Probability in the Engineering and Informational Sciences, page 1 of 28, 2017. doi:10.1017/S0269964817000080 FINITE CAPACITY ENERGY PACKET NETWORKS YASIN MURAT KADIOGLU Intelligent Systems and Networks Group, Department of Electrical and Electronic Engineering, Imperial College, London SW7 2BT, UK E-mail: y.kadioglu14@imperial.ac.uk This paper surveys research on mathematical models that predict the performance of dig- ital devices that operate with intermittent energy sources. The approach taken in this work is based on the “Energy Packet Network” paradigm where the arrival of data to be processed or transmitted, and the energy to operate the system, are modeled as dis- crete random processes. Our assumption is that these devices will capture energy from intermittent ambient sources such as vibrations, heat or light, and capture it onto electri- cal energy that may be stored in batteries or capacitors. The devices consume this energy intermittently for processing and for wired or wireless transmission. Thus, both the arrival of energy to the device, and the devices workload, are modeled as random processes. Based on these assumptions, we discuss probability models based on Markov chains that can be used to predict the effective rates at which such devices operate. We also survey related work that models networks of such systems. Keywords: data packets, energy harvesting, energy packet networks, markov chains, random walk 1. INTRODUCTION Energy is a primary driver for the manufacturing and operation of information processing and transmission devices such as computers, network nodes, wireless receivers and trans- mitters, and so on. Thus, there has been increasing concern about the massive amount of electrical energy that is being used in this context (see, e.g., Gelenbe and Caseau [17]), which is approaching 10% of the total amount of electricity consumed worldwide. In addition, there has been much work done on the design of systems that can exploit “free” energy captured from the ambient environment via energy harvesting (EH) (see, e.g., Rodopln and Meng [35], Meshkati et al. [33], Alippi and Galperti [2], Seah, Eu, and Tan [36]) from thermal, light, chemical, vibrational, or electromagnetic sources and converted into electrical energy. Of course, when both the workload in a computer system and the net- work are intermittent, and the process of acquiring energy to operate them and service the workload is intermittent, it is important to investigate such systems in terms of stochastic processes. Significant work by Berl et al. [3] has addressed techniques to reduce or optimize the energy consumption of Cloud servers, which are major consumers of electricity, and energy c  Cambridge University Press 2017 0269-9648/17 $25.00 1 available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S0269964817000080 Downloaded from https:/www.cambridge.org/core. Imperial College London Library, on 02 Jun 2017 at 14:18:34, subject to the Cambridge Core terms of use,