, privacy, and machine learning. Born in Suzhou, China, he received a BS degree in electrical engineering (2009) from the University of Illinois Urbana-Champaign, and a PhD degree in electrical engineering and computer science (2014) from the Massachusetts Institute of Technology. Kuang Xu is an associate professor of operations, information and technology at Stanford’s Graduate School of Business, and associate professor by courtesy with the Electrical Engineering Department, Stanford University. He has won best paper awards at the ACM SIGMETRICS conference and was awarded the 2018 Erlang Prize by the INFORMS Applied Probability Society. He is an associate editor for the journals Operations Research, Operations Research Letters, and Stochastic Systems. His is interested in all aspects of applied probability, and his research principally concerns the decentralized minimization of congestion in networks. Neil Walton is a reader in mathematics at the University of Manchester. Finally, we review recent advances in the theory of reinforcement learning and queueing, as well as provide discussion of current research challenges. Here we contrast the roles of epistemic information (information on uncertain parameters) and aleatoric information (information on an uncertain state). Next, we discuss the role of state information in improved decision making. As an example, we show how queue size regret can be bounded when applying a perceptron algorithm to classify service. We then discuss the requirements of statistical learning for service parameter estimation. This connects queueing theoretic results with adversarial learning.
We prove that the MaxWeight policy is an application of Blackwell’s Approachability Theorem. We present observations and new results that help rationalize the application of these areas to queueing systems. In recent years, techniques from supervised learning, online learning and reinforcement learning have been applied to queueing systems supported by the increasing role of information in decision making. We review the role of information and learning in the stability and optimization of queueing systems. Learning and Information in Stochastic Networks and Queues