Optimal Rate Schedules with Data Sharing in Energy Harvesting Communication Systems
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<p>Performance of O<span class="html-small-caps">nline</span>-S<span class="html-small-caps">elect</span> as the harvestings change.</p> "> Figure 5
<p>Effect of exploiting data sharing as the average harvesting amount/workload changes.</p> ">
Abstract
:1. Introduction
- This paper introduces a rate scheduling problem for energy harvesting wireless devices that transmit required data of requests with the goal of minimizing the completion time. We exploit the data sharing among data requests from the platform, e.g., a participatory sensing system, to actively enhance the energy utilization of the wireless device.
- We first study a closely related min-energy problem that aims to minimize the energy consumption within a given deadline while transmitting all required data. By decomposing the original problem into two simplified known sub-problems, we derive the optimal offline algorithm Bottleneck-Select that minimizes the energy consumption or determines that no feasible solution exists within the given deadline.
- Then, by adopting Bottleneck-Select as a building block, we develop an optimal offline algorithm for the completion time minimization problem. The idea is to use Bottleneck-Select to narrow down the lower bound and upper bound of the minimum completion time, and then precisely locate the optimal solution.
- We also design an event-driven online heuristic algorithm to deal with the dynamic energy and request arrivals. Simulation results validate that its performance is close to the optimal offline solution.
2. Related Work
2.1. Rate-Adaptive Transmission
2.2. Data Sharing
3. Preliminaries
3.1. System Model
3.2. Problem Formulation
3.3. Overview of Our Solutions
4. Min-Energy Rate Schedule under a Given Deadline
4.1. Basic Properties of Optimal Rate Schedule
4.2. Problem Decomposition
4.3. The Bottleneck-Select Algorithm
Algorithm 1 Update() |
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Algorithm 2 Bottleneck-Select () |
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5. Optimal Rate Schedule for Min-T Problem
- is a non-decreasing step function and only changes the rate at harvesting point or arrival point.
- If increases only at an arrival point, then the total transmitted data from this point to the end of the transmission will be equal to the data required at this point;
- if increases only at a harvesting point, then the battery must be used up just right before this point;
- if increases at a point e at which both a task and a harvesting event occur, then either the total transmitted data from this point to the end of transmission will be equal to , or the battery is used up just right before e.
Algorithm 3 Estimate () |
|
Algorithm 4 Locate () |
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6. Online Rate Schedule
Algorithm 5 Online-Select () |
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7. Simulations
- OPT, which is the optimal offline solution returned by the optimal algorithm developed in this work.
- OPT without sharing, which is the optimal offline solution of a variant of the min-T problem that does not consider data sharing [16].
- Jing’s algorithm with sharing, which is an offline algorithm in [16] that is adopted to work in the data sharing scenario by keeping its rate policy unchanged.
- Online-Select without sharing, which is a slightly modified version of our online algorithm Online-Select by simply adding new arrived workloads into the data buffer and transmitting with local optimal rate.
8. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A. Proof of Theorem 2
- (3)
- for all .
References
- Kansal, A.; Hsu, J.; Zahedi, S.; Srivastava, M.B. Power management in energy harvesting sensor networks. Acm Trans. Embedded Comput. Syst. 2007, 6, 32. [Google Scholar] [CrossRef]
- Jiang, X.; Polastre, J.; Culler, D. Perpetual environmentally powered sensor networks. In Proceedings of the Fourth International Symposium on Information Processing in Sensor Networks (IPSN 2005), Los Angeles, CA, USA, 24–27 April 2005; pp. 463–468. [Google Scholar]
- Perton, M.; Audoin, B.; Pan, Y.D.; Rossignol, C. Energy harvesting vibration sources for microsystems applications. Meas. Sci. Technol. 2006, 17, R175–R195. [Google Scholar]
- Nanda, S.; Balachandran, K.; Kumar, S. Adaptation techniques in wireless packet data services. IEEE Commun. Mag. 2000, 38, 54–64. [Google Scholar] [CrossRef]
- Prabhakar, B.; Biyikoglu, E.U.; Gamal, A.E. Energy-efficient transmission over a wireless link via lazy packet scheduling. In Proceedings of the Twentieth Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2001), Anchorage, AK, USA, 22–26 April 2001; Volume 1, pp. 386–394. [Google Scholar]
- Trigoni, N.; Yao, Y.; Demers, A.; Gehrke, J.; Rajaraman, R. Multi-query Optimization for Sensor Networks. Lect. Notes Comput. Sci. 2005, 3560, 307–321. [Google Scholar]
- Kansal, A.; Nath, S.; Liu, J.; Zhao, F. SenseWeb: An Infrastructure for Shared Sensing. IEEE MultiMedia 2007, 14, 8–13. [Google Scholar] [CrossRef]
- Tavakoli, A.; Kansal, A.; Nath, S. On-line sensing task optimization for shared sensors. In Proceedings of the 9th ACM/IEEE International Conference on Information Processing in Sensor Networks, Stockholm, Sweden, 12–16 April 2010; pp. 47–57. [Google Scholar]
- Wu, W.; Wang, J.; Li, M.; Liu, K.; Shan, F.; Luo, J. Energy-efficient Transmission with Data Sharing in Participatory Sensing Systems. IEEE J. Sel. Areas Commun. 2016, 34, 4048–4062. [Google Scholar] [CrossRef]
- Gatzianas, M.; Georgiadis, L.; Tassiulas, L. Control of wireless networks with rechargeable batteries [transactions papers]. IEEE Trans. Wirel. Commun. 2010, 9, 581–593. [Google Scholar] [CrossRef]
- Sharma, V.; Mukherji, U.; Joseph, V.; Gupta, S. Optimal energy management policies for energy harvesting sensor nodes. IEEE Trans. Wirel. Commun. 2010, 9, 1326–1336. [Google Scholar] [CrossRef]
- Vaze, R.; Garg, R.; Pathak, N. Dynamic Power Allocation for Maximizing Throughput in Energy-Harvesting Communication System. IEEE/ACM Trans. Netw. 2014, 22, 1621–1630. [Google Scholar] [CrossRef]
- Wu, W.; Wang, J.; Wang, X.; Shan, F.; Luo, J. Online Throughput Maximization for Energy Harvesting Communication Systems with Battery Overflow. IEEE Trans. Mob. Comput. 2017, 16, 185–197. [Google Scholar] [CrossRef]
- Xu, J.; Zhang, R. Throughput Optimal Policies for Energy Harvesting Wireless Transmitters with Non-Ideal Circuit Power. IEEE J. Sel. Areas Commun. 2014, 32, 322–332. [Google Scholar]
- Yang, J.; Ulukus, S. Transmission completion time minimization in an energy harvesting system. In Proceedings of the 2010 44th Annual Conference on Information Sciences and Systems (CISS), Princeton, NJ, USA, 17–19 March 2010; pp. 1–6. [Google Scholar]
- Yang, J.; Ulukus, S. Optimal Packet Scheduling in an Energy Harvesting Communication System. IEEE Trans. Commun. 2012, 60, 220–230. [Google Scholar] [CrossRef]
- Chen, X.; Wang, X.; Sun, Y. Energy-harvesting powered transmissions of bursty data packets with strict deadlines. In Proceedings of the 2014 IEEE International Conference on Communications (ICC), Sydney, Australia, 10–14 June 2014; pp. 4060–4065. [Google Scholar]
- Chen, X.; Ni, W.; Wang, X.; Sun, Y. Provisioning quality-of-service to energy harvesting wireless communications. IEEE Commun. Mag. 2015, 53, 102–109. [Google Scholar] [CrossRef]
- Chen, X.; Ni, W.; Wang, X.; Sun, Y. Optimal quality-of-service scheduling for energy-harvesting powered wireless communications. IEEE Trans.Wirel. Commun. 2016, 15, 3269–3280. [Google Scholar] [CrossRef]
- Shan, F.; Luo, J.; Wu, W.; Li, M.; Shen, X. Discrete rate scheduling for packets with individual deadlines in energy harvesting systems. IEEE J. Sel. Areas Commun. 2015, 33, 438–451. [Google Scholar] [CrossRef]
- Ozel, O.; Tutuncuoglu, K.; Yang, J.; Ulukus, S.; Yener, A. Resource management for fading wireless channels with energy harvesting nodes. In Proceedings of the 2011 IEEE INFOCOM, Shanghai, China, 10–15 April 2011; pp. 456–460. [Google Scholar]
- Deshmukh, A.; Vaze, R. Online Energy-Efficient Packet Scheduling for a Common Deadline With and Without Energy Harvesting. IEEE J. Sel. Areas Commun. 2016, 34, 3661–3674. [Google Scholar] [CrossRef]
- Fang, X.; Gao, H.; Li, J.; Li, Y. Application-aware data collection in Wireless Sensor Networks. In Proceedings of the 2013 IEEE INFOCOM, Turin, Italy, 14–19 April 2013; pp. 1645–1653. [Google Scholar]
- Zhao, Q.; Zhu, Y.; Zhu, H.; Cao, J.; Xue, G.; Li, B. Fair energy-efficient sensing task allocation in participatory sensing with smartphones. In Proceedings of the 2014 IEEE INFOCOM, Toronto, ON, Canada, 27 April–2 May 2014; pp. 1366–1374. [Google Scholar]
- Zhao, Y.; Guo, D.; Xu, J.; Lv, P.; Chen, T.; Yin, J. CATS: Cooperative Allocation of Tasks and Scheduling of Sampling Intervals for Maximizing Data Sharing in WSNs. ACM Trans. Sens. Netw. (TOSN) 2016, 12, 29. [Google Scholar] [CrossRef]
- Wu, W.; Wang, J.; Li, M.; Liu, K.; Luo, J. Energy-efficient transmission with data sharing. In Proceedings of the 2015 IEEE Conference on Computer Communications (INFOCOM), Kowloon, Hong Kong, China, 26 April–1 May 2015; pp. 73–81. [Google Scholar]
- Zafer, M.A.; Modiano, E. A Calculus Approach to Energy-Efficient Data Transmission With Quality-of-Service Constraints. IEEE/ACM Trans. Netw. 2009, 17, 898–911. [Google Scholar] [CrossRef]
- Luo, Y.; Zhang, J.; Letaief, K.B. Optimal scheduling and power allocation for two-hop energy harvesting communication systems. IEEE Trans. Wirel. Commun. 2013, 12, 4729–4741. [Google Scholar] [CrossRef]
Symbol | Semantics |
---|---|
task set | |
ith task | |
arrival time of | |
amount of data requested by | |
the set of harvesting events | |
ith harvesting | |
harvesting time of | |
amount of energy harvested by | |
rate-power function, the power consumed to achieve a rate r | |
T | transmission completion time |
data rate specified in time t | |
optimal rate function for the min-T problem | |
optimal rate function for the min-E problem |
Parameter | Meaning | Setting |
---|---|---|
n | the number of tasks | by default |
arrival time of the i-th task | random integer that obeys the uniform distribution of | |
workload of the i-th task | follows the normal distribution of | |
m | the number of harvestings | by default |
harvesting time of | random integer that obeys the uniform distribution of | |
amount of harvested energy by | follows the uniform distribution , where h is 1000 mJ |
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Wu, W.; Li, H.; Shan, F.; Zhao, Y. Optimal Rate Schedules with Data Sharing in Energy Harvesting Communication Systems. Sensors 2017, 17, 2958. https://doi.org/10.3390/s17122958
Wu W, Li H, Shan F, Zhao Y. Optimal Rate Schedules with Data Sharing in Energy Harvesting Communication Systems. Sensors. 2017; 17(12):2958. https://doi.org/10.3390/s17122958
Chicago/Turabian StyleWu, Weiwei, Huafan Li, Feng Shan, and Yingchao Zhao. 2017. "Optimal Rate Schedules with Data Sharing in Energy Harvesting Communication Systems" Sensors 17, no. 12: 2958. https://doi.org/10.3390/s17122958