Abstract

1. Academia Fixing: Fix all ’s for which Fix the rates in all the slots with no extra energy preceding Fix the rates off all the descendants of ’s fixed in 1. and 2., in the same time slots The sink Maximization: For each node , find the maximum supported rate, assuming ’s descendants can support the same rate Return the minimum rate from 1. • Finding Single-path Routes • An approximation to a “good” routing tree is NP-hard to determine • Finding a “good” single-path routing is NP-hard • However, we have designed an algorithm that determines(in polynomial time) a time-invariable routing that maximizes the minimum sensing rate Abstract We study max-min fair rate allocation and routing in energy harvesting networks where fairness is required among both the nodes and the time slots. Unlike most previous work on fairness, we focus on multihop topologies and consider different routing methods. We assume a predictable energy profile and focus on the design of efficient and optimal algorithms. Our analysis provides insights into the problem structure and can be applied to other related fairness problems. . 8 6 7 4 5 9 10 • Routing Topologies 1 2 3 T-1 T , for , for =1 =2 11 … … Single-path Routing Multi-path Routing Routing Tree … Algorithms for Max-min Fair Rate Assignment and Routing in Energy Harvesting NetworksJelena Marašević1, Cliff Stein2, Gil Zussman11Department of Electrical Engineering,2Department of Industrial Engineeringand Operations Research,Columbia University, New York, NY Motivation: IoT . . System Model • Restructuring constraints get a packing problem • Feasible rates: at least as hard as feasible 2-commodity flow • Unlikely to be solved optimally without linear programming • PTAS design: • Maximization: packing algorithm [5] + structural properties • Fixing: 1 LP over current solution’s -neighborhood Routing can be time-variable (change from one time slot to another ), or time-invariable (remain fixed over time slots ) • Networks of devices that traditionally have not been networked. Fractional (Multi-path) Routing • A sink • nodes • links • time slots • ’s known • Battery capacity: • Rates: Future Work • Fairness guarantees with a: • Distributed algorithm? (Challenge: communication overhead) • Online algorithm? (Challenge: small prediction window) • Different types of fairness: • Proportional fairness? • General -fairness? Rate Assignment and Routing Algorithms • Water-filling framework; max-min fairness lexicographic maximization Challenge: guaranteed convergence time • Rate Assignment in a Single-path Routing Importance of Fairness References [1] B. Radunovic and J.-Y. L. Boudec. A unified framework for max-min and min-max fairness with applications. IEEE/ACM Trans. Netw.,15(5):1073-1083, Oct. 2007. [2] R. Srivastava and C. E. Koksal. Basic performance limits and tradeoffs in energy- harvesting sensor nodes with finite data and energy storage, IEEE/ACM Trans. Netw., 21(4):1049-1062, 2013. [3] B. Gurakan, O. Ozel, J. Yang, and S. Ulukus. Energy cooperation in energy harvesting two-way communications. In Proc. IEEE ICC, 2013. [4] S. Sarkar, M. Khouzani, and K. Kar. Optimal routing and scheduling in multihop wireless renewable energy networks. IEEE Trans. Autom. Control, 58(7):1792-1798, 2013. [5] S. Plotkin., D. Shmoys, and É. Tardos. Fast approximation algorithms for fractional packing and covering problems. Math. of OR,20.2 (1995): 257-301. Total throughput maximization: 2 • Nodes: • 2 gets 0 rate • gets 0 rate • Time: • High rates at the peak, zero over night descendants We are grateful to Professor Mihalis Yannakakis for useful discussions. This research was supported in part by NSF grants CCF-1349602, CCF-09-64497, and CNS-10-54856. Poster based on: J. Marašević, C. Stein, G. Zussman. Max-min Fair Rate Allocation and Routing in Energy Harvesting Networks: Algorithmic Analysis. ACM MobiHoc’14, 2014.