An Efficient SS-MAC Protocol for IEEE 802.15.4-Based WSNs of Cluster Tree Topology

Abstract

Wireless sensor networks (WSNs) based on the IEEE 802.15.4 standard have important applications in many fields, such as the Internet of Things and smart cities because of their low energy consumption. Hybrid carrier sense multiple access/time division multiple access (CSMA/TDMA) is the key technique to reduce energy consumption in the standard, but it also increases packet delay and reduces network throughput. Although the cluster tree topology is a typical topology defined by the IEEE 802.15.4 standard, there are few efficient medium access control (MAC) protocols specifically for this type of topology. To this end, we present an improved hybrid CSMA/TDMA MAC protocol based on a sharable slot algorithm for WSNs with cluster tree topology, called sharable slot-based MAC (SS-MAC). By designing the operating mechanism and frame structure, improving the hybrid CSMA/TDMA and channel-hopping techniques of IEEE 802.15.4 MAC, and introducing a sharable slot algorithm to wake up tree nodes asynchronously as well as a short address strategy to identify member nodes, the proposed protocol improves packet delay and throughput under the premise of low collision and low node energy consumption. Moreover, we derive mathematical expressions of the parameters of the sharable slot algorithm and evaluate the energy consumption, throughput and packet delay of the SS-MAC based on the queue modeling of packet arrivals. Numerical simulations verify that the proposed MAC protocol outperforms the other three existing MAC protocols, namely, IEEE 802.15.4 MAC, SSMA and LELLMAC, in terms of energy consumption, throughput and packet delay.

1. Introduction

The IEEE 802.15.4-2006 standard defines medium access control (MAC) and physical layer (PHY) specifications for low-rate wireless personal area networks (LR-WPANs). It defines two types of devices: full functional devices (FFDs) and reduced functional devices (RFDs). FFD can play any role in a WPAN, such as personal area network (PAN) coordinator, coordinator and device. It can communicate with any type of device, whereas RFD can only communicate with FFD because of hardware limitations.

A cluster tree network is a typical network structure for WPANs as well as wireless sensor networks (WSNs). All cluster heads (CHs) establish a tree topology according to a certain routing algorithm and notify the nearby devices to join them by broadcasting messages. To reduce the cost of the network layout, the sink (i.e., the root node) of the sharable slot-based MAC (SS-MAC) proposed in this paper is served by the PAN coordinator, the remaining tree nodes (i.e., CHs) are coordinators, and the cluster member nodes can be RFDs.

The MAC protocols of WSNs are mainly divided into the following two categories: (1) contention-based and (2) contention-free (or slot scheduling-based) [1,2,3]. In contention-based MAC protocols, nodes and their neighbors typically follow a carrier sense multiple access/collision avoidance (CSMA/CA) technique to compete for medium resources. Nodes use medium resources on demand and can achieve flexible and efficient data transmission under low traffic load conditions. However, when the load increases, multiple nodes try to access the medium at the same time and network performance is degraded due to the number of collisions and packet retransmissions increase. Researchers have proposed many contention-based MAC protocols, such as SPEECH-MAC [4], DCO-MAC [5] and others.

In contention-free-based MAC protocols, time-division multiple access (TDMA) is one of the most commonly used techniques. A manager node or sink divides the system time into slots and allocates slots to nodes in the network according to the demands of the nodes or in a fixed way. A node can access only the allocated slots without any contention with its neighbors. Therefore, less collision and avoiding idle listening are the main advantages of this type of MAC protocol. It also provides predictable packet delay. However, if the allocated slots cannot meet the communication requirements exactly, it is easy to cause either medium resource wasting or an increase in packet delay.

Because of the aforementioned shortcomings, it is difficult to meet the requirements for reliable and efficient data transmission in WSNs using only one category of the MAC protocols above. Therefore, the MAC protocols of hybrid CSMA/TDMA have attracted many researchers’ attention, such as iQueue-MAC [2], MPCB-HM [6], Asym-MAC [7], SSMA [8] and IEEE 802.15.4 [9,10,11,12,13,14,15,16]. To reduce the overhead of the nodes, MPCB-HM utilizes CSMA/CA to exchange the data and TDMA to inform the data transmission sequence. iQueue-MAC selects a CSMA/CA technique to transmit data at low load, and changes to TDMA when the load becomes high, which helps to improve the utilization of medium resources. The Asym-MAC was proposed to combat performance degradation due to asymmetric links in low duty-cycled WSNs. The SSMA utilizes a distributed slot scheduling mechanism to solve the problem of obtaining global topology information in large-scale networks. In beacon-enabled mode, the IEEE 802.15.4 standard realizes the combination of CSMA/CA and TDMA mechanisms by setting a contention access period (CAP) and a contention-free period (CFP) in the superframe structure of beacons.

The CSMA/CA technique based on IEEE 802.15.4-2006 requires the source node to perform exponential backoff several times and clear channel assessment (CCA) operations twice before data frame transmission. After sending a data frame, the source node needs to wait for an acknowledgement (ACK) frame from the destination. The technique effectively reduces the conflicts between nodes accessing the same channel, and is simple and flexible for low-load dynamic WSNs. However, multiple carrier sensing and ACK frames create additional overhead, which, in turn, reduces network throughput. Therefore, many researchers have established discrete-time Markov models to evaluate the performance of the CSMA/CA technique based on IEEE 802.15.4 and improve the technique [10,11,12,13,14,15]. The throughput, delay, energy consumption and other performance of the slotted CSMA/CA technique of beacon-enabled IEEE 802.15.4 networks have been evaluated, and compared and analyzed against the performances of slotted and unslotted CSMA/CA techniques in [11]. References [12,13] apply the MAC layer to perform CCA operation only once instead of twice to improve the transmission efficiency of the data frames. Furthermore, some researchers have sought to evaluate the impact of various factors, such as parameters setting [16], a hidden terminal [14] and interference from IEEE 802.11 [15], on the performance of the IEEE 802.15.4 network.

The IEEE 802.15.4-2006 standard defines two address formats: a 64-bit extended address and a 16-bit short address. The former is a globally unique address that is assigned before the device accesses the network. Nodes in the same network can use assigned short addresses to communicate with each other. The BEST-MAC protocol proposed in [3] assigns each node an 8-bit shorter address to reduce the control overhead. Use of a channel-hopping mechanism is an effective method to reduce communication interference between nodes in wireless sensor networks. The IEEE 802.15.4-2006 standard divides the 2.4 GHz band into 16 channels. By setting the channel page field of the command frame format, nodes can implement communication in any of the channels.

Mobile wireless sensor networks(MWSNs), which support the movement of nodes or sink in the deployment area, have eventual application in various areas, such as health care monitoring, wildlife monitoring and so on. In order to prolong the lifetime of MWSNs, researchers have developed many effective routing algorithms for various mobility patterns. In reference [17], the network was divided into different regions. The nodes in region 1 are closer to the sink and can communicate directly with the sink, whereas the nodes in region 2 need to forward their sensed data to the sink through routing nodes as described in [17]. Reference [18] proposed an Energy Constrained Mobile Routing (ECMR) algorithm for real-time applications and compared various performance with other existing routing protocols. In addition, many researchers enhance the performance of MWSNs by optimizing the routes of mobile sinks, such as [19,20,21]. They have proposed routing protocols based on expected area, target location algorithm and bipartite graph theory, respectively. In [22], the authors proposed a routing protocol called dynamic multi-hop low energy adaptive clustering hierarchy (DMH-LEACH), which combines multi-hop transmissions, dynamic clustering and node mobility. There are three types of nodes deployed in the network defined by [22], sink, CHs and other nodes, and all the nodes are mobile after deployment. The data transmission between the nodes and their CHs adopts a single-hop mode, while the data transmission between CHs and sink adopts a multi-hop (i.e., level-by-level) mode. In our proposed SS-MAC, the DMH-LEACH protocol can be adopted to construct tree routing between CHs.

Based on the above techniques, a sharable slot-based MAC (SS-MAC) is proposed in this study by combining the superframe structure of the IEEE 802.15.4-2006 standard with the sharable slot idea in SSMA [8], which makes the protocol more suitable for cluster tree structered topologies networks. In addition, the SS-MAC adopts a design of short node address (8-bit) that is similar to BEST-MAC [3] to reduce packet size and control overhead. The SS-MAC improves the channel-hopping mechanism of the IEEE 802.15.4-2006 standard by dividing channels into public and private to reduce external interference of nodes. The SS-MAC selects two channels as public channels, which are used for communication between CHs, where one is the primary channel and the other is the alternate channel. The remaining channels are allocated to CHs according to a DMH-LEACH protocol proposed in [22]. CHs use allocated channels to communicate with their members. At present, the channel-hopping mechanism and the similar rate-splitting multiple access (RSMA) technique are important methods for suppressing interference and improving spectral efficiency in large-scale wireless communication networks, such as the Internet of Things and satellite communications [23].

As mentioned above, large-scale MWSNs have broad application prospects. At present, the research on these focuses on either routing algorithm design or MAC layer technical improvements, and few studies combine them together. This paper aims to propose a MAC layer data collection protocol for MWSNs, called SS-MAC, which combines routing design and MAC layer technical improvements. The SS-MAC provides an overall plan for the data collection process of the network, and describes in detail the whole process from member node to CH, which forwards the data to the sink node level-by-level through tree routing. In brief, the major contributions of the SS-MAC protocol proposed in this paper can be outlined as follows:

(1)

It uses a hybrid CSMA/TDMA technique and channel-hopping mechanism to reduce inter-node interference;

(2)

It improves the sharable slot (SS) algorithm proposed in [8] to wake up tree nodes level-by-level according to the network topology, thereby reducing the energy consumption caused by node listening;

(3)

It employs an 8-bit short address to identify member nodes, thereby reducing the control overhead of nodes;

(4)

It improves the knapsack algorithm proposed in [3] to determine the number of slots and assignment order for each member node;

(5)

The whole network adjusts the duty cycle and the length of the sharable slot periodically to better adapt to the dynamic traffic load.

Moreover, we derive and analyze the mathematical expressions of the parameters of the sharable slot algorithm, and evaluate the energy consumption, throughput and packet delay performance of the SS-MAC-based WSN. Then, we compare the above performance of SS-MAC and IEEE 802.15.4 MAC using MATLAB to verify the validity of the SS-MAC protocol.

The remainder of this paper is organized as follows: Section 2 summarizes related research work about the proposed scheme. Section 3 presents the principle of SS-MAC. The system model and performance analysis are described in Section 4. Simulations and corresponding discussions are presented in Section 5. Finally, Section 6 concludes the paper.

2. Related Work

Based on hybrid CSMA/TDMA and low duty-cycle techniques, the iQueue-MAC [2] proposes a traffic feedback mechanism to implement traffic adaptation: the protocol uses a CSMA mechanism to transmit data at light load, and changes to a TDMA mechanism to allocate transmission slots when traffic increases. BEST-MAC [3] and MPCB-HM [6] combine CSMA and TDMA techniques by detailing the various phases of the network process. They use CSMA to build the cluster topology and reserve slots required to data transmission, while TDMA is adopted for data transmission. However, the protocols above mainly target the problems of cluster topology construction and data transmission from member nodes to CH in a cluster, while effectively forwarding data from member nodes to sink through CHs remains a problem. It is worth mentioning that BEST-MAC [3] improves the address formats defined in the IEEE 802.15.4-2006 standard, adopting an 8-bit shorter address to reduce control overhead. It also proposes a knapsack algorithm for CHs to determine the number of slots and order allocated to each member node.

SSMA (Slotted Sense Multiple Access) reported in [8] proposes a distributed scheduling algorithm for WSNs of tree topology. It allocates a sharable slot to each level of the tree topology, and all nodes in the same level perform data transmission by using CSMA/CA in their sharable slot. In SSMA, an exponential wait time function is defined to ensure that the nodes at lower level have a larger sharable slot, and the allocated sharable slots are gradually reduced from the sink (at level one, that is, the lowest level) to leaf nodes. Each tree node can calculate the size and start time of the sharable slot as long as it knows its level. However, the performance of SSMA is heavily dependent on the function. Unreasonable parameters selection can easily lead to network performance degradation. The LELLMAC described in [9] makes use of three algorithms to control idle listening, collisions, and address the hidden terminal issue. The protocol uses the logical link choice algorithm to ensure that two source nodes do not send packets to the same receiver at the same time. Before transmitting data packets, the nodes need to send "Request to send" (RTS) packets to adjacent layer nodes, and to reply "Clear to send" (CTS) packets after transmission. The protocol requires that the maximum amount of time allowed for data transmission in each wake-up period is 60 ms.

Like the improvement of MAC layer techniques, the design of routing algorithms or topology structures is also a major research area of MWSNs. Researchers generally propose their routing protocols based on network topology (i.e., data forwarding path) design [17,18] and sink mobile path design [19,20,21,22]. The DMH-LEACH protocol proposed in [22] is a cluster-based routing protocol, and all nodes are movable. Ordinary nodes send their packets to nearby CHs in a single-hop manner, and then the CHs forward the packets to the sink in a multi-hop manner. The protocol details the tree routing algorithm between the CHs and the sink.

In order to build a cluster tree topology network of our proposed SS-MAC, we employ the routing algorithm of DMH-LEACH [22] to build the tree topology between CHs, and design a strategy of cluster topology construction between ordinary nodes and CHs (tree nodes). However, the MAC protocols proposed in the above references are mainly based on WSNs of cluster or tree topology, rather than cluster tree topology. Thus, we upgrade and improve the above technologies; especially, we introduce the sharable slot algorithm of [8], then improve and optimize the algorithm to realize data packets forwarding level-by-level between CHs. In addition, we also adopt the short address (8-bit) design from reference [3] to reduce packet size and control overhead, and improve its knapsack algorithm for CHs to allocate slots to member nodes.

3. The Proposed SS-MAC Protocol

This section details the design and mechanism of each network phase of the proposed SS-MAC.

3.1. Network Phase Design

Figure 1 shows the topology of the SS-MAC. Node S is a sink, nodes labeled 1 to 18 are CHs, and unmarked nodes are member nodes. Member nodes are used for raw data sensing, while sink and CHs are only used for data relay and aggregation. All nodes, including CHs, are randomly deployed in the sensing area, either remaining stationary or moving slowly. All CHs and sink construct a tree topology first, then each CH and its member nodes form a cluster, which is a hierarchical cluster topology that can be defined as a cluster tree topology. For a sparse WSN, limiting CHs to data forwarding and aggregating could only have a significant impact on protocol performance. For SS-MAC which mainly serves large-scale and dense networks, whether CHs can sense data has little impact on the network performance. In large-scale wireless sensor networks with cluster tree topology, the sink needs to collect and process a large number of data packets from nearby CHs. To reduce channel competition and traffic conflicts, member nodes cannot directly communicate with the sink in the topology of SS-MAC.

Figure 2 illustrates the network phase design. The Initial Construction Phase (ICP) mainly completes the network initialization, including clock synchronization. This is followed by a fixed duration of data collection round (Round), which is the longest time unit of network operation. Each Round includes a Setup Phase (SP) and a Steady-State Phase (SSP). The network must rebuild the route in SP to prevent energy “holes” or link interruptions in subsequent SSP caused by mobility or energy depletion of nodes, especially CHs, which act as routers in the network and whose link interruptions will significantly affect the network. In each Round, the first data collection from member nodes to CHs is completed in SP, and then the process is performed in each Session. The SSP consists of several Sessions of the same duration. The length of Round (i.e., the number of Sessions in a Round) is dynamically adjusted according to the average moving speed of the nodes in the network. The faster the nodes move, the shorter the length of the Round, and the more frequent the route rebuild.

3.2. Setup Phase (SP)

The task in SP is to construct a cluster tree topology and collect data from member nodes to CHs. Topology construction is carried out in three steps: first, the sink broadcasts a tree topology construction (TREE_CON) message, indicating that all CHs in the network establish a tree routing according to the DMH-LEACH algorithm proposed in reference [22]; second, each tree node (i.e., CH) broadcasts a CH broadcast declaration (CH_DEC) message, and non-cluster head nodes reply with a join cluster unit request (JC_REQ) message to request to join the nearest CH after receiving CH_DECs; finally, CHs allocate a short address and a CP slot to each node that requested to join, and respond to each node with a control slot allocation (CS_AOC) message.

The SP can be divided into four sub-periods, as shown in Figure 2. The following sections will introduce the four sub-periods separately.

3.2.1. Routing Construction Period (RCP)

The CH broadcasts CH_DEC messages to guide surrounding nodes to build cluster units. Its frame consists of the following fields: frame control (2 bytes), extended address (8 bytes), broadcast address (1 byte), and frame check sequence (FCS) (2 bytes).

The non-cluster head nodes that received CH_DECs select the best CH according to the Received Signal Strength Indicator (RSSI), and reply to the JC_REQ message to join the cluster through CSMA/CA. The JC_REQ message consists of frame control (2 bytes), the node’s extended address (8 bytes), CH’s extended address (8 bytes) and FCS (2 bytes).

Each CH waits for a sufficiently long time to ensure that all JC_REQ requests are received, then the number of member nodes is determined based on the number of JC_REQs received.

Each CH allocates a short address (1 byte) for itself and each member node, which is used to reduce control overhead in future communications. Each CH can be associated with up to 255 member nodes, which is sufficient for most applications. In WSNs with a cluster tree topology (hierarchical cluster topology), if there are too many member nodes in a cluster, traffic conflicts among them are likely to occur. If the network is to scale up, increasing the number of CHs (i.e., the number of clusters) is often more advantageous and effective than increasing the number of member nodes per cluster.

Figure 3 shows the structure of a CS_AOC message. It is used to broadcast short addresses and control slots of member nodes. The $S_i$ field indicates the control slot number allocated by CH to node i. The Control Slot Length ($L\_CS$) field indicates the duration of a single control slot. The $TOT\_CS$ field indicates the total number of control slots allocated, which is also the total number of member nodes. The length of CS_AOC is 10N + 7 bytes, where N is the number of member nodes.

After receiving CS_AOC, the non-cluster head node checks the extended address field. If the field has its extended address, it indicates that the node has successfully joined the CH. The start time of the control slot of node i, $ST\_CS\left(i\right)$, can be calculated as $ST\_CS\left(i\right)=(S_i-1)\times L\_CS$.

3.2.2. Control Period (CP)

Each CH calculates its channel according to the identification number (ID) allocated in RCP, and informs all member nodes through CS_AOC. From CP, communication between CH and its member nodes is performed on this channel. This multi-channel mechanism avoids mutual interference when multiple CHs and their member nodes communicate simultaneously.

In CP, each member node sends a data slot request (DS_REQ) message to its CH in its control slot in the order specified by the CS_AOC message, as illustrated in Figure 4. A DS_REQ message is used to report the number of slots required to send data stored in the buffer. The protocol specifies that only one data frame is transmitted per data slot, so the number of slots is related to the payload size of the data frame. Assuming that the payload of each data frame is $P_{load}^{SN}$ bytes, node i has M bytes of data to be transmitted, the number of slots required by node i is $N_{slot}\left(i\right)=Int{[M/P_{load}^{SN}]}^{+}$, where $Int{\left[X\right]}^{+}$ represents the smallest integer greater than or equal to X.

3.2.3. Contention Access Period (CAP)

CAP is designed for those non-cluster head nodes that failed to join the cluster or moved position to join the cluster again, such as $N_1$ in Figure 4. The process is implemented by sending a join request and data slot declaration (JAD_REQ) message to CH in a CSMA/CA manner, and declaring the number of data slots required. JAD_REQ is similar in format to JC_REQ, except that the former has 1 extra byte to indicate the required data slots. If a non-cluster node wants to join a cluster in CAP, it needs to listen to the CS_AOC message to calculate the start time of CAP, that is, $CAP\_ST=L\_CS\times TOT\_CS$.

Since each cluster can hold up to 256 member nodes, the maximum duration of CAP is $(256-TOT\_CS)\times T_{cap}^u$, where $T_{cap}^u$ is the unit slot duration of CAP.

Before sending JAD_REQ, every non-cluster head node sets a random backoff period ($R\_backoff$) for collision avoidance, and $R\_backoff=random(0,MaxBW)\times T_{delay}$, where $MaxBW$ is defined as the maximum backoff window and is a fixed integer, and $T_{delay}$ is the unit length of random backoff. The node performs CCA to sense the channel after completing the backoff process. If the channel is idle, the node sends JAD_REQ to its CH; otherwise, it performs backoff and CCA again until the channel is idle.

$T_{cap}^u$ is determined using $MaxBW$ and $T_{delay}$. Assume that the time it takes for a node to perform a CCA is $T_{cca}$, and the time it takes to send a JAD_REQ message is $T_{data}$, $T_{cap}^u=T_{cca}+MaxBW\times T_{delay}+T_{data}$.

3.2.4. Data Collection Period (DCP)

In DCP, each member node receives a data slot announcement (DS_ANN) message from its CH, which informs the number and start time of the data slot allocated. Each CH utilizes its private channel to collect data from its member nodes in a TDMA manner. The TDMA mechanism within cluster units and the FDMA mechanism between cluster units effectively avoid interference between member nodes in the network. We improved the knapsack algorithm proposed in reference [3] to determine the number of slots and order allocated to each member node.

(1)

DS_ANN message

Taking a cluster with four member nodes as an example, Figure 5 shows the frame structure of the DS_ANN message. The payload portion includes the following: (1) The number of nodes that have allocated slots (1 byte). It is also the length of the node ID list; (2) The node ID list. Each byte of this field indicates an ID (short address) of member nodes. Later, member nodes sequentially send data packets in the order of the list; (3) Slot allocation list. This field indicates the number of slots allocated to each node, and each 1 byte of field corresponds to the node ID list.

If a CH allocates data slots for N nodes, the DS_ANN message length is $3N+5$ bytes. If the CAP duration set by the network is K unit slots, the start time of DS_ANN can be calculated as $ADS\_ST=CAP\_ST+K\times T_{cap}^u$.

(2)

Knapsack optimization algorithm

A knapsack optimization algorithm is employed by CHs to allocate data slots for member nodes. Algorithm 1 is designed to select the maximum node number with the maximum slot utilization. The protocol requires a node to transmit all of its data as a whole, so the Algorithm 1 is a 0–1 knapsack algorithm. Algorithm 1 assumes that the number of slots requested by a node is the same as its weight.

Suppose there are n member nodes requesting data slots, the number of slots requested by the ith node is $W_i$, and the total available slots that CH can allocate is W. The basic thought of Algorithm 1 is:

(1)

If the total number of requested slots is less than or equal to W, that is, $W_1+W_2+\cdots +W_n\le W$, the output of Algorithm 1 is $C[n,W]$. CH can allocate slots as requests, but the order of transmission is optimized by Algorithm 2.

(2)

If the total number of requested slots is greater than W, that is, $W_1+W_2+\cdots +W_n>W,$ CH cannot meet the data slot requests of all nodes, Algorithm 1 is implemented to provide an optimal slot allocation scheme $C[i,W]$.

Algorithm 1 SS-MAC Knapsack optimization algorithm.

Input:      1: n: Total number of node requesting slots   2: ${\omega }_i$: Number of slots that requested by $i_{th}$ node   3: W: Max number of slots that can be allocated   4: $\omega$: Current slot, its value is the element of array $\omega =\langle {\omega }_1,{\omega }_2,\cdots ,{\omega }_n\rangle$ Output:      5: $C[i,\omega ]$: Optimal value of Knapsack algorithm   6: for $\omega =0$ to W do   7:   $C[0,\omega ]=0$; $//$Initialize row 1 with 0   8:     9: end for 10: for $i=1$ to n do 11:   $C[i,0]=0$; $//$Initialize column 1 with 0 12:   for $i=1$ to n do 13:    if  ${\omega }_i\le \omega$  then 14:     if  ${\omega }_i+C[i-1,\omega -{\omega }_i]>C[i-1,\omega ]$  then 15:      $C[i,\omega ]={\omega }_i+C[i-1,\omega -{\omega }_i]$; 16:     else 17:      $C[i,\omega ]=C[i-1,\omega ]$; 18:     end if 19:    else 20:     $C[i,\omega ]=C[i-1,\omega ]$; 21:    end if 22:   end for 23: end for 24: return $C[n,W]$;

Algorithm 2 is designed to determine the order in which member nodes send data. CH processes the node with the least requesting slots first. All member nodes are sorted in ascending order based on the number of requesting slots. If multiple nodes have the same number of requested slots, they are sorted by their IDs from small to large. The nodes $N_1$ to $N_6$ in Figure 4 are a typical case of using the knapsack optimization algorithm.

(3)

Data collection process in DCP

Data collection of SS-MAC is completed by two steps: First, member nodes forward their sensed data to their CHs. Then, from the highest level, CHs send the data received from members to their respective parents. After forwarding level-by-level, the data are finally aggregated to the sink. If $T_{slot}$, $SID\left(i\right)$ and $SAN\left(t\right)$ represent the duration of a data slot, the order of node i in the node ID list and the number of slots allocated to the t-th node, respectively. The time that node i needs to wait before sending its data packets is:

$$Tstart\left(i\right)=T_{slot}\times \sum _{t=1}^{SID\left(i\right)-1}SAN\left(t\right)$$

To reduce energy consumption and delay, CHs do not respond to data packets sent by member nodes individually, but reply to all member nodes through an ACK broadcast after receiving all data packets. The ACK contains information about packet errors and packet loss. Nodes will resend the problematic packets to the next DCP.

Algorithm 2 SS-MAC node sorting algorithm.

Input:          $C[i,\omega ]$: Optimal value of algorithm Output:          $B[i,\omega ]$: Node sorting result   1: $B[i,\omega ]=C[i,\omega ]$;   2: $i=n$;   3: $\omega =W$;   4: while $i>1$ and $\omega >1$ do   5:    if  $B[i,\omega ]>B[i-1,\omega ]$  then   6:      $i=i-1$;   7:      $\omega =\omega -{\omega }_i$;   8:    else   9:      $i=i-1$; 10:    end if 11: end while

3.3. Steady State Phase (SSP)

After DCP, the sink broadcasts a Session_ST beacon to synchronize all CHs in the network, and the network enters SSP, which is divided into several sessions of equal duration and repetition. During each session, the network must complete data collection tasks from CHs to sink and from member nodes to their CHs.

3.3.1. Session _ST Beacon

The role of the Session_ST beacon is to synchronize the network and to set communication parameters of the tree nodes in SSP. The payload of the beacon contains the following information: (1) Public channels. They are two channels and are used for communication between tree nodes. When the main channel is unavailable for some reason (such as electromagnetic interference from other wireless networks or electronics), it switches to the standby one; (2) Tree topology scale L. It indicates the highest level of tree topology; (3) Session duration $W_s$. It refers to the duration of a single session; (4) Parameter $\alpha$ of sharable slot generation function. It is used to calculate the length of the sharable slot for each level. $\alpha$ and $W_s$ are updated according to changes in network traffic; (5) Beacon transmission duration. $T_B=L_{SS}^B/R_c$, where $L_{SS}^B$ is the length of the Session_ST beacon (bit) and $R_c$ is the physical channel data rate (bps).

3.3.2. Sharable Slot

To achieve distributed data collection from all tree nodes to sink in a session, the following factors are considered in this study:

(1)

The lower the level (i.e., the closer to the sink) of a tree node, the more data the tree node needs to send, and the longer it takes to send the data;

(2)

CH has a data fusion function. The amount of data that a tree node sends to its parent is less than the sum of the amount that the node receives from its children and the amount that it collects from member nodes. It leads to increasing the amount of data level-by-level from the leaf nodes to sink.

The SS-MAC protocol divides different data transmission periods, called sharable slots, for tree nodes at different levels. A tree node can calculate its sharable slot length and start time as long as it knows its level. We introduce the exponential wait time function from [8], $Wtime\left(l\right)=W_s\times a^{l-1}$, and construct a Session_ST beacon delay function, $Sdelay\left(l\right)=(L-l)\times T_B$, to determine the start time and length of each level’s sharable slot, where l is the level of the node.

As shown in Figure 6, the time that a node at level l waits to send or receive data packets after receiving the beacon is:

$$WT\left(l\right)=\left\{\begin{array}{cc}0,\hfill & l=L\hfill \\ Sdelay\left(l\right),\hfill & l=L-1\hfill \\ Sdelay\left(l\right)+Wtime(l+1),\hfill & \mathrm{else}\hfill \end{array}\right.$$

Tree nodes at level $l(l\ne L)$ wake up at $WT\left(l\right)$, then keep actively receiving data from tree nodes at level $l+1$. This period is defined as a receiving sharable slot, $S{S}^{RX}\left(l\right)$, which is equal to the difference between $Wtime\left(l\right)$ and $Wtime(l+1)$; after receiving data from level $l+1$, the tree nodes at level l perform fusion processing, then send fused data to the tree nodes at level $l-1$ in the transmitting sharable slot, $S{S}^{TX}\left(l\right)$. Note that the tree nodes at level L directly enter $S{S}^{TX}\left(l\right)$ after receiving the Session_ST beacon. The size of the sharable slot at level l, $SS\left(l\right)$ is equal to the sum of $S{S}^{RX}\left(l\right)$ and $S{S}^{TX}\left(l\right)$. We have:

$$\begin{array}{cc}\hfill S{S}^{RX}\left(l\right)& =Wtime\left(l\right)-Wtime(l+1)\hfill \\ \hfill & =\left\{\begin{array}{cc}{W}_s(1-\alpha ){\alpha }^{l-1},\hfill & l\ne L\hfill \\ 0,\hfill & l=L\hfill \end{array}\right.\hfill \end{array}$$

$$\begin{array}{cc}\hfill S{S}^{TX}\left(l\right)& =S{S}^{RX}(l-1)\hfill \\ \hfill & =\left\{\begin{array}{cc}{W}_s(1-\alpha ){\alpha }^{l-2},\hfill & l\ne 1\hfill \\ 0,\hfill & l=1\hfill \end{array}\right.\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill SS\left(l\right)& =S{S}^{TX}\left(l\right)+S{S}^{RX}\left(l\right)\hfill \\ \hfill & =\left\{\begin{array}{cc}{W}_s({\alpha }^{l-1}-{\alpha }^l),\hfill & l=1\hfill \\ W_s({\alpha }^{l-2}-{\alpha }^{l-1}),\hfill & l=L\hfill \\ W_s({\alpha }^{l-1}-{\alpha }^l),\hfill & \mathrm{else}\hfill \end{array}\right.\hfill \end{array}$$

The tree nodes at the highest two levels enter sharable slots first, while other tree nodes go to sleep until their sharable slots arrive.

3.3.3. Transmission Mechanism

In a sharable slot, each tree node in the same level performs the CSMA/CA operation to compete with the public channel for sending data packets to its parent. This competition only occurs between tree nodes of the same parent. Since the number of child nodes of a parent is usually small, this competition is local and controllable. Due to the different transmission channels and the non-overlapping transmission time, there is generally no traffic collision between member nodes and other CHs in the network. SS-MAC specifies that the maximum size and payload of packets transmitted between tree nodes are 127 and 121 bytes, respectively. Using large packets can reduce the number of packets as well as the number of nodes competing for public channels. When a node receives a correct packet, it responds with an ACK; otherwise, it uses a NACK to notify the sender that the received packet is incorrect or lost.

The number of packets that a tree node needs to send varies. When the number of packets in the nodes’ buffer increases due to retransmission caused by packet errors or other cause, some tree nodes may not complete the transmission of all packets within their sharable slots. Thus, the SS-MAC protocol designs a field named number of remaining packets indicator (RDI) in each packet to indicate the number of remaining packets in the nodes’ buffer. The information will eventually be forwarded to the sink, which then updates $W_s$ and $\alpha$ of the next Session_ST according to RDI and the levels in which the remaining packets are located. If the number of packets in the nodes’ buffer exceeds a certain threshold, there is an overflow risk. To reduce this risk, the network can increase the length of their sharable slots by resetting $W_s$ and $\alpha$ to ensure that the packets in their buffers have enough time to be sent.

Tree nodes begin to collect data from member nodes after $SS\left(l\right)$. The communication between tree nodes is performed on the public channel, while the communication between tree nodes and member nodes is performed on private channels. This frequency division multiplexing (FDM) mechanism effectively avoids inter-node interference.

4. Modeling Analysis

In this section, we derive and analyze mathematical expressions of the parameters of sharable slots, $W_s$ and $\alpha$. By considering the packet arrivals in CP and non-CP, we use queuing theory to calculate the average packet wait time and the energy performance of the protocol.

Table 1. Parameters and definitions.

L	The highest level of topology tree	$P_{load}^{SN}$	Packet payload of member node (bit)
$R_c$	Data rate of PHY (bps)	$P_{head}^{SN}$	Packet overhead of member node (bit)
$R_i$	Data sensing rate of member node i (bps)	$P_{load}^{CH}$	Packet payload sent by tree node (bit)
$W_s$	Session duration (s)	$P_{head}^{CH}$	Packet overhead sent by tree node (bit)
$\alpha$	Sharable slot index	$P_{ack}$	ACK frame length of tree node (bit)
$\gamma$	Data fusion degree of CHs	$P_{tx}$	Node transmitting power (W)
${\lambda }_i$	Packet arrival rate of member node i (pps)	$P_{rx}$	Node receiving power (W)
$\lambda$	Avg packet arrival rate of member nodes (pps)	$P_{idle}$	Node sleep & channel listening power (W)
${\lambda }_{max}$	Max packet arrival rate of member nodes (pps)	$L_{TR}^B$	TREE_CON message frame length (bit)
$N_m$	Max number of member nodes in a cluster	$L_{CHD}^B$	CH_DEC message frame length (bit)
$N_t$	Max number of children of a tree node	$L_{CSA}^B$	CS_AOC message frame length (bit)
$N_{ch}$	Total number of tree nodes in network	$L_{JR}^B$	JC_REQ message frame length (bit)
$N_{node}$	Total number of non-cluster-head nodes	$L_{DSR}^B$	DS_REQ message frame length (bit)
$N_r$	Number of sessions in SSP	$L_{DSA}^B$	DS_ANN message frame length (bit)
$T_{slot}$	Data slot duration (s)	$L_{SS}^B$	Session_ST beacon frame length (bit)

lists the parameters and definitions involved in this section.

4.1. $W_s$ and $\alpha$

It is assumed that non-cluster-head nodes and CHs are approximately uniformly distributed in coverage area, and the number of member nodes in each cluster is basically the same (less than or equal to $N_m$). Meanwhile, the routing algorithm can guarantee that each parent in the tree-structured topology has the same number of child nodes (less than or equal to $N_t$). The packet arrival process of member node i follows the Poisson process with parameter ${\lambda }_i$; its value is determined by the data sensing rate $R_i$, that is, ${\lambda }_i=R_i/P_{load}^{SN}$.

The amount of data collected by a CH from its member nodes in each session is (bit):

$$Q_{ch}=W_s·P_{load}^{SN}\sum _{i=1}^{N_m}{\lambda }_i=W_s·P_{load}^{SN}·N_m·\lambda$$

The number of packets sent by a CH at the highest level to its parent in each session is:

$$N_p=Int{[\gamma Q_{ch}/P_{load}^{CH}]}^{+}$$

where $\gamma$ is the data fusion degree of CHs, which is the ratio of the amount of data after to before fusion $(\gamma <1)$. The time taken by the parent at the second-highest level to receive these packets is:

$$T_{ch}=N_t{N}_p(\frac{P_{load}^{CH}+P_{head}^{CH}+P_{ack}}{R_c}+E\left[D\right])$$

where $E\left[D\right]$ is the average packet delay caused by performing the backoff and CCA operations of CSMA/CA. It can be calculated using Formulas (22) and (23) of [24] as follows:

$$Pr\left(A_j\right|A_i)=\frac{P_c^j{(1-x^{m+1})}^j}{{\sum }_{k=0}^n{\left(P_c(1-x^{m+1})\right)}^k}=\frac{(1-P_c(1-x^{m+1}))P_c^j{(1-x^{m+1})}^j}{1-{\left(P_c(1-x^{m+1})\right)}^{n+1}}$$

$$E\left[D\right]=\sum _{j=0}^{n}Pr\left(A_j\right|A_t)(T_s+j{T}_c+\sum _{h=0}^{j}E\left[T_h\right])$$

where $p_c$ is the collision probability of packet sending, $(1-x^{m+1})$ is the probability of a node successfully accessing the channel within number of m backoff stages. $T_s$, $T_c$ and $T_h$ are the time taken for successful packet transmission, collided packet transmission and backoff stage, respectively. To simplify the calculation, $E\left[D\right]$ can also be set as a constant empirically or even ignored.

Since the tree nodes at the highest level enter a sharable slot immediately after the beginning of the session, the data collected from member nodes are sent to their respective parents at the second-highest level, that is, $SS\left(L\right)=S{S}^{TX}\left(L\right)=S{S}^{RX}(L-1)=T_{ch}$. The amount of data received from $N_t$ child nodes by each tree node at the second-highest level is $N_t{N}_p{P}_{load}^{CH}$. In addition, each tree node at the second-highest level will receive data packets from member nodes with a data volume of $Q_{ch}$. By fusion of the two parts of the data, the total data volume to be sent by a tree node at the second-highest level can be obtained as:

$$Q_{L-1}=\gamma (N_t{N}_p{P}_{load}^{CH}+Q_{ch})=\gamma Q_{ch}(\gamma N_t+1)$$

(2)

For each tree node at level $L-2$, the time it takes to receive data from these child nodes is:

$$S{S}^{RX}(L-2)=S{S}^{TX}(L-1)=\frac{N_t{Q}_{L-1}}{P_{load}^{CH}}·(\frac{P_{load}^{CH}+P_{head}^{CH}+P_{ack}}{R_c}+E\left[D\right])$$

(3)

Using expressions (1), (2) and (3), the parameter $\alpha$ can be expressed as:

$$\alpha =\frac{S{S}^{TX}\left(L\right)}{S{S}^{TX}(L-1)}=\frac{N_p{P}_{load}^{CH}}{Q_{L-1}}=\frac{1}{\gamma N_t+1}$$

(4)

Expression (4) shows that $\alpha$ is determined by the data fusion degree $\gamma$ and the size of the tree topology $N_t$; it affects the duration of session, $W_s$, which, in turn, affects the average packet delay. When $\gamma$ is fixed, the increase in $N_t$ results in decrease in $\alpha$ and increase in the session duration. Therefore, the size of the tree topology should be limited to a reasonable range.

From Figure 6, $W_s$ can be obtained as:

$$W_s=\sum _{i=2}^{L}S{S}^{TX}\left(i\right)=S{S}^{TX}\left(L\right)\sum _{i=0}^{L-2}{\alpha }^{-i}=\frac{T_{ch({\alpha }^{L-1}-1)}}{{\alpha }^{L-1}-{\alpha }^{L-2}}$$

(5)

Expression (5) shows that $W_s$ is determined by $\alpha$ and $T_{ch}$. When $T_{ch}$ is fixed, the closer $\alpha$ is to 1, the smaller $W_s$ is; when $\alpha$ is fixed, the smaller $T_{ch}$ is, the smaller $W_s$ is. $W_s$ is ultimately determined by $N_t$, $N_p$, $\gamma$, $R_c$ and the packet size.

4.2. Average Packet Waiting Time Analysis

The behavior of the tree nodes and their member nodes at any two adjacent levels in a session is shown in Figure 7.

Each member node goes through four periods: vacation, CP, CAP and DCP. The duration of each period is fixed and cycled sequentially. It sends data packets to its CH only in DCP (a small segment of DCP). The packet of a member node can be generated at any period; if we define packet generation as packet arrival, the packet arrival process can be divided into the following two cases:

(1)

Packet arrives during CP. CP consists of control slots allocated to member nodes to reserve data slots. If packet l of member node i arrives before the start of its slot in CP, packet l can complete the reservation in this CP and complete transmission in the upcoming DCP, as moment ➀, shown in Figure 8—the packet waiting time is $T_{cp1}$; if packet l arrives after the start of its slot in CP, as moment ➁, the node i will complete reservation in the next CP, and the packet waiting time will increase significantly to $T_{cp2}$.

(2)

Packet arrives outside CP. Node i needs to reserve slot for sending packet l in the next CP and sends it in the subsequent DCP. Figure 9 shows the scenarios when packet l arrives at CAP, DCP and vacation. The packet waiting times are $T_{c2}$, $T_{d2}$ and $T_{v2}$, respectively.

The probability of packet arrival in one of four periods is related to the duration proportion of the period. The conditional probability that packet l of node i arrives before (or after) its control slot in CP is approximately 0.5. For a packet l of any member node i, the average waiting time can be calculated as:

$$\overline{W}=E\left[w\right]=\sum _{k=1}^5{\overline{w}}_k{P}_k$$

where $E\left[w\right]$ is the expectation of the waiting time of packet l, ${\overline{w}}_k$ is the mean of the waiting time when packet l arrives in period k, $P_k$ is the probability that packet l arrives in period k. $k=1$ (or 2) indicates that packet l arrives before (or after) its control slot in CP; $k=$ 3, 4 and 5 indicate that packet l arrives in CAP, DCP and vacation, respectively. $E\left[w\right]$ can be further expressed as:

$$\begin{array}{cc}\hfill & \overline{W}=E\left[w\right]=\sum _{k=1}^5{\overline{w}}_k{P}_k.\hfill \\ \hfill & ={\overline{w}}_{1}P\left\{\mathrm{Packet}l\mathrm{arrives}\mathrm{in}\mathrm{CP}\right\}·P\{\mathrm{Arrives}\mathrm{before}\mathrm{its}\mathrm{control}\mathrm{slot}\mid \mathrm{Packet}l\mathrm{arrives}\mathrm{in}\mathrm{CP}\}\hfill \\ \hfill & +{\overline{w}}_{2}P\left\{\mathrm{Packet}l\mathrm{arrives}\mathrm{in}\mathrm{CP}\right\}·P\{\mathrm{Arrives}\mathrm{after}\mathrm{its}\mathrm{control}\mathrm{slot}\mid \mathrm{Packet}l\mathrm{arrives}\mathrm{in}\mathrm{CP}\}\hfill \\ \hfill & +{\overline{w}}_{3}P\left\{\mathrm{Packet}l\mathrm{arrives}\mathrm{in}\mathrm{CAP}\right\}+{\overline{w}}_{4}P\left\{\mathrm{Packet}l\mathrm{arrives}\mathrm{in}\mathrm{DCP}\right\}\hfill \\ \hfill & +{\overline{w}}_{5}P\left\{\mathrm{Packet}l\mathrm{arrives}\mathrm{in}\mathrm{Vacation}\right\}\hfill \\ \hfill & =\frac{T_{cp}{\overline{T}}_{cp1}}{2W_s}+\frac{T_{cp}{\overline{T}}_{cp2}}{2W_s}+\frac{T_{cap}{\overline{T}}_{c2}}{W_s}+\frac{T_{dcp}{\overline{T}}_{d2}}{W_s}+\frac{T_v{\overline{T}}_{v2}}{W_s}\hfill \\ \hfill & =\frac{T_{cp}}{2W_s}(\frac{T_{cp}}{2}+T_{cap}+\frac{T_{dcp}}{2}+\frac{3T_{cp}}{2}+2T_{cap}+\frac{3T_{dcp}}{2}+T_v)+\frac{T_{cap}}{W_s}(\frac{3T_{cap}}{2}+\frac{3T_{dcp}}{2}+T_v+T_{cp})\hfill \\ \hfill & +\frac{T_{dcp}}{W_s}(T_{dcp}+T_v+T_{cp}+T_{cap})+\frac{T_v}{W_s}(\frac{T_v}{2}+T_{cp}+T_{cap}+\frac{T_{dcp}}{2})\hfill \\ \hfill & =W_s+\frac{W_s-T_2}{W_s}(\frac{T_{cap}}{2}-\frac{T_v}{2})+\frac{T_{cap}}{W_s}(\frac{T_2}{2}-\frac{T_v}{2})-\frac{T_v}{W_s}(\frac{T_2}{2}-\frac{T_{cap}}{2})=W_s+\frac{T_{cap}}{2}-\frac{T_v}{2}\hfill \end{array}$$

(6)

The result of expression (6) shows that the average packet waiting time of the member nodes is related to the session duration $W_s$ and the proportion of each period. Generally, $T_{cap}\ll T_v$, so $\overline{W}\approx W_s-\frac{T_v}{2}<W_s$; that is, the average packet waiting time is less than the session duration. It also suggests that methods to reduce the average packet waiting time are shortening the session duration, and reducing the proportion of CP, CAP and DCP to increase the proportion of vacation (low duty-cycle technique).

4.3. Energy Consumption Analysis

The energy consumption of SS-MAC ($E_{tot}$) consists of two parts: energy consumption during SP ($E_{setup}$) and energy consumption during SSP ($E_{steady}$). The former is equal to the sum of energy consumption of four sub-periods of SP, which are defined as $E_{RC}$, $E_{CP}$, $E_{CAP}$ and $E_{DCP}$, respectively. The latter is equal to the sum of energy consumption during SSP caused by data collection between CHs in a session ($E_{tree}^s$), caused by data collection within cluster ($E_{cl}^s$), and caused by broadcast Session_ST ($E_{SS}^B$). So, the total energy consumption of SS-MAC is:

$$E_{tot}=E_{setup}+E_{steady}=E_{RC}+E_{CP}+E_{CAP}+E_{DCP}+E_{SS}^B+N_r(E_{tree}^s+E_{cl}^s)$$

(7)

The energy consumption of each period, that is, the right side of expression (7), is calculated as follows:

$$\begin{array}{cc}\hfill E_{RC}& =\frac{L_{TR}^B}{R_c}(P_{tx}\sum _{i=0}^{L-2}{N}_t^i+P_{rx}\sum _{i=1}^{L-1}{N}_t^i)+\frac{L_{CHD}^B+L_{CSA}^B}{R_c}(P_{tx}(N_{ch}-1)+P_{rx}{N}_{node})\hfill \\ \hfill & +\frac{L_{JR}^B{N}_{node}}{R_c}(P_{tx}+P_{rx})\hfill \end{array}$$

$$E_{CP}=\frac{L_{DSR}^B{N}_{node}}{R_c}(P_{tx}+P_{rx})$$

$$E_{CAP}=P_{idle}{T}_{cap}(N_{ch}+N_{node}-1)$$

$$E_{DCP}=\frac{L_{DSA}^B+P_{ack}}{R_c}(P_{tx}(N_{ch}-1)+P_{rx}{N}_{node})+T_{slot}{N}_{node}(P_{tx}+P_{rx})$$

$$E_{SS}^B=\frac{L_{SS}^B}{R_c}(P_{tx}\sum _{i=0}^{L-2}{N}_t^i+P_{rx}\sum _{i=1}^{L-1}{N}_t^i)$$

$$E_{tree}^s=(P_{tx}+P_{rx})\sum _{i=1}^{L-1}S{S}^{RX}\left(i\right)N_t^{i-1}$$

$$\begin{array}{cc}\hfill E_{cl}^s& =\frac{L_{CSA}^B+L_{DSA}^B+P_{ack}}{R_c}(P_{tx}(N_{ch}-1)+P_{rx}{N}_{node})+E_{CAP}\hfill \\ \hfill & +N_{node}(\frac{L_{DSR}^B}{R_c}+T_{slot}Int{\left[W_s{\lambda }_{max}\right]}^{+})(P_{tx}+P_{rx})\hfill \end{array}$$

5. Performance Evaluation

The SS-MAC improves many techniques defined by the IEEE 802.15.4 standard, such as the cluster tree topology network, the hybrid CSMA/TDMA technique and the channel-hopping mechanism. It focuses on improving the IEEE 802.15.4 standard and draws on the sharable slot algorithm of SSMA (Slotted Sense Multiple Access) [8]. Therefore, in this section, we compare SS-MAC with three other protocols, namely, the IEEE 802.15.4 standard, SSMA and LELLMAC (Lifetime Extension Low Latency MAC) [9]. In terms of the topology and distributed transmission mechanism, LELLMAC has a similar design to SS-MAC. Based on the operation mechanism, we build the SS-MAC and IEEE 802.15.4 MAC models on the MATLAB platform and evaluate the performance of SS-MAC under different network scales. Using the formulas given in the above references and the parameter values in

Table 2. Parameters for simulation.

LELLMAC				SSMA
Packet size (Bytes)			64	Packet size (Bytes)					10
Sending and receiving slot (ms)			60	Receiver-initiated mini slot (ms)					5
Average idle (sleep) duration (ms)			100	Sender-initiated mini slot (ms)					15
The maximum number of nodes a node can send packets			3	Duration of one data collection round (s)					1.6
IEEE 802.15.4 MAC				SS-MAC			Common parameters of the four protocols
System size (frames)			51	$\gamma$	0.7		$R_c$ (bps)		19,200
Minimum value of backoff exponent (macMinBE)			3	$T_{slot}\left(s\right)$	0.005		$P_{ack}$ (bit)		88
Maximum value of backoff exponent (macMaxBE)			5	$P_{load}^{SN}$(bit)	48		$P_{tx}$ (W)		0.08
Max number of backoffs (macMaxCSMABackoffs)			4	$P_{head}^{SN}$(bit)	48		$P_{rx}$ (W)		0.07
Max number of retries (macMaxFrameRetries)			3	$P_{load}^{CH}$(bit)	968		$P_{idle}$ (W)		0.07
MAC frame payload (bit)			968	$P_{head}^{CH}$ (bit)	48
Overhead added in PHY layer (bit)			48	$N_r$	50
Translation coefficient from frame to slot (bit/slot)			80

, we conduct numerical calculations on the MATLAB platform to compare the packet delay and throughput performance of the four protocols. Table 2 lists the values of the simulation parameters.

5.1. Average Waiting Time in SS-MAC

Using the expressions derived in Section 4 to analyze the various performances of the SS-MAC under different network sizes, we obtain the average packet waiting time $E\left[w\right]$, session duration $W_s$, and the maximum packet arrival rate ${\lambda }_{max}$ of each member node, as shown in

Table 3. Average packet waiting time and session duration under different network sizes.

L	3				4				5
$N_t$	3		5		3		5		3		5
$N_m$	5	10	5	10	5	10	5	10	5	10	5	10
$N_{ch}$	13	13	31	31	40	40	156	156	121	121	781	781
$N_{node}$	60	120	150	300	195	390	775	1550	600	1200	3900	7800
$\lambda$	7.495	3.747	3.352	1.676	2.241	1.120	0.716	0.358	0.706	0.353	0.157	0.078
$W_s$	0.768	0.768	1.718	1.718	2.570	2.570	8.046	8.046	8.156	8.156	36.523	36.523
$E\left[W\right]$	0.444	0.463	0.919	0.938	1.345	1.364	4.083	4.102	4.138	4.157	18.322	18.341

. When $L=3,N_t=3$ and $N_m=3$, the total number of tree nodes and member nodes of the network are 13 and 60, respectively. Each member node in this network can support a maximum packet arrival rate of 7.495 p/s, the session duration $W_s$ is 0.768 s, which is also the time taken by the sink to complete a round of data collection from all nodes of the network, and the average packet waiting time for each member node is 0.444 s. Table 3 also suggests that $E\left[w\right]$ and $W_s$ increase as the topology level L and the number of member nodes increase, but ${\lambda }_{max}$ decreases gradually. Increase in L leads to an increase in the number of sharable slots and increase in $N_t$ leads to an increase in the length of each sharable slot. As a result of the combined effect of these two parameters, the session duration $W_s$ continuously increases. If the packet arrival rate for each member does not exceed ${\lambda }_{max}$, the network can run steadily. Obviously, the SS-MAC protocol can adapt to large-scale WSNs.

5.2. Energy Consumption in SS-MAC

The mathematical expression derived in Section 4.3 illustrates that the network size is a vital factor affecting the total energy consumption of the network. Using these expressions and the parameter values in Table 2, we analyze the relationship between the total energy consumption of the network $\left(E_{tot}\right)$ and the number of member nodes $\left(N_m\right)$ when L is 3, 4, 5 and 6, respectively, as shown in Figure 10.

By comparing the four sub-figures, we can reach the conclusion that the energy consumption of the network increases with increase in L and $N_m$. However, compared with $N_m$, $N_t$ has a more significant impact on energy consumption, because the former mainly affects the energy consumption of the data collection process within a cluster, while increase in $N_t$ means the sharable slot duration of each level increases. Ultimately, the total energy consumption of the network has increased significantly.

5.3. Performance Comparison of the Four Protocols

Different from the CSMA/CA technique adopted by IEEE 802.15.4 MAC, in SS-MAC, the data collection process within a cluster employs a slot-based reservation transmission mechanism, which avoids CCA and backoff operations before packet transmission. The SSMA protocol [8] also adopts this transmission mechanism, but it requires the receiver to reply an ACK to the sender for each packet received, which will affect the protocol’s performance. The LELLMAC [9] make use of three algorithms to ensure that two source nodes do not send packets to the same recipient at the exact same moment. Each node needs to send a Request to Send (RTS) to the target node before sending a packet, and wait for a Clear to Send (CTS) after the packet has been sent. The protocol adopts low-duty cycle technology to reduce node energy consumption, and the maximum amount of time allowed to data transmission per wake-up cycle is 60 ms. For the LELLMAC, frequent RTS and CTS packets transmission and a 60 ms transmission duration limit may have a significant impact on the protocol’s performance. So far, there are few MAC protocols proposed specifically for WSNs with cluster tree topology. For a better performance comparison, we simulate the data collection process using the four protocols above in a WSN composed of one sink and $N_m$ member nodes, and explore their average packet delay and throughput performance.

The average packet delay versus the arrival rate is shown in Figure 11. The average packet delay of the four protocols increases with increase in the packet arrival rate. The curve of IEEE 802.15.4 MAC is the steepest; the average packet delay of IEEE 802.15.4 MAC increases faster than the other three protocols.

For SS-MAC, when the packet arrival rate is 8 p/s, the average packet delay with $N_m=10$ is almost twice that of $N_m=5$, which are 0.13 s and 0.22 s, respectively. Compared with SS-MAC, SSMA has similar simulation curves and the average packet delay under the same conditions is larger, which is related to the transmission mechanism that SSMA requires nodes to reply to an ACK for each received packet. Because of the staggered scheduling method, the average packet delay of the LELLMAC is lower than that of the SSMA under the same conditions, but it is still higher than that of SS-MAC, as the nodes need to send RTS packets before transmitting data packets and reply with CTS packets after completing data packets transmission. For IEEE 802.15.4 MAC, the average packet delay is least affected by $N_m$. Moreover, in the case of a low packet arrival rate, IEEE 802.15.4 MAC has the lowest average packet delay and the best performance among the four protocols. Because the channel is basically idle under low load, it is easy for the nodes to obtain channel resources for sending data packets by performing backoff and CCA operations. However, with a continuous increase in packet arrival rate, the average packet delay of SS-MAC is gradually lower than that of IEEE 802.15.4 MAC, and its superiority becomes obvious.

Figure 12 shows throughput per node under different load. The throughput of SS-MAC is significantly higher than IEEE 802.15.4 MAC, SSMA and LELLMAC under the same conditions. In a network using IEEE 802.15.4 MAC and $N_m=5$, the throughput of each node reaches a peak at about 1200 b/s when the load per node is about 2600 b/s; if $N_m=10$, the throughput peaks at about 550 b/s when the load is about 1200 b/s. For a network using IEEE 802.15.4 MAC, an increase in load will increase the number of nodes competing for the channel and the number of backoff operations, resulting in throughput degradation, which will not occur in SS-MAC. If the data rate of PHY is 19,200 b/s, for the SS-MAC protocol, it can be predicted that the throughput per node of a network with $N_m=5$ will tend to $19,200/(2\times 5)=1920$ b/s (the payload of the SS-MAC data frame is half the frame length). Similarly, for a network with $N_m=10$, the throughput per node will tend to 960 b/s. The SSMA protocol requires nodes to reply with an ACK for each packet received, which results in lower throughput than SS-MAC under the same conditions. Figure 12 also illustrates that the throughput performance of LELLMAC is better than that of IEEE 802.15.4 MAC and SSMA under the same conditions. For LELLMAC, when the offered load approaches 6000 bits/node, the throughput of each node in the network with $N_m=5$ and $N_m=10$ is 1369 bits and 822 bits, respectively, which are 25.1% and 12.4% lower than SS-MAC, respectively.

The above simulation results fully demonstrate that compared with IEEE 802.15.4 MAC, SSMA and LELLMAC, the SS-MAC proposed in this paper can adapt to large-scale cluster tree networks relatively. Moreover, it also performs best in packet delay and throughput under the same conditions.

6. Conclusions

The SS-MAC protocol proposed in this paper is an efficient MAC protocol for WSNs with cluster tree topology. The protocol integrates and improves many techniques, such as the hybrid CSMA/TDMA technique, the short address technique and the sharable slot technique. It provides a detailed design of the frame structure and data collection process for each phase of network operation. It has the benefit of reducing competition and energy consumption between nodes, as well as improving network throughput. In addition, it can be applied to large-scale MWSNs. There are three limitations of SS-MAC as follows: first, the topology cannot be rebuilt in time when a node fails; second, the design, so that CHs do not perform sensing tasks; third, lack of direct communication between the sink and the member nodes will limit the protocol use cases. In the future, we aim to address the existing drawbacks of the SS-MAC protocol by implementing a Markov model that takes into account the various states of nodes. This model will enable us to conduct a thorough analysis of the protocol’s performances and provide a sound basis for future optimization.