Combined Sweeping and Jumping Method to Enhance Node Insertion Algorithm for Wi-Fi Sensor Networks

Abstract

Two dominant driving forces for evolving communication technologies in the current society have been the proliferation of wireless access networks to the Internet and the broadbandization of access and infrastructure networks. Through these evolutions of communication technologies, high-resolution contents are instantly delivered to wireless devices such as mobile phones, wireless tablets, and headsets. Recently, wireless sensor networks, where up to 1000 low-power sensors are wirelessly connected to each other, have been created and connected to the Internet, which presents a new challenge of efficiently coordinating the transmissions of many wireless sensors with minimal transmission overheads. Developing an efficient Medium Access Control (MAC) protocol governing the transmissions of wireless sensor networks is crucial for the success of wireless sensor networks for the realization of the Internet of Things (IoT). In 2023, the node insertion algorithm was proposed to efficiently derive the minimal number of serially connected multipolling sequences of many wireless sensors, by which Access Points (APs) can poll wireless sensors with minimal polling overheads. In this paper, the combined sweeping and jumping method is presented to dramatically enhance the searching performance of the node insertion algorithm. To validate the performance of the combined sweeping and jumping method, simulation results are presented for wireless sensor networks where wireless sensors with varying transmission ranges exist.

1. Introduction

Wi-Fi and Wireless Personal Area Network (WPAN) communication technologies have been employed to create wireless sensor networks [1,2,3,4]. In [1], the applications, the routing and connectivity schemes, the challenges, and the energy supply methods for wireless sensor networks are reviewed. In [2], the Medium Access Control (MAC), routing, and security protocols and energy management methods that are necessary for the medical applications in wireless sensor networks are reviewed. The survey of the technologies for improving the security of wireless sensor networks using machine learning techniques is provided in [3]. In [4], the node insertion algorithm is proposed for the connectivity-based multipolling MAC protocol to be applied to wireless sensor networks based on Wi-Fi networks where a large number of sensors exist. Each sensor has a short transmission range in wireless sensor networks based on WPAN networks like Bluetooth and Zigbee networks; therefore, in some cases, data should traverse through multi-hop links in wireless sensor networks based on WPAN networks. On the other hand, in wireless sensor networks based on Wi-Fi networks, sensors have larger transmission ranges, and can be connected to the Internet via single-hop links with small transmission delay.

In [5], the contention-based MAC protocols for Internet of Things (IoT) applications in Wi-Fi-based networks are presented. In [6], a Wi-Fi-based underwater sensor network was demonstrated. In [7], the contention-based MAC protocol was presented to minimize the energy consumption in wireless sensor networks based on non-802.11 networks. In [8], the contention-based cooperative receiver-initiated MAC protocol was proposed to reduce energy consumption and data collisions in wireless sensor networks based on non-802.11 networks. The hybrid MAC protocol combining Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) and Time Division Multiple Access (TDMA) schemes was presented for satisfying Quality of Service (QoS) requirements in wireless sensor networks based on non-802.11 networks in [9]. The TDMA-based MAC protocol was proposed to optimize the power-saving mechanism in wireless sensor networks based on non-802.11 networks in [10]. The approach for developing the contention-free MAC protocols in Wi-Fi-based wireless sensor networks draws little attention in the literature. However, as stated in [4], an efficient contention-free or polling-based MAC protocol should be developed for Wi-Fi-based wireless sensor networks because the contention-based MAC protocols suffer from severe performance degradation due to the contentions among sensors.

Since the initial development of Wi-Fi communication technology, the Distributed Coordination Function (DCF) and Point Coordination Function (PCF) protocols have been the basic MAC protocols to govern the transmissions in Wi-Fi networks [11]. In the DCF protocol, all nodes contend to access a Wireless Medium (WM) to transmit their data, and the DCF protocol functions well in Wi-Fi networks with a small number of nodes. However, in large Wi-Fi networks like wireless sensor networks with a large number of sensors, the DCF protocol has been known to have exponentially degraded MAC performance [12]. In the PCF protocol, each node polled by Access Points (APs) is granted the contention-free access to WM [11]. Therefore, the PCF protocol functions better than the DCF protocol in wireless sensor networks where many sensors attempt to send data. The DCF and PCF protocols are compared in terms of the channel access method and the appropriate network scenario in

Table 1. Comparison between DCF and PCF Protocols.

MAC Protocol	Channel Access Method	Appropriate Network Scenario
DCF	Contention-Based	Small Network with Small Number of Attempts of Simultaneous Transmissions
PCF	Contention-Free and Polling-Based	Large Network with Large Number of Attempts of Simultaneous Transmissions

.

For maximizing the performance of the PCF protocol, the connectivity-based multipolling MAC protocol was presented in [13,14] where the number of multipolling frame transmissions is minimized by the serially connected multipolling sequences derived based on the connectivity information among nodes. The connectivity-based multipolling MAC protocol was employed for the direct communication between nodes in [13], and for the reliable multicast transmission in [14]. In [13,14], the backtracking algorithm was employed to derive the minimal number of serially connected multipolling sequences for the nodes in Wi-Fi networks. However, in some cases of Wi-Fi networks with a large number of nodes, more than 100, the backtracking algorithm consumes excessive time to derive the minimal number of serially connected multipolling sequences. The search space of possible multipolling sequences of nodes should be reduced to alleviate the problem of excessive time taken by the backtracking algorithm so that Wi-Fi networks are seamlessly evolved to wireless sensor networks.

In [4], the node insertion algorithm was proposed to reduce the search space of multipolling sequences of sensors by composing the multipolling sequences in the manner by which the new sensors are inserted that have the greatest connectivities with the recently inserted sensors, without retracting the existing sensors in the multipolling sequences in the process. Whereas the backtracking algorithm has the computational complexity of O(l!), the node insertion algorithm has the computational complexity of O(l³). As the numbers of sensors existing in wireless sensor networks grow, the numbers of derived serially connected multipolling sequences converge to 1. The search space of multipolling sequences of sensors still needs to be reduced so that the connectivity-based multipolling MAC protocol is more easily applied to wireless sensor networks.

To further reduce the search space of multipolling sequences of sensors, the new sweeping method eliminates the repetitive search for the connectivity information with the sensors that have been inserted. To accelerate the search process, over the two-dimensional search space of the connectivity information between the inserted sensors and the remaining sensors that have not been inserted yet, the jumping method skips the unnecessary search. Thanks to the combined sweeping and jumping method, the node insertion algorithm can be enhanced so that the resulting computational complexity is reduced to O(l²).

This paper is organized as follows. Following the introduction, in the next section, the proposed combined sweeping and jumping method is introduced. Numerical results are presented to validate the proposed combined sweeping and jumping method in Section 3. The issues including scalability, hardware implementation, and performance metrics of data loss and delay that are relevant to the node insertion algorithm with the combined sweeping and jumping method are discussed in Section 4. Finally, some conclusions are drawn, and future research themes are suggested in Section 5.

2. Combined Sweeping and Jumping Method

Assume a wireless sensor network where an AP and l sensors of sensor 1, sensor 2, …, sensor l exist. When sensor i transmits a data frame to the AP, the transmission signal from sensor i can be picked up and understood by sensor j (≠ i). This status of the wireless channel between sensors i and j is represented by C_i,j = 1. C_i,j = 0 represents the status of the wireless channel that sensor j cannot interpret the transmission signal from sensor i. The connectivity information of C_i,j can be efficiently collected by the connectivity-based multipolling MAC protocol described in [13,14].

For convenience of explanation of the proposed combined sweeping and jumping method, Figure 1 depicts a wireless sensor network where l = 12 sensors that are located at the boundary of the circular service area with a radius of r, and an AP is located at the center of the service area.

If the transmission signal from each sensor in Figure 1 is propagated in the circular form with the transmission range of r, the connectivity information among 12 sensors is represented by the following matrix:

$$\left[c_{i,j}\right]=\left[\begin{array}{c}\begin{array}{cccccccccccc}0& 1& 1& 0& 0& 0& 0& 0& 0& 0& 1& 1\\ 1& 0& 1& 1& 0& 0& 0& 0& 0& 0& 0& 1\\ 1& 1& 0& 1& 1& 0& 0& 0& 0& 0& 0& 0\\ 0& 1& 1& 0& 1& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 1& 0& 1& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 1& 0& 1& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 1& 0& 1& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 1& 0& 1& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 1& 0& 1& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1& 1& 0& 1& 1\\ 1& 0& 0& 0& 0& 0& 0& 0& 1& 1& 0& 1\\ 1& 1& 0& 0& 0& 0& 0& 0& 0& 1& 1& 0\end{array}\end{array}\right]$$

In Figure 1, the angle between the lines from the AP to two sensors that have a common neighboring sensor is 60°, and the distance between two sensors that have a common neighbor is r. Therefore, two neighboring sensors and two sensors that have a common neighbor are connected with each other because two sensors are located within the transmission range of each other.

The backtracking algorithm in [13,14] and the node insertion algorithm in [4] try to sequence the sensors in the manner in which the cases where sensor j cannot interpret the transmission signal from the previous sensor i in the sequence, that is, C_i,j = 0, occur as little as possible. By the minimization of the cases where a sensor cannot interpret the transmission signal from the previous sensor in the sequence, the connectivity-based multipolling MAC protocol can minimize the transmissions of multipolling frames, which are the transmission overhead for uplink data transmissions from sensors in wireless sensor networks.

In the node insertion algorithm in [4], after selecting an arbitrary sensor as the first inserted sensor, the next sensor inserted into the sequence in the process is selected by searching for the set of sensor j’s that have not been selected for each sensor i in the sequence, such as C_k,j = 1 for all the recently inserted sensor k’s up to sensor i. The set of these sensor j’s for sensor i will be denoted by S_i. The search for the set of sensor j’s is sequentially conducted for each sensor i from the most recently inserted sensor i to the firstly inserted sensor i until the obtained set of sensor j’s is empty or S_i’s have been obtained for all the sensor i’s in the sequence. A sensor in the lastly obtained non-empty set of sensor j’s is selected as the next sensor inserted into the sequence of sensors. The selected sensor is a sensor that is connected from as many most recently inserted sensors in the sequence in the process as possible.

Let us apply the node insertion algorithm to the wireless sensor network in Figure 1. Let sensor 5 be the first inserted sensor in the sequence of sensors. Then, S₅ = {3, 4, 6, 7} is obtained because C_5,3 = C_5,4 = C_5,6 = C_5,7 = 1, and C_5,j = 0 for other j’s. Sensor 6 can be arbitrarily selected as the next inserted sensor from S₅. Then, S₆ = {4, 7, 8} can be obtained because C_6,4 = C_6,7 = C_6,8 = 1, and C_6,j = 0 for other unselected j’s. Furthermore, S₅ = {4, 7} can be obtained because C_6,4 = C_6,7 = C_5,4 = C_5,7 = 1, and C_6,j = 0 or C_5,j = 0 for other unselected j’s. Sensor 4 can be arbitrarily selected as the third inserted sensor from S₅. S₄ = {2, 3} can be obtained because C_4,2 = C_4,3 = 1, and C_4,j = 0 for other unselected j’s. S₆ = ϕ can be obtained because C_4,j = 0 or C_6,j = 0 for all the unselected j’s. Therefore, the fourth inserted sensor should be selected from S₄. Sensor 2 can be arbitrarily selected as the fourth inserted sensor from S₄. Then, S₂ = {1, 3, 12}, S₄ = {3}, and S₆ = ϕ can be obtained. Therefore, the fifth inserted sensor should be sensor 3. In this manner, the next inserted sensors can be sequentially selected until all the sensors are covered by the constructed sequence of sensors. For the wireless sensor network in Figure 1, a single serially connected multipolling sequence can be obtained as [sensors 5, 6, 4, 2, 3, 1, 12, 11, 10, 9, 8, 7] by the node insertion algorithm.

Generally, without the preknowledge of the sets S_i’s, which were obtained for inserting the previous sensor in the multipolling sequence, or exploiting the old sets S_i’s for the previous sensor to obtain the new sets S_i’s for selecting the new sensor, to select a sensor that is inserted into the multipolling sequence in the process, the connectivities between the sensors in the multipolling sequence and the unselected sensors should be taken into account. Therefore, the computational complexity for selecting a sensor that is inserted into the multipolling sequence in the process is O(l²), and the overall computational complexity for selecting l sensors by the original node insertion algorithm amounts to O(l³).

Now, the combined sweeping and jumping method is proposed to enhance the node insertion algorithm. During the course of inserting the sensors into the sequence in the process of construction, let N be the number of sensors in the current sequence, and sensor F(i) for i ≤ N be the ith inserted sensor in the sequence. For the proposed sweeping method, D_j for unselected sensor j is defined as

$$D_j=Max\left\{i|C_{F\left(i\right),j}=0\right\},$$

which is the place of the most recently inserted sensor, from which the transmission signal cannot be successfully received and interpreted by unselected sensor j. For the convenience of explanation, D_j = 0 when unselected sensor j can interpret the transmission signal from all the sensors in the current sequence, and D_j = −1 for selected sensor j. D denotes the vector $\left[D_1, D_2,\dots , D_l\right]$. After a sensor is inserted into the sequence, D_j for unselected sensor j can be updated by the following:

$$D_j=N \mathrm{for} \mathrm{unselected} \mathrm{sensor} j \mathrm{such} \mathrm{that} C_{F\left(N\right),j}=0.$$

Note that the smaller D_j is, the greater connectivity sensor j has with the recently inserted sensors, and during the course of inserting the sensors into the sequence, D_j does not decrease. According to the node insertion algorithm, sensor j that has the smallest value of D_j should be selected as the next inserted sensor in the sequence.

For example, in Figure 1, assume that after the initial insertion of sensor 1, sensor 3 was inserted into the multipolling sequence. Sensor 2 has the connectivities with all the selected sensors, sensors 1 and 3; therefore, D₂ = 0. Sensors 4 and 5 have the connectivity with the second selected sensor, which is sensor 3; however, they do not have the connectivity with the first selected sensor, which is sensor 1. Therefore, D₄ = D₅ = 1. Sensors 6 to 12 do not have the connectivity with the last selected sensor, which is sensor 3; therefore, D₆ = D₇ = … = D₁₂ = 2. This process of updating D_j’s can be simplified by the preceding equation. Initially, all D_j’s are set to 0. After the insertion of sensor 1, for all the unselected sensor j’s that do not have the connectivity with sensor 1, D_j’s are switched to 1; therefore, D₄ = D₅ = … = D₁₀ = 1. After the second insertion of sensor 3, for all the unselected sensor j’s that do not have the connectivity with sensor 3, D_j’s are switched to 2; therefore, D₆ = D₇ = … = D₁₂ = 2. Sequentially updating D_j’s using the preceding equation, the result of D_j’s matches with D_j’s that are directly obtained from the equation that defines D_j’s.

In the proposed sweeping method, an arbitrary sensor is initially inserted into the sequence, and after that, D_j is scanned for sensor j from j = 1 to j = l, and all the unselected sensor j’s such that D_j = m = 0 are sequentially inserted into the sequence. Every time when a new sensor is inserted into the sequence, D_j should be updated according to the preceding equation before the insertion of a new sensor into the sequence. After the completion of scanning D_j with m = 0, D_j is scanned for sensor j from j = 1 to j = l, and all the unselected sensor j’s such that D_j = m = 1 are sequentially inserted into the sequence. Continuously increasing m by 1, D_j is scanned for sensor j from j = 1 to j = l, and all the unselected sensor j’s such that D_j = m are sequentially inserted into the sequence. Every time when a new sensor is inserted into the sequence, D_j should be updated according to the preceding equation. This process of inserting the sensors into the sequence continues until all the sensors are covered by the constructed sequence. In the proposed sweeping method, m cannot exceed l; therefore, the proposed sweeping method has the computational complexity of O(l²), which is far lower than the computational complexity of the original node insertion algorithm.

Let us apply the proposed sweeping method to the wireless sensor network in Figure 1. After inserting the first sensor of sensor 5, D = $\left[1, 1, 0, 0,-1, 0, 0, 1, 1, 1, 1, 1\right]$. Scanning D with m = 0 from j = 1, sensor 3 is inserted as the second sensor in the sequence, and D = $\left[1, 1,-1, 0,-1, 2, 2, 2, 2, 2, 2, 2\right]$. Scanning D with m = 0 from j = 4, sensor 4 is inserted as the third sensor in the sequence, and D = $\left[3, 1,-1,-1,-1, 2, 3, 3, 3, 3, 3, 3\right]$. Scanning D with m = 1 from j = 1, sensor 2 is inserted as the fourth sensor in the sequence, and D = $\left[3,-1,-1,-1,-1, 4, 4, 4, 4, 4, 4, 3\right]$. Scanning D with m = 2, no sensor j is found such that D_j = m = 2. Scanning D with m = 3, sensor 1 is inserted as the fifth sensor in the sequence, and D = $\left[-1,-1,-1,-1,-1, 5, 5, 5, 5, 5, 4, 3\right]$. Continuing the proposed sweeping method for the wireless sensor network in Figure 1, [sensors 5, 3, 4, 2, 1, 12, 11, 10, 9, 8, 7, 6] is the final constructed serially connected single multipolling sequence, by which all 12 sensors can be multipolled by the AP.

Now, the proposed jumping method is explained. After each scanning process of the proposed sweeping method for D_j from j = 1 to j = l, the minimal value of D_j’s for unselected sensor j can be obtained. Since D_j does not decrease, it is advantageous to scan D_j with the m set to this minimal value instead of increasing m by just 1, for the next scanning process for D_j from j = 1. This method of scanning D with the m set to the minimal value of the previous scanned values of D_j’s for unselected sensor j is called the jumping method. The proposed jumping method accelerates the search speed of the sweeping method by scanning D with m increased by more than 1. The flow chart of the node insertion algorithm with the combined sweeping and jumping method is depicted in Figure 2 where MIN represents the minimal value of D_j’s for unselected sensor j.

3. Numerical Results

For wireless sensor networks where l = 10, 20, 30, …, 100, 200, 400, 600, 800, 1000, sensors are randomly located over the circular service area with a radius of r, and an AP is centered; the performances of the node insertion algorithm with and without the enhancement in the combined sweeping and jumping method are compared. The transmission signal from each sensor is assumed to be propagated in the circular form. The transmission range of sensor i for i = 1, 2, …, l is assumed to vary as $r+0.1\times \left(i mod 6\right)\times r$.

To obtain the accurate numerical results, 50 random networks were generated for each case of the node insertion algorithm with and without the proposed combined sweeping and jumping method, and l’s. The mean numbers of serially connected multipolling sequences for l sensors, and the mean times taken to derive the serially connected multipolling sequences, are compared for the node insertion algorithm with and without the enhancement in the proposed combined sweeping and jumping method in

Table 2. Mean number of serially connected sequences and mean time taken for derivation (circular service area).

		l
		10	20	30	40	50	60	70	80	90	100	200	400	600	800	1000
W/o Sweep and Jump	Avg. # of Polls	1.5	1.5	1.5	1.2	1.4	1.3	1.3	1.2	1.2	1.3	1.2	1.2	1.1	1.1	1.1
	Time Taken (ms)	0.02	0.1	0.2	0.4	0.8	1.3	1.9	2.2	2.0	1.6	7.7	46.8	153.1	362.8	709.4
With Sweep and Jump	Avg. # of Polls	1.4	1.3	1.4	1.4	1.3	1.4	1.3	1.3	1.3	1.3	1.2	1.0	1.1	1.1	1.1
	Time Taken (ms)	0.006	0.01	0.04	0.07	0.1	0.09	0.09	0.1	0.1	0.1	0.3	0.5	0.8	1.2	1.6

. Additionally, for the stress test for the node insertion algorithm with and without the proposed combined sweeping and jumping method, l sensors are let to be concentrated near the boundary of the circular service area so that the sensors are randomly located outside the distance of 0.8r from the AP. By concentrating the sensors on the donut-shaped area near the boundary of the circular service area, the connectivities between the sensors located at the opposite sides are cut off. The circular and donut-shaped service areas are depicted in Figure 3. When the sensors are located over the donut-shaped area, the mean numbers of serially connected multipolling sequences, and the mean times taken to derive the serially connected multipolling sequences, are also presented for the node insertion algorithm with and without the combined sweeping and jumping method in

Table 3. Mean number of serially connected sequences and mean time taken for derivation (donut-shaped service area).

		l
		10	20	30	40	50	60	70	80	90	100	200	400	600	800	1000
W/o Sweep and Jump	Avg. # of Polls	1.88	1.5	1.1	1.1	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
	Time Taken (ms)	0.03	0.09	0.2	0.4	0.7	1.3	1.5	2.3	2.3	2.9	6.3	54.8	190.8	441.2	708.6
With Sweep and Jump	Avg. # of Polls	1.68	1.42	1.16	1.0	1.02	1.1	1.1	1.1	1.1	1.1	1.0	1.0	1.02	1.0	1.0
	Time Taken (ms)	0.01	0.03	0.07	0.1	0.1	0.1	0.1	0.09	0.2	0.2	0.4	0.7	1.0	2.1	2.9

. The simulations are conducted using a computer of 1.6 GHz CPU and 8 GB RAM.

As can be seen in Table 2 and Table 3, for the circular and donut-shaped service areas, the node insertion algorithm derives a smaller number of serially connected multipolling sequences of sensors both with and without the proposed combined sweeping and jumping method as the number l of sensors grows in wireless sensor networks. It can be seen that in the case of l = 1000, almost a single serially connected multipolling sequence is produced by the node insertion algorithm both with and without the proposed sweeping and jumping method. It also can be seen that for the circular and donut-shaped service areas, the times taken for the node insertion algorithm both with and without the proposed sweeping and jumping method to derive the serially connected multipolling sequences of sensors grow as the number l of sensors grows in wireless sensor networks. The proposed combined sweeping and jumping method significantly reduces the time taken to produce the near-optimal number of serially connected multipolling sequences for the sensors in wireless sensor networks. When l = 1000, the node insertion algorithm with the proposed combined sweeping and jumping method on the average produces the near-optimal solution within 1.6 ms and 2.9 ms in the cases of the circular and donut-shaped service areas, respectively.

The results of the stress test for the node insertion algorithm by concentrating the sensors near the boundary of the service area rather than distributing the sensors over the circular service area are explained. Compared to the results of the circular service area, the results of the donut-shaped service area show that the node insertion algorithm without the combined sweeping and jumping method on the average produces about a 13.2% smaller number of serially connected multipolling sequences within about a 9.5% larger amount of time. Furthermore, compared to the results of the circular service area, the results of the donut-shaped service area show that the node insertion algorithm with the combined sweeping and jumping method on the average produces about an 11.1% smaller number of serially connected multipolling sequences within about a 5.9% larger amount of time. In can be seen that even though the node insertion algorithm with the combined sweeping and jumping method takes slightly more time to produce the pseudo-optimal number of serially connected multipolling sequences for the donut-shaped service area than it does for the circular service area, it works fine to produce the pseudo-minimal number of serially connected multipolling sequences.

By the node insertion algorithm with the proposed combined sweeping and jumping method, APs can update the near-optimal numbers of serially connected multipolling sequences that cover all the sensors in wireless sensor networks about every 3 or 4 ms, reflecting the connectivity information among sensors in an almost real-time manner. Thanks to the node insertion algorithm with the proposed combined sweeping and jumping method, the connectivity-based multipolling MAC protocol is able to be applied to wireless sensor networks with an immense number of sensors.

4. Discussions

Originally, the connectivity-based multipolling MAC protocol was proposed to optimize the mutipolling sequence of nodes in Wi-Fi networks using the backtracking algorithm, which is one Artificial Intelligence (AI) technique. However, the backtracking algorithm is inappropriate to be applied to wireless sensor networks, where a large number of sensors exist, because it sometimes takes too much time to derive the minimal number of serially connected multipolling sequences. The node insertion algorithm was proposed for the connectivity-based multipolling MAC protocol to be more easily applied to wireless sensor networks by cutting down the computational complexity and the actual time taken for deriving the pseudo-optimal number of serially connected multipolling sequences even in wireless sensor networks with up to 1000 sensors. The combined sweeping and jumping method is proposed to significantly reduce further the computational complexity and the actual time taken for deriving the pseudo-optimal number of serially connected multipolling sequences. As far as is known to the author, the combined sweeping and jumping method is unique in enhancing the node insertion algorithm for the connectivity-based multipolling MAC protocol for wireless sensor networks.

As stated in [4], all the MAC protocols for wireless sensor networks based on Wi-Fi networks are categorized into the contention-based and polling-based MAC protocols. The contention-based MAC protocols suffer from the immense interference among sensors in wireless sensor networks where a large number of sensors exist. On the other hand, the polling-based MAC protocols can effectively avoid the interference among sensors because APs grant uplink transmission opportunities to sensors in a centralized manner. The connectivity-based multipolling MAC protocol modifies the PCF protocol, which is the basic polling-based MAC protocol for Wi-Fi networks, so that the transmission overhead is minimized; therefore, the polling efficiency is maximized. The connectivity-based multipolling MAC protocol, which is powered by the node insertion algorithm with the combined sweeping and jumping method, is unique in maintaining the framework of the original polling-based MAC protocol for Wi-Fi networks and achieving the maximized efficiency of the polling-based MAC protocol.

As illustrated in [13,14], the connectivity-based multipolling MAC protocol can be employed for the efficient direct communication between nodes and the reliable multicast transmission in Wi-Fi networks. However, due to the lack of the scalability of the backtracking algorithm that was used to derive the minimal number of serially connected multipolling sequences, the direct communication and reliable multicast MAC protocols that were specified in [13,14] cannot be easily applied to wireless sensor networks where a large number of sensors exist. Thanks to the node insertion algorithm with the combined sweeping and jumping method, the connectivity-based multipolling MAC protocol can be directly applied for the direct communication between sensors and the reliable multicast transmission in wireless sensor networks where a large number of sensors exist.

Even though the node insertion algorithm with the combined sweeping and jumping method was experimented for wireless sensor networks with up to 1000 sensors in the previous section, it was also found that the node insertion algorithm with the combined sweeping and jumping method on the average produces 1.02 and 1.0 serially connected multipolling sequences within 102.5 and 175.0 ms in the circular and donut-shaped service areas of wireless sensor networks with 10,000 sensors, respectively. The node insertion algorithm with the combined sweeping and jumping method can be implemented in about 40 lines of the Java program; therefore, the hardware can be developed for implementing the node insertion algorithm with the combined sweeping and jumping method without much difficulties. Through the hardware implementation of the node insertion algorithm with the combined sweeping and jumping method, the pseudo-optimal number of serially connected multipolling sequences are expected to be derived in real time even in wireless sensor networks with up to 10,000 sensors.

As explained in [4], the connectivity-based multipolling MAC protocol supports the reliable unicast data transmission. The reduction in the transmission delay through the connectivity-based multipolling MAC protocol can be explained as follows: When the connectivity-based multipolling MAC protocol is employed for the uplink transmission from each sensor to an AP, the queueing delay of the transmission buffer in each sensor can be approximately analyzed by the G/D/1 queueing model where the polling cycle time of the connectivity-based multipolling MAC protocol is the service time for the uplink transfer of data queued in the transmission buffer of each sensor. According to the queueing analysis for the G/D/1 model in [15], the mean queueing delay is exponentially proportional to the polling cycle. Through the pseudo-minimal number of serially connected multipolling sequences that are derived by the node insertion algorithm with the combined sweeping and jumping method, the AP can poll each sensor with the pseudo-minimal polling cycle time for the uplink transfer of data queued in the transmission buffer of each sensor. Therefore, the effective reduction in transmission delay through the connectivity-based multipolling MAC protocol can be achieved.

The various environmental factors like humans and other objects that obstruct the transmission signal, the interference from other devices that operate in the overlapped frequency band, and the addition or removal of sensors in wireless sensor networks can affect the connectivity information among sensors in wireless sensor networks. As specified in [4,13,14], under the connectivity-based multipolling MAC protocol, APs can efficiently collect the updated connectivity information from sensors, and derive the serially connected multipolling sequences from the updated connectivity information among sensors.

5. Conclusions

For the development of the efficient MAC protocol for wireless sensor networks, the connectivity among sensors should be taken into account for the design of the MAC protocol. The connectivity-based multipolling MAC protocol modifies the PCF protocol, which is a basic MAC protocol for Wi-Fi networks, and optimizes the MAC efficiency by minimizing the polling transmissions based on the connectivity among sensors. For the connectivity-based multipolling MAC protocol to be easily applied to wireless sensor networks, an efficient algorithm for deriving the optimal number of serially connected multipolling sequences of sensors is needed. The node insertion algorithm was proposed to efficiently derive the near-optimal number of serially connected multipolling sequences by eliminating the retracting process in composing the sequences of sensors, and inserting the sensors that have the greatest connectivities with the recently inserted sensors.

In this paper, to enhance the performance of the node insertion algorithm, the combined sweeping and jumping method was proposed to reduce the search space required for the node insertion algorithm. The computational complexity for the node insertion algorithm has been significantly reduced by the proposed combined sweeping method. By numerical results, it has been verified that the time for the node insertion algorithm to take for deriving the near-optimal number of serially connected multipolling sequences can also be significantly enhanced by the proposed combined sweeping and jumping method.

To tackle the issue of the energy consumption of sensors under the connectivity-based multipolling MAC protocol, the connectivity-based multipolling MAC protocol should be improved so that only the sensors having data to transfer are polled by APs. Furthermore, the security issue for detecting fraudulent sensors and authenticating genuine sensors should be addressed for the connectivity-based multipolling MAC protocol. These problems are left for future researchers.