Sleep Scheduling Towards Geographic Routing in Duty-Cycled Sensor Networks With A Mobile Sink Chunsheng Zhu∗ , Laurence T. Yang∗ , Lei Shu† , Lei Wang‡ , Takahiro Hara† ∗ Department

of Computer Science, St. Francis Xavier University, Canada Email: {chunsheng.tom.zhu, ltyang}@gmail.com † Department of Multimedia Engineering, Osaka University, Japan Email: {lei.shu, hara}@ist.osaka-u.ac.jp ‡ Department of Network Engineering, Dalian University of Technology, China Email: [email protected]

Abstract—Focusing on achieving better geographic routing performance of the two-phase geographic greedy forwarding (TPGF) in duty-cycled wireless sensor networks (WSNs) when there is a mobile sink, this paper proposes a geographic distance based connected-k neighborhood (GCKN) algorithm. The algorithm analysis and simulation results show that GCKN can obtain shorter length of the transmission paths explored by TPGF in duty-cycled mobile sink WSNs, compared with the original connected-k neighborhood (CKN). Index Terms—Geographic Routing; TPGF; Duty-Cycle; WSNs; Mobile Sink; CKN

I. T HE RESEARCH PROBLEM Two-phase geographic greedy forwarding (TPGF) is a geographic routing algorithm proposed by Shu et al. in [1] for facilitating data transmission in WSNs and it focuses on exploring the maximum number of optimal node-disjoint routing paths while minimizing the length of paths. Specially, TPGF employs two phases to achieve the multipath, holebypassing as well as shortest path transmission. The first phase utilizes a greedy forwarding principle and a step & mark approach to explore the possible delivery guaranteed routing path while bypassing holes. And the second phase uses a label based method for optimizing the found routing path with the least number of hops. Apart from that, TPGF does not have the well-known local minimum problem [2] [3], hole problem [2] [3] or require the planar graph [2] [3] of geographic routing. All these desirable features of TPGF make it very unique and efficient. One example of the transmission paths explored by TPGF is presented in Fig. 1. Connected-k neighborhood (CKN) is a sleep scheduling algorithm proposed by Nath et al. in [4] to create a desirable duty-cycled wireless sensor network (WSN) for geographic routing and it aims at allowing only a portion of nodes to be awake for saving energy consumption while the whole network is still connected by these awake nodes. With CKN, every node picks a random rank and determines the asleep or awake state of itself by the number and connectivity status of its currently awake neighbor nodes. Moreover, every node will have at least some certain number of awake neighbors after running CKN and the awake nodes in the network can be increased by growing the value of k in CKN as shown in Fig.

Fig. 1. One example of the transmission paths from a source node (red color) to the sink node (green color) explored by TPGF in an always-on WSN. There are total 500 sensor nodes and they are all awake.

2. All these make CKN very effective and popular in dutycycled WSNs. However, CKN overlooks one important fact that sink can be mobile to enhance the energy efficiency, channel capacity, etc of WSNs [5] [6] [7]. For example, because sensors can move, they can make the transmission more disperse to get rid of the flaw that sensors near the gateway or sink always lose their energy first, thus energy usage can be more efficient. Also, as a result of mobility, sensors having mobility property such as mobile phones or mobile cars can become the interface between the information center and the customers, thus realtime information (e.g., traffic information) transmitting from information center to these mobile objects can be provided to near customers. Actually as the asleep or awake state of each node is decided by CKN without considering the geographic location of the node and the mobile sink, it may make substantial nodes far away from the sink be awake thus increase the length of the paths explored by geographic routing.

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Fig. 2. One example of a CKN based WSN with different k. There are total 500 nodes and the k in CKN is 1, 2, 4, 8 in (a) (b) (c) (d), respectively. The red node is the source node and the green node is the sink node. The black nodes are asleep nodes and the blue nodes are awake nodes. The line between two nodes means they are neighbors. When the k in CKN increases, the number of asleep nodes decreases.

In this paper, considering the situation when there is a mobile sink in a duty-cycled WSN, we are extremely interested in providing a new sleep scheduling algorithm to provide better transmission length of geographic routing. Specially, our interest falls into the following aspect: • How to revise the CKN algorithm to achieve shorter length for the paths explored by TPGF when there is a mobile sink in the duty-cycled WSN, while keeping the majority features of original CKN algorithm unchanged? II. P ROPOSED M ETHOD We incorporate both the connected-k neighborhood requirement and geographic routing requirement while designing the new sleep scheduling algorithm. Specially, we consider the following four design factors: (1) a node should go to sleep assuming that at least k of its neighbors will remain awake so as to save energy consumption as well as keep it k-connected; (2) the outcome of the asleep or awake state of nodes should be able to change over epoches so that all nodes can have the opportunity to be asleep to avoid making any node always be awake, thus the whole network lifetime can be prolonged; (3) although each node decides to be asleep or awake locally, the whole network should be globally connected so that data transmission can be performed; (4) there should be as more as possible closer neighbor nodes to the sink for each node so as to make geographic routing obtain more available nodes to get shorter transmission path length. We define our new method as geographic distance based connected-k neighborhood algorithm (GCKN) and the pseudocode is shown below. Specially, for each node u, the geo-

graphic distance1 between itself and the sink granku is picked (Step 1 of the algorithm) and the subset Cu of u’s currently awake neighbors having grank < granku is computed (Step 5 of the algorithm). Before u can go to sleep, it needs to ensure that (1) all nodes in Cu are connected by nodes with grank < granku (2) each of its neighbors has at least k neighbors from Cu (Step 6 of the algorithm). The last factor of the four design factors of GCKN is the extra element and also unconsidered element in contrast with the original CKN considered factors. Pseudocode of GCKN algorithm Run the following at each node u. 1. Get the geographic distance between itself and the mobile sink granku . 2. Broadcast granku and receive the geographic distance ranks of its currently awake neighbors Nu . Let Ru be the set of these ranks. 3. Broadcast Ru and receive Rv from each v ∈ Nu . 4. If |Nu | < k or |Nv | < k for any v ∈ Nu , remain awake. Return. 5. Compute Cu = {v|v ∈ Nu and grankv < granku }. 6. Go to sleep if both the following conditions hold. Remain awake otherwise. • Any two nodes in Cu are connected either directly themselves or indirectly through nodes within u’s 2-hop neighborhood that have grank less than granku . • Any node in Nu has at least k neighbors from Cu . 7. Return.

III. E VALUATION To demonstrate the effectiveness of our GCKN compared with CKN, we conduct extensive simulations in NetTopo2 [8] with respect to the length of all transmission paths explored by TPGF in duty-cycled mobile sink WSNs. The network size is 800×600 m2 . The number of deployed sensor nodes ranges from 100 to 1000 (each time increased by 100) and the value of k in CKN is changed from 1 to 10 (each time increased by 1). For every number of deployed sensor nodes, 100 different network topologies are generated using 100 different random seeds and the transmission radius of each node is 60 m. A source node is deployed at the location (50, 50) and a sink node will be randomly moving 10 times in every deployed network field. One snapshot of the transmission paths from the source node to sink node explored by TPGF in a GCKN based WSN when the sink is at different locations is shown in Fig. 3. Fig. 4(a) and Fig. 4(b) show the average length of all transmission paths explored by TPGF in GCKN based mobile sink WSNs and CKN based mobile sink WSNs. From these two figures, we can clearly see that the average length explored by TPGF in GCKN based WSNs with a mobile sink is almost always much shorter than that in CKN based WSNs with a mobile sink. It is because more closer nodes to sink are kept awake in a GCKN based WSN than that in a CKN based WSN. Moreover, we can see that when there are more number of 1 We assume each node can know the location of itself by using GPS and nodes can also know the location of the sink by flooding the sink location information. 2 NetTopo (available online at http://sourceforge.net/projects/nettopo/) is an open source software on SourceForge for simulating and visualizing WSNs.

k=1 k=2 k=3 k=4 k=5 k=6 k=7 k=8 k=9 k=10

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Fig. 4. Average length of all transmission paths explored by TPGF in GCKN based WSNs with a mobile sink (a) and in CKN based WSNs with a mobile sink (b).

cycled mobile sink WSNs which can be taken to utilize both advantage of duty-cycling and mobility. We believe this work will provide essential contribution and impact on future geographic routing and sleep scheduling researches. ACKNOWLEDGMENT (b)

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This research work was supported by Grant-in-Aid for Scientific Research (S)(21220002) of the Ministry of Education, Culture, Sports, Science and Technology, Japan. This work is also partially supported by Natural Science Foundation of China under Grant No. 61070181, and Natural Science Foundation of Liaoning Province (China) under Grant No. 20102021. R EFERENCES

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Fig. 3. One snapshot of the transmission paths from source node (red color) to the sink node (green color) explored by TPGF in a GCKN based mobile sink WSN. The source node is at the location (50, 50) and the sink node is at the location (400, 300), (50, 550), (400, 550), (750, 550) in (a) (b) (c) (d), respectively. There are total 500 sensor nodes and the k in CKN is 1. The black nodes are asleep nodes and the rest nodes are awake nodes.

sensor nodes, this advantage is more obvious. That’s because higher network density will enable GCKN to create more favorable nodes for TPGF to utilize while the sink is mobile. IV. C ONCLUSION Considering there is a mobile sink in the duty-cycled WSNs, the above algorithm descriptions and simulation results reveal that: the proposed geographic distance based connected-k neighborhood (GCKN) algorithm can achieve better length of transmission paths explored by the two-phase geographic greedy forwarding (TPGF), compared with the original connected-k neighborhood (CKN) algorithm. To the best of our knowledge, this paper is the first work considering and analyzing implementing geographic routing into duty-

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