Minimizing the Number of Clusters in IEEE 802.15.4 Wireless ...

Minimizing the Number of Clusters in IEEE 802.15.4 Wireless Sensor Networks Chang Wu Yu, Chin-Chih Chang*, and Ju-Hsien Chou Department of Computer Science and Information Engineering Chung Hua University, Hsinchu, Taiwan {cwyu, changc}@chu.edu.tw

Abstract Traditionally, in IEEE 802.15.4 wireless sensor networks (WSN), cluster trees are constructed by connecting cluster heads. Though this way may reduce the number of routers, excess clusters may cause extra data transmission delay and will reduce the collection efficiency of sensing data. In this paper, we proposed a method that can effectively reduce the data transmission delay by minimizing the number of clusters in IEEE 802.15.4 WSN. Bridges are used to connect two cluster heads to perform a two-hop transmission in one cluster active time slot. Moreover, based on the idea of the maximum independent set in a tree cluster, heads, bridges, and leaf nodes can be properly assigned to construct a cluster tree that can minimize the number of clusters. The simulation results showed the proposed method can effectively reduce the total number of clusters up to 40% than the previous work. As a result, the average delay time of IEEE 802.15.4 wireless sensor networks can be reduced significantly.

1. Introduction IEEE 802.15.4, which features low cost, low power consumption, low data transfer rate, short range, and high node expansion [1], is especially useful in the applications of short range, low data volume, and dense deployment. The ZigBee Alliance uses the IEEE 802.15.4 to build a complete protocol stack for the implementation of wireless sensor networks (WSN) [2]. In a WSN sensors might not be able to directly communicate with the sink and has to response via some relay sensors called routers. * To whom all correspondences should be sent.

A cluster is usually built to reduce router power consumption. In each cluster there is a cluster head (CH) to connect all sensors in the cluster and collect the data from these sensors. Through a number of clusters the data is transmitted to the sink [3, 4]. A cluster tree is formed by connection of CHs. Sensor nodes which only need to transmit data to the CH are called leaf nodes. In a cluster tree the data are usually transmitted using time division multiple access (TDMA) scheme. Each cluster needs specific time slot during its operation. The time from sensors to the sink is equivalent to the total time slots of passing clusters. The more the passing clusters are, the slower the data is transferred from sensors to the sink. Hence, decreasing the number of clusters will reduce the transfer delay time in a cluster tree. Various reasons cause excess clusters. A cluster tree can be constructed from the sink or nodes of random selection [5, 6, 7, 8]. As a result, a sensor connects with neighbors and decides if it can be a CH. The benefit of this kind of approach is that nodes can be clustered faster and the drawback is there is no promise to guarantee the number of clusters and the length of the transfer path. This will increase the number of the clusters (in the whole network or from sensors to the sink) and cause the data transfer delay. In each cluster operating time slot, only one-hop transmission is undertaken. If in each cluster operating time slot nodes can do two-hop transmission, the delay time will greatly reduced. So the idea of bridges has emerged [5, 6, 7, 8]. Here a bridge is also a router and works between two CHs to transmit and receive the data. In this work, novel algorithms to construct a cluster tree with near minimum delay are proposed. Specifically, the goal of this work consists of:

1. adjusting CHs, bridges, and leaf nodes to obtain the near minimum number of clusters in the cluster tree ; and, at the same time, 2. reducing the largest number of the clusters traversed from sensors to the sink. The most important issue to build such a cluster tree is to assign CHs, bridges, and leaf nodes properly. Bridges and leaf nodes have to receive and transmit through CHs. So they cannot connect to each other directly. In the graph theory, they do not share a common edge and can be treated as an independent set. By finding a maximum independent set, we can construct a cluster tree with minimum number of clusters as expected. We also conduct simulations to show the effectiveness of the proposed algorithms. The simulation results showed the proposed methods can effectively reduce the total number of clusters up to 40% than the previous work. As a result, the average delay time of IEEE 802.15.4 wireless sensor networks can be reduced significantly. The rest of this work is organized as follows. Section 2 discusses the IEEE 802.15.4 and related work. Section 3 defines the minimum delay cluster tree. Section 4 presents the formation of the minimum delay cluster tree. Section 5 shows the simulation results and comparison with previous methods. Section 6 concludes the paper.

once. The time complexity is O(n). Ordinal pruning can save a lot of routers because all sensors can fully grasp the distance information of themselves and neighbors to the sink. But while the cluster tree is built, each router acts as a CH to receive neighbor’s information, becomes a member of another cluster, and then transfers the data to the CH that is nearer to the sink. In [7], Wang and Li used the minimum connected dominating set to form a backbone and construct a cluster tree. The algorithm selects a CH based on its priority (ID and power). If a sensor listens to a CH in another cluster, then this cluster acts as a bridge. If the sensor only connects to one CH, then this sensor acts as a leaf node. In [8], Chen and Lin proposed a hybrid algorithm of cluster tree and mesh network. In this scheme a cluster tree is formed from the cluster at the sink and expands from the sink cluster. Two nearby sensors cannot be CHs at the same time. A CH can only connect to the other CH through a bridge. The number of clusters from sensors to the sink is reduced because of the additional bridges. Some sensors which are supposed to be leaf nodes become CHs when the nearby nodes are bridges such as the node I shown in Figure 1(a). It is possible for a bridge to connect to a CH that has the same number of hops from the sink. For these sensors the number of hops on the path to the sink will increase as those leaf nodes shown in Figure 1(b).

2. Related Work An IEEE 802.15.4 WPAN is composed of one personal area network (PAN) coordinator and a set of devices. The PAN coordinator is the primary controller of the network. There are three types of network topologies: star, mesh, and cluster tree. The implication of network topology over the overall performance of WSNs can be found in [13]. A recent study on the topology on formation strategies in IEEE 802.15.4 networks is presented in [14]. In [9], Ma and Gao proposed an algorithm to build a cluster tree with the reduced number of routers. In their algorithm all sensors are set as routers (CHs) by default and then sort routers by the distance (number of the hops) to the sink. A sensor checks if it can be a leaf node. If the sensor cannot be a router and still can connect to other node, then it can be a leaf node. In ordinal pruning the sink starts to send a control packet to let all sensors know their neighbors. Then the sensor which is farthest (largest hop number) and has the smallest ID starts to check if the node can be removed from the router. This method can effectively reduce the number of routers but every sensor has to be checked

Figure 1. The cluster tree proposed by Chen and Lin In [10], Lu et al. studied the relation between topologies and scheduling. They proved that finding the best schedule in a tree topology is a NP-complete problem. Therefore, a solution by heuristic algorithms can be designed. They found in the ring topology there is an optimal solution. The low bound of scheduling can be further formalized to facilitate scheduling. In [11], Tseng and Pan studied scheduling in Zigbee. They found in the line topology, the time slot can be assigned from the farthest node from the sink. In the ring topology the time slot is also assigned from the farthest node to fill the first half ring. The next half is filled from the node nearest to the sink and the time slot is chosen from the one that does not conflict with neighbors. In the line and ring topologies the best

scheduling can be found. In a breadth-first search (BFS) tree topology centralized and disturbed scheduling can be studied. These two methods can be used for scheduling in a cluster tree.

3. Role assignments in a cluster tree A wireless sensor network is composed of a sink and sensors. Here the distance between two sensors or the sink and a sensor is measured by the numbers of sensors between them. Each count of a sensor or the sink is called a hop. If two neighboring sensors have the same hop number from the sink, they are called brother neighbors. If a neighbor sensor has the one fewer hop number, it is called a father neighbor of the node. If a neighbor sensor has the one more hop number, it is called a child neighbor of the node. A leaf node is a sensor without the routing function. There are two situations to be a leaf node: (1) a sensor without any child neighbor which won’t make a shorter path for other sensor even if it is a CH or a bridge or (2) a sensor whose possible child neighbors have all chosen other sensors as a CH or a bridge and which no other sensor will choose as a CH or a bridge. A cluster head (CH) is the only one sensor which can synchronize and integrate with other members in the cluster. On the other hand, a leaf node or a bridge has to transmit and receive the data via a CH. In order to avoid the long transmission path, the selected CH of a given sensor is better to be their father neighbor. The purpose of the existence of bridges is to reduce the number of the clusters on the path from each sensor to the sink. Therefore, bridges need to span between two CHs. If these two CHs are the father and child neighbor of the bridge, the number of clusters can be reduced. The generation of a bridge is chosen by the cluster.

nodes selected from bridges or leaf nodes can not directly communicate. Since a subset S of V is called an independent set of G=(V, E) is no two vertices of S are adjacent, in graph theory, bridges and leaf nodes can be treated as an independent set. On the other hand, the nodes not in the independent set can be treated as CHs. To minimize the number of clusters is equivalent to minimize the number of CHs. As a result, we will focus on finding a maximum size of independent set in a given tree and setting these nodes as bridges and leaf nodes. Given a tree, a maximum set can be found by a greedy algorithm which selects vertices from a leave [12]. Its correctness can be assured by the following theorem. Theorem 1: If v is a leaf in a tree, there must be a maximum independent set including v. In the example of Figure 2, a tree as shown in Figure 2(a) is given to construct the maximum independent set according to the greedy algorithm. First, a leaf node v is chosen to add into the independent set and u which is linked with v cannot be added in the independent set because two independent points cannot share the same edge (Figure 2(b)). Hence, the points of u and v and all edges incident to them are cut as shown in Figure 2(b). We continue to work on the other leaf nodes in the resulting tree and repeat the steps of selection and addition. Then the maximum independent set is built as shown in Figure 2(e). The procedure is simply a greedy algorithm to construct the maximum independent set in the tree.

4. Construction of a cluster tree with the minimum number of clusters Figure 2. Finding a maximum independent set in a tree In this section, novel algorithms to construct a cluster tree with the minimum number of clusters are proposed. The effort is also aimed at minimizing the number of clusters. Referring to the maximum independent set in a tree, a cluster is built from a leaf node. 4.1 The maximum independent set referring to the tree topology A cluster tree can be constructed with the help of finding an independent set in a tree. Bridges and leaf nodes need to follow the beacon format of the CH to transmit and receive the data. As a result, any pair of

A tree is composed of a root, internal nodes, and leaves. In order to reduce the transmission delay a cluster tree is built such that the leaves and bridges in the tree belong to the independent set; the CHs belong to the nodes not in the independent set. In a tree topology, the idea of the maximum independent set starts from constructing the cluster tree from a leaf. In this way the CHs and bridges can be evenly distributed from sensors to the sink so that the longest delay time (i.e., the largest number of passed clusters) of the resulting cluster tree can also be reduced.

The proposed algorithms include four procedures: (1) exchanging sensor information, (2) initiating the cluster tree construction, (3) selecting CHs, and (4) selecting bridges, which are described as follows. 4.2 Exchange mechanism of sensor’s information A sensor broadcasts its control packet to the neighbors in the broadcasting range. The beacon contains ID and the hop numbers from the sink. When a neighbor receives the control packet from a sensor, they will set the sensor as its father, brother, or child neighbor and transmit an acknowledgement (ACK) beacon back to the sensor. The beacon contains ID and the hop number from the sink. When the sensor receives the ACK, it will know the complete information of its neighbor. If the sensor has no neighbor, it becomes a leaf node. 4.3 Two methods of constructing a cluster tree from leaf nodes Here we design two methods for constructing a cluster tree from leaf nodes. A sensor decides if it is a leaf node based on the network and neighbor’s information acquired from the control packet. So in order to get the information of itself and its neighbors, the sink starts to transmit the control packet and gradually all nodes in the whole network. 4.3.1 Constructing a cluster tree once a sensor recognizes itself as a leaf node Once a sensor recognizes itself as a leaf node, the minimum delay tree begins to build. The key point is the time to construct the whole cluster tree can be shortened. But some path that is already built might have to be changed because a sensor that is farther from the sink will recognize itself as a leaf node later and require the shorter delay; even a leaf node near the sink has already set its cluster path, the path and roles could be changed because of the need of reducing the delay for those remote leaf nodes. Usually, this method is usually used in the situation that a network is required to build in an emergency. 4.3.2 Constructing a cluster tree from the leaf node farthest from the sink The benefit of constructing the minimum delay tree from the leaf node farthest from the sink is that the farthest leaf node can select the path first to achieve the goal of the minimum delay and reduce the waste of control packets. However, the cost is the time to build the network topology is longer. The backoff-time mechanism can be used for building the clusters from the farthest leaf node. After each sensor finishes transmission of the control packet and receiving of the ACK packet, the backoff time starts to count down to decide the time to build the clusters. The larger the hop number is, the shorter the

backoff time is so that the clusters can be built from the farthest leave. This backoff time set as TActive where TActive =(HopMax –Hop)THop (1), where HopMax is the farthest hop number which is estimated by the sink before the network is built according to the network range and the transmission radius. 4.4 Selection of CHs A sensor will select a CH from its father or brother neighbors. These neighbors are required to reply information including the total number of their brother and child neighbors. The larger the total number is, the larger the chance to be selected as a CH is. So we will select the neighbors with the largest total number as a CH. If there are multiple neighbors with the largest total number, the one with the largest ID will be selected as a CH. The neighbor which is selected as a CH will transmit the CH packet to declare the establishment of the cluster. Once the CH is established or a new node joins in the CH, the CH will record the hop number of the farthest leaf node on the path and set it as Longest_Hop. Based on the selection priority, the methods of selecting a CH are described from Rule (1) to Rule (5) in more detail: Rule (1) Selecting a father neighbor without any role: If a father neighbor which does not act as any role is selected as a sensor’s CH, this new CH searches for bridges in order to set up a new path (Note that the selection of bridges is described in Section 4.5). Rule (2) Selecting a father neighbor which is already a CH: A father neighbor which is already a CH can be selected as the CH. A bridge has to select a CH from its father neighbors. If a father neighbor is found to be a CH, a bridge will directly connect to this CH. The purpose is to save the number of CHs. Rule (3) Selecting a brother neighbor which is already a CH: If all father neighbors are bridges or leaf nodes but are not a CH, then a brother neighbor which is already a CH is selected as a CH. If all father neighbors are not CHs but the brother neighbor is a CH, the brother neighbor is selected as the CH. Rule (4) Selecting a father neighbor which is already a bridge: Rule (4) has two sub-rules listed below. Rule (4.1) Bridge with fewer Longest_Hop: If all father neighbors of a node are bridges, then one of these bridges will be selected as the CH. First, a father neighbor which has the fewer Longest_Hop than the Longest_Hop of the node is selected as the CH. When the father neighbor of the bridge becomes a CH, the path previously built by this CH is released. All CHs and bridges on the original path become a node without any role. These CHs

and bridges are given backoff time to let them start to recognize their roles and build a new path. Rule (4.2) Bridge with larger Longest_Hop: If all father neighbors of a node are bridges and their Longest_Hops are larger than the node, then one of these bridges with the least Longest_Hop will be selected as the CH. After this bridge becomes CH, the new path is not built. Rule (5) Issuing CH packets for clustering: When a CH is newly built or a new node joins in a CH, the CH will send a CH packet to declare a cluster has been established. If the child neighbor of the CH is a bridge or a leaf node or the brother neighbor of the CH is a leaf node and these bridges or leaf nodes have not selected a CH, these nodes will join the CH which sends the CH packet. If there is a child neighbor which is a CH and also a CH that is connected by the child neighbor of another leaf node, then the CH which transmits the CH packet should include this leaf node into its cluster. If the CH which just loses a member has only a child neighbor which is also a CH, this CH can convert itself to a bridge. Similarly, if a CH is generated newly and broadcasts its control packet, a father neighbor connected to the CH must decide if it can convert from a CH to a bridge. 4.5 Selection of Bridges Only a CH can select a bridge and can only select a bridge from the father neighbors. These neighbors are requested to reply the information about the total number of their brother and child neighbors. Remind that the fewer the total number is, the less the chance the node is selected as a CH. In the proposed protocol, a CH will select the neighbor with the least total number of neighbors as a bridge. If there are a number of neighbors with the least total number of neighbors, the one with the largest ID is selected as a bridge. When a bridge is newly established, Longest_Hop will be set as in the same way as it is set in the CH. Two rules for selecting bridges are as follows. Rule (6) Selecting a father neighbor without any role: If a father neighbor which does not act any role is selected as a bridge, the father neighbors will start to look for a CH in order to establish a new path. Rule (7) Selecting a father neighbor which is already a CH: If the father neighbors of a CH are all CHs, one of them has to be selected as a bridge. From the father neighbors of these CHs, one with the fewer Longest_Hop is selected as a bridge. When a father neighbor of a CH becomes a bridge, the origin path to the sink is released. All CHs and bridges on the original path become a node without any role. These

CHs, bridges, and nodes connected to them are given the back-off time to let them start to recognize their roles and build a new path. In order to build a new path the father neighbor of this new bridge starts to look for a CH. Rule (8) Selecting a father neighbor which is a leaf node: When a father neighbor of a leaf node is selected as bridge, the CH selects the sensor with fewer neighbors as a bridge. If a CH cannot select an appropriate bridge after following the procedures in Section 4.5, then it has to go back to Section 4.4 to select an appropriate CH. 4.6 Exception Handling Two exceptions should be considered. (1) If a node has a child neighbor which has one father neighbor and no brother neighbor, then this node cannot be a bridge of any other node. (2) If a sensor has two child neighbors which have one father neighbor and no brother neighbor, then this sensor can only be the CH of its child neighbors.

5. Simulations The simulation environment is set in an area of 1000 square meters where 1 to 199 sensors and one sink are randomly distributed. Here the transmission radius is 5 meters. Only connected networks are chosen as the simulation environment. The cluster tree we establish is called minimum-delay cluster tree (MDCT). Because a cluster tree can be built from different leaf nodes, the first method (introduced in subsection 4.3.1) is called leaf MDCT and the other one the last leaf MDCT (introduced in subsection 4.3.2). These methods which are compared are Ordinal Pruning [9] and QoS Routing [8]. The network nodes are increased from 5 to 200 by adding 5 extra nodes. Each point in the following figures is an average of 100 simulation results. 5.1 Comparison of CH and Bridge numbers The comparison of the CH number is shown in Figure 3. In ordinal pruning, all CHs are next to each other. In the proposed methods the concept of bridges is introduced into the cluster tree, the cluster number is greatly reduced in the entire network. In the case of 200 nodes, Last Leaf MDCT and Leaf MDCT can save 36.78% and 30.97% of CHs respectively. In QoS routing, some leaf nodes become a CH or a bridge because leaf nodes cannot connect each other directly. In the case of 200 nodes, Last Leaf MDCT and Leaf MDCT can save 8.95% and 0.57% of CHs which QoS routing uses respectively.

5.2 Comparison of the number of clusters and hops which the farthest leaf node has crossed

Figure 3. Comparisons of required CH numbers The comparison of the bridge number is shown in Figure 4. There is no bridge in ordinal pruning. In MDCT the bridge number is the CH number that is saved plus the number of few leaf nodes which become bridges. In QoS routing, the bridge number is increased in order to connect quite a number of CHs. In the case of 200 nodes, Last Leaf MDCT and Leaf MDCT can save 18.36% and 12.47% of CHs which QoS routing uses respectively.

Through the connection of bridges, 2-hop transmission can proceed in a cluster active slot time to quickly reduce the cluster number from sensors to the sink. In MDCT, a CH and a bridge are first selected from father neighbors. This straightens the path from sensors to the sink and reduces the hop number on the path. Figure 6 shows the comparison of the cluster number the farthest sensor has to cross to reach the sink. Ordinal pruning has no bridge. In the case of 200 nodes, Last Leaf MDCT and Leaf MDCT can reduce 40.04% and 38.54% of cluster number respectively. In QoS Routing quite amount of bridges are connected to the CH of a brother neighbor but not directly connected to the CH. This will increase the cluster number. Compared with QoS Routing, the proposed two methods still can reduce 8.55% and 6.26% of cluster numbers.

Figure 4. Comparisons of required bridge numbers

Figure 6. Comparisons on number of clusters which the farthest leaf node has crossed

A router can act as a CH or a bridge here. The comparison of router numbers is shown in Figure 5. The reason why MDCT needs more leaf nodes than ordinal routing is some leaf nodes are selected as bridges. QoS routing needs more routers because CHs cannot connect to each other.

The hop number from sensors to the sink is shown in Figure 7. Ordinal pruning and the proposed two methods have the higher criteria for two neighbors of the same hops to connect so the hop number is almost identical. QoS routing needs more hop number because the clusters are more than our methods.

Figure 5. Comparisons of required router numbers

Figure 7. Comparisons on number of hops which the farthest leaf node has crossed

5.3 Comparison of the number of leaf nodes The comparison of the number of leaf nodes is shown in Figure 8. The proposed two MDCT methods build a cluster tree from leaf nodes and allow leaf nodes to connect to a CH so that the number of bridges can be increased. The chance of generating a leaf node is higher. In 200 nodes the number of leaf nodes of Last leaf MDCT and Leaf MDCT are only 5.04% and 9.5% less than those of ordinal pruning respectively. The reason why leaf nodes are not generated a little bit fewer is some leaf nodes nearby the sink will be adjusted to be a bridge to reduce the delay time. QoS routing emphasizes too much on distribution restrictions. This will make a lot of leaf nodes to become a CH or a bridge and the number of leaf nodes are decreased. Our two methods have 8.26% and 4.06% more leaf nodes than those in QoS routing.

[2] [3]

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Figure 8. Comparisons of leaf node number

[9]

6. Conclusion In this work a cluster construction algorithm that reduces the number of clusters and thus the average delay time is proposed. The method is composed of three key points: the cluster tree is built from leaf nodes; the minimum delay is derived from the idea of the maximum independent set in a tree; and bridges are used to link two clusters. These strategies effectively reduce the cluster number on the path from leaf nodes to the sink about 40% less than the previous work. The clusters in the cluster are about 32% less than the previous work. Our continuing work is to improve the cluster tree construction algorithm to reduce time complexity and balance network flow. The other work is to enhance the algorithm to cope with the problem of heterogeneous components in Zigbee networks.

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