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IEEE/CIC ICCC 2015 Symposium on Wireless Communications Systems

Low-latency TDMA Sleep Scheduling in Wireless Sensor Networks Zihao Wang, Jinlan Li, Lin Kang, Chaowei Wang, Yinghai Zhang Information & Electronics Technology Lab, Beijing University of Posts and Telecommunications Key Laboratory of Universal Wireless Communications, Ministry of Education Beijing, China Email: [email protected] Abstract—Sleep scheduling is a widely used mechanism in WSNs to reduce the energy consumption since it can save the energy wastage caused by idle listening. In traditional TDMA sleep scheduling, sensors are assigned with consecutive time slots to save the energy consumption of state transitions. However, this consecutive time slots allocation scheme will lead to a longer time delay when data is transmitted from a leaf node to a sink node when nodes are organized in a tree model topology. To address this problem, we present a novel contiguous link scheduling called hierarchical link scheduling with proactive time slots acquisition (H-TSAC). Its main novelty is that contiguous time slots can be acquired by each node to transfer object data based on the layer of nodes in the tree model topology, therefore, a new-type node named multi-parent node is designed to proactively control time slots . The simulation studies corroborate the theoretical results, and show the efficiency in using the H-TSAC scheme. Keywords—sleep schduling ; TDMA; WSNs

I. INTRODUCTION Wireless sensor networks (WSNs) are a type of selforganizing network, which consist of a number of stationary or mobile sensor nodes.These range from simple, very localized 1 or 2 hop wireless personal area networks [1], to much larger, more widespread, multi-hop WSNs – our focus in on the latter. Due to the limited battery-life of sensor nodes, WSNs are typically designed with energy conservation in mind. Sensors can be designed to spend large amounts of time in a low-power “sleep” mode [12]. In addition the design of such WSNs which comprise energy constrained nodes is typically dictated by a longevity concern. Here, a key challenge for WSNs is the design of sleep scheduling that not only strives to reduce average energy consumption but also provides low-delay packet delivery over potentially multiple hops. Current approaches to reduce the average energy consumptionemploysleep scheduling where nodes stayinD low-power “sleep” mode most of the time. Previous work [2] [3] used out-of-band wakeup scheduling. These exploit a special frequency band different to the data transmission frequency. This wakeup plane is used by an initiator node to wake up its target node so that there is less interference between the wakeup and data transfer communication. Ye et al. [4] presented a scheduler to control sensor connectivity based on the TDMA protocols, which can directly support low duty cycle operations by applying different communication strategies in different time slots. Apart from the natural advantage of avoiding interference,

overhearing and idle listening, TDMA can provide a deterministic delay bound [5]. In this paper, we are interested in designing an efficient TDMA sleep scheduling for WSNs.The configuration of the sleep schedule in [4] was notoptimal since large amounts of energy are wasted with idle listening, as it assigns symmetrical time slots to nodes and their parent nodes simultaneously. Van Dam et al. [6] proposed an adjusted duty cycling approach which asynchronously assigns time slots to nodes to further reduce the energy consumption for idle listening. Lu et al. [7] presented a sleep scheduler in which the sink node and the leaf node wakes up once during every transmission interval, and consequently, the energy cost of state transitions is saved in comparison to other nodes. Ma et al. [8] proposed contiguous sleep scheduling, which assigns nodes with consecutive time slots during a scheduled period to reduce the frequency of state transitions. However, the method of decreasing energy by reducing the frequency of state transitions in [8] is at the cost of increasing the data transmission delay of the system. Furthermore, the complexity of the time slot allocation algorithm will increase as the network scale increases. Fundamentally, it is the need for every node across a wireless domain to share whatever portion of the channel it is utilizing, with nodes in its local neighborhood, which constrains the network capacity [9]. Wang et al. [10] proposed a centralized algorithm. Here, the sensors are scheduled individually in a predefined order without consecutive assignment of time slots, which does not consider the energy consumption of radio in the state transition [13]. ,Q this paper, we propose novel TDMA wakeup/sleep scheduling called hierarchical link scheduling with proactive time slots acquisition (H-TSAC). This reduces the frequency of state transitions of nodes and minimizes the system time delay induced by contiguous link scheduling. In this scheduling, child nodes can strive proactively for interference-free and consecutive time slots so that nodes just start up to monitor the channel once per scheduling period T. A further contribution is that it is designed to effectively decrease the system time delay. The remainder of this paper is organized as follows. In Section II, we discuss the system model and then formulate the energy consumption and time delay problem for the contiguous link schedule. Section III presents hierarchical link scheduling with proactive time slots acquisition (H-TSAC) algorithm. Section IV describes and analyzes the simulation results for the proposed algorithm. The paper concludes in Section V.

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IEEE/CIC ICCC 2015 Symposium on Wireless Communications Systems

II. SYSTEM MODEL AND PROBLEM FORMULATION In this section, we present the system model including the network model, the interference model and the energy model. Then the energy consumption and time delay problem is formulated for contiguous link scheduling using hierarchical link scheduling. A. System model 1) Network Model: We assume a two-dimensional WSN with n static omnidirectional sensor nodes which have the same transmission range r. The network is represented by a graph G = (V, E). V  {v1 , v2  vn } denotes the set of nodes. 𝑁 =_9_ is the number of nodes in G. The edges E ⊂ V × V are the transmission links to be scheduled. The graph forms a tree which is referred to the data gathering tree in the rest of the paper. The data gathering tree is a tree rooted from a sink node. The leaf nodes are responsible for object information collection. The intermediate nodes are in charge of fusing and forwarding the data from its child nodes. We assume that each intermediate node has two parent nodes at most. To express the relationship among the nodes, we present two functions named 𝑃 and 𝑆 , the former denotes the parent nodes of 𝑣 Dnd the latter denotes the child nodes of 𝑣 . A scheduling frame is the time duration that starts when each leaf node has generated a packet and ends when all these packets have reached the sink node. It is divided into time slots and the schedule assigns one time slot to each edge in G. A slot is long enough to transmit one data packet plus a guard interval to compensate for synchronization errors. 2) Interference Model: Four types of transmission conflicts between isolated pairs of links are shown in Fig. 1. The first three types of conflicts are between the links that share a neighborü primary conflicts. For the case of a transmission-transmission conflict, parallel transmissions interfere with each other at a common receiver. For the case of a reception-reception conflict, a single node cannot transmit separate packets intended for two different receivers. The transmission-reception conflict happens because the node cannot transmit and receive at the same time. In addition to the three direct neighbor conflicts, a TDMA network also restricts the usage of second hop neighbor links— secondary conflicts. We show this as the transmission-receptiontransmission conflict, the two conflicting links are shown with a solid line. They cannot transmit at the same time because the two transmitters share a neighbor, which hears both transmission. This is shown using a dashed line representing the overheard transmission.

Transmission-transmission

Reception-reception

Transmission-reception Transmission-reception-transmission Fig. 1. Interference in TDMA network

The interference graph C = (V, I) is assumed known. I ⊂V×V is the set of edges such that (u, v) ∈ I if either u or v can hear each other or one of them can interfere with a signal intended for the other (even if they cannot hear each other). Corresponding to G = (V, E) and C = (V, I), we assume a conflict graph 𝐺 = (L, LE). In 𝐺 , each vertex 𝑙 ∈ L corresponds to the link (𝑣 ,𝑃 )∈ E, LE comprises the edges between a node pair in G that should not transmit at the same time. It is generated by taking into account the primary conflicts and secondary conflicts. TABLE І The Data Sheet Of A MICA2 Mote With A CC1100 Transceiver Process Sleep Radio initialization Turn on Radio State Switch Recevie 1 byte Transmit 1 byte

Time ̣ 0.35ms 1.50ms 0.25ms 0.416ms 0.416ms

Power 90­W 18mW 3mW 45mW 45mW 60mW

3) Energy Model: Table I lists the time and energy consumption of a Mica2 mote with a CC1100 transceiver, see [14]. Differences in the actual transmission power due to hardware differences can be compensated by setting up links based on received signal strength as explained in [11]. The radio is in one of four states: transmitting, receiving, listening and switching, and each of them corresponds to energy consumption represented by 𝐸 ,𝐸 ,𝐸 and 𝐸 respectively. The energy consumption in a state switch is about 11.25ȣJ. This consumes far more energy than used for radio initialization and turnning on radio. In our model, we assume that each node operates in three patterns: low-power pattern (sleep, radio initialization and listen), data transmission pattern (receive and transmit), and transient pattern (state switch). B. Problem formulation 1) Energy consumption for contiguous link scheduling:The energy cost of the state switch process can be reduced effectively in contiguous link scheduling. However, a further improvement in energy saving can be achieved if fewer neighbor nodes are listening on the data traffic channel when a node is using the data transmission operation pattern. The total energy consumption of an arbitrary node 𝑣 in data gathering tree is defined as follows.

(Etvi  Ervi  kElvi )*L  2Esvi , vi vi | svi  0  pvi 1 (Etvi  kElvi )*L  Esvi ,vi vi | svi  0  pvi 1 (1) (Ervi  kElvi )* L  Esvi , vi vi | svi  0  pvi  0 Where k denotes the number of neighbor nodes that are listening to the channel when node 𝑣 uses the data transmission pattern. To reduce k, we present a novel algorithm called proactive time slots acquisition (TSAC) to assign interferencefree time slots to each node in the data gathering tree. Thus each

IEEE/CIC ICCC 2015 Symposium on Wireless Communications Systems

node will transfer data in its own time slot which avoid the ineffective listening while its neighbor nodes are in the data transmission pattern. 2) Time delay for contiguous link scheduling: The contiguous link schedule in [8] can decrease the energy cost of a state switch so as to minimize the energy consumption by each node using the data gathering tree topology. However, the contiguous link schedule proposed in [8] assigns time slots to each link 𝑒 in non-decreasing order by the number of child nodes of node 𝑣 , whichmeans a node that has the most number of child nodes gets the first time slot. This increases the system time delay, see Fig. 2. In Fig. 2(c), link 𝑒 ,𝑒 and 𝑒 will first be assigned time slots first before the object information collected by leaf nodes is transmitted to the intermediate nodes. In this case, the time slots assigned to link 𝑒 , 𝑒 and 𝑒 are useless because there is no data transmission, yet the time delay will increase.

𝐾 , we use an assembly 𝑘 (𝑙 , 𝑝 , 𝑠 ) ∈ K to denote a vertex corresponding to the node in G. 𝑘 is the name of this assembly, 𝑙 , 𝑝 , 𝑠 in the assembly 𝑘 denotes the attributions of node 𝑣 . In (2), 𝑙 denotes the layer of node 𝑣 ; 𝑝 denotes the number of parent nodes of node 𝑣 ; 𝑠 denotes the number of child nodes of node 𝑣 , and equals the weight of node 𝑣 called 𝒘𝒊 . KE comprises the edges between any two vertices if and only if at least one pair of the corresponding links in G interfere with each other. lvi  lsin k  J (v i , v sink )

(2)

In (2), J(a,b) denotes the hop between node a and b. As shown in Fig. 3(c), we can see that the 𝑘 (𝑙 , 𝑝 , 𝑠 ) can indicate the layer of 𝑣 in G and the relationship between 𝑣 and its parent or child nodes. .

Definition 1. The problem that parent links are assigned time slots prior to child links, especially when data has not yet been transferred from child nodes to parent nodes, is addressed as the reverse time slots allocation problem.

(a)

(b)

(c)

Fig. 3. (a)Network topology G (b)Conflict graph 𝐺 (c) Aggregative conflict graph 𝐾

(a) E 

˄c˅ Fig. 2. (a).Network topology (b).Contiguous link scheduling (c).Contiguous link scheduling with time delay problem

A novel sleep scheduling called hierarchical link scheduling is designed to solve the problem given in definition 1. We first define a new conflict graph used in hierarchical link scheduling. Given an interference model in Section II-A, we propose an aggregative conflict graph 𝐾 = (K, KE) to model the interference among nodes and the attributions of each node. In

III.

HIERARCHICAL LINK SCHEDULING WITH PROACTIVE TIME SLOTS ACQUISITION (H-TSAC)

In this section, we describe a new algorithm called hierarchical link scheduling with proactive time slots acquisition (H-TSAC) that combines the hierarchical link scheduling and proactive time slots acquisition algorithm. The proposed link scheduling algorithm yields an efficient and yet simple performance which can reduce the energy consumption of nodes in the data gathering tree while reducing the time delay. We first study a kind of special node called a multi-parent node. The multi-parent node has two or more parent nodes to whom the multi-parent will forward the message.As shown in Fig. 4(a), if consecutive time slots are assigned to link1 and link2, the parent nodes 𝑃 (𝑣1) and 𝑃 (𝑣2) are transparent to child node 𝑣 in that when one of the parent nodes is awoken, the other can sleep and vice versa. The child node does not see any difference between this and a single-parent node. Moreover this method can improve the link redundancy and reduce transmission energy consumption of parent nodes. As shown in Fig. 5, we first divide the data gathering tree into different layers using Algorithm 1. Each node in the aggregative conflict graph 𝐾 obtains its layer value using formula (2) and obtains its relative network of parent and child nodes using 𝑃 and 𝑆 . The layer whose value calculated by (2)

IEEE/CIC ICCC 2015 Symposium on Wireless Communications Systems

is maximum is chosen as the basic layer named leaf layer, a continuous incremental set of time slots are first assigned to nodes belonging to the leaf layer. Then we ergodic next layer in a non-increasing order of layer value to monitor if there exists multi-parent nodes in this layer. Algorithm 3 will be used if multi-parent nodes exist in the layer. Otherwise if all the nodes have a single parent, Algorithm 2 will be employed. The ergodic process will continue unless the sink node is assigned time slots to receive all the object information collected by the leaf nodes

Fig. (a)Multi-parent

Fig. (b)Single-parent

MAX Tpvj1 , Tpvj 2 Tpvjn  , vi vi | svi  0  pvi  0 Tsvi   (3) 0, vi vi | svi  0  pvi  0 Algorithm 1 Hierarchical link scheduling with proactive time slots acquisition Input: the aggregated conflict graph 𝑲𝑮𝑪 , the time slots function𝑻𝒑𝒗𝒊 ,𝑻𝒔𝒗𝒊 , the relationship function 𝑷𝒗𝒊 , 𝑺𝒗𝒊 ,number of nodes 𝑁 , m,T={𝑡 , 𝑡 , … …} Output: a valid link scheduling , time delay 𝜏∆ , maximum number of state transitions 𝑁 , average number of state transitions 𝑁 , number of time slots 𝑁 1. 𝑙 ĕ0; 𝑙 =𝑙 +J(𝑉 , 𝑉 ) 2. mĕMAX{𝑙 , 𝑙 , … … 𝑙 } 3. 𝑡 = 𝑡 = 𝑡 =ĂĂ=𝑡 ĕt; 𝑗 ← 1; 𝑁 ← 1 4. For i=1;iİ𝑁 ;i++ 5. If 𝑙 =m 6. 𝑡 ĕt ;j++;𝑁 ++ 7. For m=MAX{𝑙 , 𝑙 , … … 𝑙 }-1;mı0;i-8. ergodic node 𝑣 where 𝑙 =m 9. If there is no 𝑝 ı2 10. Using Algorithm 2 to find a solution 11. Else 12. Using Algorithm 3 to find a solution Algorithm 2 is used when no multi-parent nodes are detected in the layer 𝑙 . As shown in algorithm 2, the nodes that have child nodes are called backbone nodes. These can first acquire time slots (𝑻𝒔𝒗𝒊 + t). While other nodes which have the same parent nodes with the backbone nodes will acquire time slots ( 𝑻𝒔𝒗𝒊 + n*t). Number n is greater than 1 and increase consecutively. Nodes which have the same parent node with backbone node but which do not have a child node will be consecutively assigned time slots from initial time slot 𝒕𝟏 in a non-decreasing order, since the transfer links of these nodes will not interfere with the backbone nodes’ links. Algorithm 2 Layer 𝑙 link scheduling with proactive time slots acquisition for no multi-parent nodes in 𝑙

Fig. 5. Hierarchical link scheduling with proactive time slots acquisition (HTSAC)

When a node 𝑣 is assigned its time slots, it will broadcast the information to all the nodes whose incident links interfere with links incident to 𝑣 . We present two functions 𝑻𝒑𝒗𝒊 and 𝑻𝒔𝒗𝒊 to identify the time slots assigned to node 𝑣 where: 𝑻𝒑𝒗𝒊 shows the time slot allocated to node 𝑣 to execute transmission process to its parent node; 𝑻𝒔𝒗𝒊 shows the time slots allocated to node 𝑣 to execute the receive process from its child nodes. It is evident that 𝑻𝒔𝒗𝒊 depends on the value of 𝑻𝒑𝒗𝒋 where 𝑣 is one of the child nodes of 𝑣 . 𝑻𝒔𝒗𝒊 is defined in (3) .

1. 2. 3. 4. 5. 6. 7. 8. 9.

For i=1;iİ𝑁 ;i++ For k=1;kİ𝑁 ;k++ If 𝑙 =m If 𝑠 >0 𝑡 ĕ𝑡 W𝑁 ++;𝑣 ← 𝑣 Else if 𝑠 =0 If 𝑃 =𝑃 𝑡 ĕ𝑡 W 𝑁 ++;𝑣 ← 𝑣 Else 𝑣 acquire time slot from 𝑡 again As shown in Algorithm 3, a valid link scheduling design is based upon multi-parent nodes. We can see that the multi-parent node 𝑣 has a priority to acquire time slots for the incident links with their parent nodes. The value of the time slot assigned to one of the links named 𝑙𝑖𝑛𝑘1 incident to its parent nodes equals (𝑻𝒔𝒗𝒊 +𝑾𝒑𝒗𝒊(𝒎𝒂𝒙)) where 𝑾𝒑𝒗𝒊(𝒎𝒂𝒙) is the maximum value of 𝑤 . We note that 𝑤 is one of attributes for 𝑘 proposed in

IEEE/CIC ICCC 2015 Symposium on Wireless Communications Systems

Section II-B. 𝑃 is the parents node of 𝑣 . Then the other named 𝑙𝑖𝑛𝑘2 acquire time slot (𝑻𝒔𝒗𝒊 +𝑾𝒑𝒗𝒊(𝒎𝒂𝒙) - t). When the multiparent node has been scheduled, other nodes which have same parent as the multi-parent node acquire their time slots based upon the links 𝑙𝑖𝑛𝑘1 and 𝑙𝑖𝑛𝑘2 . The nodes that have same parent with link 𝑙𝑖𝑛𝑘1 acquire time slots ( 𝑻𝒔𝒗𝒊 + 𝑾𝒑𝒗𝒊(𝒎𝒂𝒙) ( 𝑾𝒑𝒗𝒊(𝒎𝒂𝒙) -j*t)), where j is an integer greater than 1 and increases consecutively. Other nodes that have same parent with link 𝑙𝑖𝑛𝑘2 acquire time slots (𝑻𝒔𝒗𝒊 +𝑾𝒑𝒗𝒊(𝒎𝒂𝒙) - (1+ j)*t). We can see an example in Fig. 6 , where node E is the multi-parent node whose parents are B and C, 𝒆𝑩𝑬 denotes 𝑣1 and 𝒆𝑪𝑬 denotes 𝑣2 , 𝑾𝒑𝒗𝒆(𝒎𝒂𝒙) equals 3t because parent node B has a largest 3 child nodes, the numbers attached to links e indicate time slots acquired by nodes.

IV. SIMULATION RESULTS Here the average-case performance of the proposed hierarchical link scheduling with proactive time slots acquisition (H-TSAC) algorithm is validated. We also compare our algorithm with the recursive backtracking and distributed-delay algorithm in [8] and the degree-based algorithm in [10] as baseline. The performance metrics used in the evaluation include the number of state transitions, the number of time slots 𝑁 , and system time delay 𝜏∆ . In the simulations, nodes are generated randomly with a transmission range of 5m and an interference range of 10m that are deployed in a square area of 100m*100m. We test the network for a WSN whose nodes varies from 200 to 400 in steps of 50. We construct a data gathering tree rooted at a sink node. Fig. 7 shows the average number of state transitions for the following scheme: degree-based, recursive backtracking, distributed-delay, and H-TSAC. We can see that for the data gathering tree model, H-TSAC has a similar performance with recursive backtracking and distributed-delay scheme, and the maximum number of state transitions is two which is much less than that of the degree-based scheme. The average number of slots is shown in Fig. 8. The number of time slots increases as the number of nodes increases. The link incident to every node are scheduled together to obtain consecutive time slots to avoid frequent state transitions. Several gaps are formed among the assigned time slots (as seen in Fig. 6), which decreases the channel utilization, requiring more time slots compared to the degree-based scheme. By rearranging and recycling the time slots in H-TSAC, a performance comparable to the degree-based scheme and better than the distributed-delay scheme is yielded.

Fig.6. an example of H-TSAC

Algorithm 3 Layer 𝑙 link scheduling with proactive time slots acquisition for multi-parent nodes in 𝑙

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 

For i=1;iİ𝑁 ;i++ For k=1;kİ𝑁 ;k++ If 𝑙 =m If 𝑝 = 2 If 𝑊 ( ) > 𝑊 ( ) 𝑡 ( ) ĕ𝑡 W 𝑊 ( ) 𝑡 ( ) ĕ𝑡 ( ) − 𝑡 𝑣 ← 𝑣 Else if 𝑊 ( ) = 𝑊 ( ) 𝑡 ( ) ĕ𝑡 W 𝑊 ( ) 𝑡 ( ) ĕ𝑡 ( ) − 𝑡𝑣 ← 𝑣 If 𝑝 < 2 If 𝑃 =𝑃 (𝑣1) 𝑡 ĕ𝑡 ( ) (𝑊 ( ) M WM  If 𝑃 =𝑃 (𝑣2) 𝑡 ĕ𝑡 ( ) (𝑊 ( ) M WM

TDMA can provide a deterministic delay bound[5]. As in (4), 𝑡 indicates the time slots assigned to the node 𝑣 in 𝑙 which , the value of it will impact the system time is under the 𝑙 delay as 𝜏∆ depends on the maximum and the minimum of ⁄𝑡 where 𝑡 .We assume the time span of a slot is 𝑇 = 𝑇 is set to 3 seconds for data transmission and attributions 𝑇 synchronization. It is noted that 𝑇 is just defined for the simulation and is irrelevant to actual transmission time. The time delay in Fig. 9 increases as the number of nodes increases in the data gathering tree model. H-TSAC has the best performance, as it employs hierarchical link scheduling, which solves the reversed time slots allocation problem more effectively and makes contribution to reduce the time delay.



   min t T  max t T  2   max t T  min t T  12

   U min t pvi Teff , max t pvi Teff E  D 

pvi

eff

pvi

eff

(4)

2

pvi

eff

pvi

eff

We summarize the observations from the simulation results as follows. First, hierarchical link scheduling can reduce the number of state transition and thus reduce the energy consumption of radio in state transitions. This achieves better energy efficiency compared with the degree-based algorithm. Second, The TSAC algorithms can achieve a performance comparable to the degree-based algorithm within the assigned time slots. Third, the H-TSAC algorithm combines TSAC

IEEE/CIC ICCC 2015 Symposium on Wireless Communications Systems

algorithm and hierarchical link scheduling, and yields a better time delay performance compared with the recursive backtracking and the distributed-delay algorithm and a better energy saving performance compared with the degree-based algorithm. Number of state transitions

5 4.5 4

recursive backtracking

3.5

distributeddelay

3 2.5

H-TSAC

2

V. CONCLUSION In this paper, we propose a novel interference-free TDMA sleep scheduling scheme for WSNs, called hierarchical link scheduling with proactive time slots acquisition (H-TSAC). In this scheduling process, a node only needs to startup and sleep once per scheduling period. The child nodes actively acquire time slots in order to transfer object data to their parent nodes. Thus, we find that, the time delay and number of state transition can be reduced. The simulation results corroborate the theoretical analysis, and show that the H-TSAC algorithm is superior to existing baseline schemes such as recursive backtracking, distributed delay and degree-based sleep scheduling in terms of the number of state transitions, the number of slots assigned, and the system time delay. ACKNOWLEDGMENT

1.5

degree-based

1 200 250 300 350 400

Number of nodes Fig. 7 average number of state transitions

This work is supported by the National Natural Science Foundation of China (No.61271186) and Research and Application of Key Technologies in Smart Grid Park Energy Management and Optimization for Smart City and the Doctoral Scientific Fund Project of the Ministry of Education of China(20120005110001) REFERENCES

250

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[1]

200 150 100

recursive backtracking

[2]

distributeddelay

[3]

H-TSAC 50

[4]

degree-based

0

[5]

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Number of nodes [6]

Time delay(s)

Fig. 8 average number of slots assigned

[7]

900 800 700 600 500 400 300 200 100 0

[8]

recursive backtracking distributeddelay

[9] [10]

H-TSAC [11]

degree-based 200 250 300 350 400

[12]

Number of nodes [13] Fig. 9 system time delay [14]

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