近幾年來，電力公司希望能利用智慧電網來取代傳統電力的紀錄方式。在智慧電網中，使用Advanced Metering Infrastructure(AMI)的架構去紀錄和收集資料。而在AMI架構下要利用集中器來收集電表的資訊，進而再透過集中器傳回資訊給電力公司。所以在智慧電網中，需要佈建集中器來讓電表的資訊得以傳回給電力公司。
在成本的考量之下，能夠使用的集中器數量越少越好，但同時也需要考慮到佈建之後的網路有一定的可靠度和品質，能夠符合AMI的基本規範。所以，如何最小化集中器之數量，並且同時確保在一定的品質下，是一個重要的問題。
在這篇論文中，我們會提出一個方法，能夠使得電表傳輸資訊的成功率達一定水準並且能使得佈建集中器的最小化。我們的方法會建構在Routing Protocol for Low Power and Lossy Networks(RPL)下。這一個Routing Protocol是在MAC層下做傳輸，並且考慮了TSCH(Time Slotted Channel Hopping)的環境。從我們的實驗結果可以看出我們所提出的演算法對於最小化佈建的集中器並且符合AMI的基本規範之下，有良好的表現。

In the smart grid network, the Advanced Metering Infrastructure
(AMI) refers to the system that measures, collects data. In the AMI, meters transmit data through concentrators, and then concentratorstransmit data to power companies. Because of the cost of concentrators, the number of concentrators, that are used in the system, should be as lower as possible. Besides, we also need to satisfy the QoS requirements which are latency and reliability in the AMI specications. Hence, how to minimize number of concentrators in the system with good quality is an import question. In this paper, we purpose the heuristic to solve the problem. Moreover, our system is based on the Routing Protocol for Low Power and Lossy Networks (RPL), which is a protocol in the MAC layer with TSCH (Time Slotted Channel Hopping). We will show that our heuristic in some areas has better performance.

1 Introduction . . . . . . . . . . . . 1
2 Related Work . . . . . . . . . . . . 5
3 The Problem . . . . . . . . . . . . 7
3.1 The Scenario and Network Model . . . . . . . . . . . . 7
3.1.1 The Scenario . . . . . . . . . . . . . . . . . . . 7
3.1.2 Network Model . . . . . . . . . . . . . . . . . . 9
3.1.3 Calculate the probability . . . . . . . . . . . . . 10
3.2 The Problem Denition . . . . . . . . . . . . . . . . . . 12
4 The Algorithm . . . . . . . . . . . . 14
4.1 The Algorithm . . . . . . . . . . . . . . . . . . . . . . 14
4.2 Analysis the time complexity . . . . . . . . . . . . . . 19
5 Experimental Evaluations . . . . . . . . . . . . 20
5.1 Experimental Results . . . . . . . . . . . . . . . . . . . 20
5.2 Experiment Result Analysis and Running Time . . . . 30
5.2.1 ExperimentResultAnalysis . . . . . . . . . . . 30
5.2.2 Runningtime ................... 33
6 Conclusion ................... 36
7 Future Work ................... 38
Bibliography ................... 39

[1] Tripathi, Joydeep, Jaudelice Cavalcante de Oliveira, and Jean Philippe Vasseur. "A performance evaluation study of rpl: Routing
protocol for low power and lossy networks." Information Sciences
and Systems (CISS) 2010 44th Annual Conference on. IEEE, 2010.
[2] Bejerano, Yigal. "Ecient integration of multihop wireless and
wired networks with QoS constraints." IEEE/ACM Transactions on Networking (TON) 12.6 (2004): 1064-1078.
[3] Banerjee, Suman, and Samir Khuller. "A clustering scheme for hierarchical control in multi-hop wireless networks." INFOCOM 2001. Twentieth annual joint conference of the IEEE computer and communications societies. Proceedings. IEEE. Vol. 2. IEEE, 2001.
[4] Aoun, Bassam, et al. "Gateway placement optimization in wireless mesh networks with QoS constraints." IEEE Journal on Selected Areas in Communications 24.11 (2006): 2127-2136.
[5] Chen, Phoebus, and Shankar Sastry. "Latency and connectivity
analysis tools for wireless mesh networks." Proceedings of the 1st
international conference on Robot communication and coordination.
IEEE Press, 2007.
[6] Souryal, Michael, et al. "A methodology to evaluate wireless technologies for the smart grid." Smart Grid Communications (Smart GridComm), 2010 First IEEE International Conference on. IEEE,
2010.