Improved Adaptive Backoff Algorithm for Optimal Channel Utilization in Large-Scale IEEE 802.15.4-Based Wireless Body Area Networks

Abstract

The backoff algorithm employed by the medium access control (MAC) protocol of the IEEE 802.15.4 standard has a significant impact on the overall performance of the wireless sensor network (WSN). This algorithm helps the MAC protocol resolve the contention among multiple nodes in accessing the wireless medium. The standard binary exponent backoff (BEB) used by the IEEE 802.15.4 MAC protocol relies on an incremental method that doubles the size of the contention window after the occurrence of a collision. In a previous work, we proposed the adaptive backoff algorithm (ABA), which adapts the contention window’s size to the value of the probability of collision, thus relating the contention resolution to the size of the WSN in an indirect manner. ABA was studied and tested using contention window sizes of up to 256. However, the latter limit on the contention window size led to degradation in the network performance as the size of the network exceeded 50 nodes. This paper introduces the Improved ABA (I-ABA), an improved version of ABA. In the design of I-ABA we observe the optimal values of the contention window that maximize performance under varying probabilities of collision. Based on that, we use curve fitting techniques to derive a mathematical expression that better describes the adaptive change in the contention window. This forms the basis of I-ABA, which demonstrates scalability and the ability to enhance performance. As a potential area of application for I-ABA, we target wireless body area networks (WBANs) that are large-scale, that is, composed of hundreds of sensor nodes. WBAN is a major application area for the emerging Internet of Things (IoT) paradigm. We evaluate the performance of I-ABA based on simulations. Our results show that, in a large-scale WBAN, I-ABA can achieve superior performance to both ABA and the standard BEB in terms of various performance metrics.

1. Introduction

The plethora of designs and applications of wireless sensor networks (WSNs) has caused them to prevail in various domains and sectors. WSNs played a significant role in paving the way for the emergence of the Internet of Things (IoT), an abundance of intelligent sensor nodes that are mounted on a variety of objects and connected to the Internet to report abundant information related to the performance/operation of those objects. As IoT applications emerge in each aspect of our day-to-day life, their performance relies on stringent requirements and specifications.

The wireless body area network (WBAN) emerges as a critical IoT application. Research into WSNs and IoT introduces WBANs as a significant building block in the health system of any nation, intended to improve health services. A WBAN is mounted on the body of a patient to monitor or collect data on the patient’s vital signs like their heartbeat, blood pressure, temperature, respiration, electromyography (EMG), electrocardiogram (ECG), and electroencephalogram (EEG) [1]. By monitoring these signs, the WBAN helps physicians to stay up to date with respect to the patient’s health status, create patient history, allow for remote assessment of the patient, receive real-time data about the patient, and notify paramedics in cases of emergency. WBANs can significantly reduce the pressure on health systems by reducing the number of people admitted to hospitals. Also, WBANs can help patients become more mobile and stay at home rather than being confined to hospitals. This latter fact even has a positive impact on the patient’s mental health, which speeds up his/her recovery. Healthcare is a vital sector that is projected to have a significant impact on the economy worldwide. According to [2], healthcare applications and related IoT-based services are expected to create an annual growth of USD 1.1–USD 2.5 trillion in the global economy by 2025. The authors also report that as dominant IoT applications, healthcare applications are projected to have a market share of 41% by 2025.

For the WBAN to achieve its set goals, it requires quality of service (QoS) guarantees. These guarantees include, but are not limited to, high packet delivery ratios, reduced delays, high throughputs, and energy conservation. These parameters are highly affected by the medium access control (MAC) protocol used by the WBAN. In other words, the design of the MAC protocol should recognize these QoS requirements in order for it to be adopted in the deployment of WBANs (see [1,3,4] for more details on suitable MAC protocols for WBANs). As a result, MAC protocols for WBANs have received significant attention in the literature; ref. [3] provides a recent comprehensive survey of the state-of-the-art MAC protocols for WBANs.

Being an example of WSNs, WBANs can be operated by deploying the IEEE 802.15.4 standard, i.e., the low-rate wireless personal area network standard that is highly suited for power-constrained, low-transmission-rate nodes like sensor nodes in WSNs [5]. The IEEE 802.15.4 (in the rest of the paper, we use the terms “802.15.4” or “the standard” interchangeably with “IEEE 802.15.4.”) standard defines the specifications of both the physical layer and the MAC sub-layer of WSNs. The performance of the WSN greatly depends on how the MAC protocol parameters are tuned or defined. Improving the design of the standard MAC has been the objective of plenty of studies over the last two decades. Several survey studies that review the achievements in this field are available, like [6,7,8]. Research efforts in this direction introduced the IEEE 802.15.6 standard, an IEEE standard for WBANs. However, 802.15.4 is still a potential candidate for WBANs (see the excellent surveys [1,8,9,10] that list 802.15.4 as a well-studied technology for deployment in WBANs). In fact, 802.15.4 is a potential technology for IoT applications in general, and WBANs more specifically [10].

In a previous work, we introduced the adaptive backoff algorithm (ABA) [11] (see also [12]) as an improvement to the standard backoff mechanism—known as the binary exponent backoff (BEB)—in the 802.15.4 MAC protocol. ABA aimed to adapt the size of the contention window used in BEB to the value of the probability of collision. Since the probability of collision is directly impacted by the size of the WSN, ABA manages to shorten or extend the contention window dynamically based on how big or small the network is. This way, ABA responds to the level of activity happening over the wireless medium. In our evaluation of the ABA’s performance, we simulated networks of sizes up to 350 nodes while imposing an upper bound of 256 on the contention window size. We observed that the overall performance degrades as the network size increases beyond 50 nodes.

This paper introduces an improved version of ABA, and we name it the improved-ABA (I-ABA). The main objective of I-ABA is to maintain a promising performance in the network compared to the standard MAC, while increasing the size of the network to accommodate hundreds of sensor nodes in a WBAN; this is referred to as large-scale WBAN in this paper. Supporting large-scale WBANs is realistic and needed in many situations. The IEEE 802.15.6 standard itself supports a WBAN of sizes up to 256 nodes (we stress again, as mentioned earlier in this section, that the focus of this work is solely the IEEE 802.15.4 standard as it is still within the scope of a huge body of works on WBANs) [13].

The main contributions of this work are outlined as follows:

• We introduce I-ABA, a new, improved IEEE 802.15.4 MAC protocol for large-scale WBANs.
• The improvements in I-ABA rely on a new mathematical definition of the contention window that is not computationally complex and poses no overhead on sensor nodes to compute.
• We use the Markov chain model developed in [11] to derive mathematical expressions for essential performance metrics that include channel utilization, channel idle time, channel collision time, delay, reliability, average energy consumption, and average energy wasted in collisions.

We evaluate the performance of I-ABA using user-defined tools (programmed in Java SE 21 and C) and conduct a comparative study with the standard BEB and ABA.

The rest of the paper is organized as follows. Section 2 provides a brief description of the binary exponent backoff (BEB) algorithm that is incorporated in the MAC protocol of the 802.15.4 standard. Section 3 reviews recent proposals on improving the performance of the 802.15.4 MAC protocol. Section 4 introduces the new I-ABA algorithm along with a mathematical model to evaluate its performance. Section 5 studies I-ABA’s performance and verifies the accuracy of the mathematical model developed in Section 4. Finally, Section 6 concludes the paper.

2. The Binary Exponent Backoff (BEB) Algorithm

The 802.15.4 standard defines the specifications of the medium access control (MAC) protocol in low-rate wireless networks [5]. In this paper, we focus on the slotted CSMA-CA mechanism of the 802.15.4 MAC protocol. In this mechanism, a superframe structure is used to organize the communications over the wireless medium. The superframe is composed of a contention access period (CAP) and an optional contention-free period (CFP) (which offers collision-free guaranteed time slots (GTSs)). During the CAP, nodes utilize the slotted CSMA-CA mechanism to resolve medium access contention. The latter resolution is achieved through the binary exponent backoff (BEB) algorithm. BEB operates as follows. Before any transmission attempt, three parameters are initialized, namely, the number of backoff stages (NB = 0), the contention window (CW = 2), and the backoff exponent (BE = macMinBE) (macMinBE is an attribute defined in IEEE 802.15.4; its default value is 3). After that, the node backs off for a random duration selected from the range $[0,2^{BE}-1]$. Once the backoff period expires, the node checks if the medium is clear during two consecutive clear channel assessments (CCA1 and CCA2). If the medium is clear in both CCAs, packet transmission will begin. If either of the CCAs reveals that the medium is busy, the value of BE will be increased by 1 (up to a maximum of macMaxBE (macMaxBE is an attribute defined in IEEE 802.15.4; its default value is 5)), CW will be reinitialized, and the node will backoff again; that is, NB is increased by 1 until it reaches a maximum of macMaxCSMABackoffs (macMaxCSMABackoffs is an attribute defined in IEEE 802.15.4; its default value is 4). If BE reaches its maximum, it cannot change unless a successful/failed packet transmission occurs or packet retransmission commences. In that case, BE is reinitialized. The packet is dismissed if the macMaxCSMABackoffs threshold is crossed, and the BEB process will start over. Once a packet is transmitted successfully, an ACK packet is expected. If the ACK packet is not received, the node attempts (to a maximum of macMaxFrameRetries attempts) to retransmit the packet using the BEB algorithm. If macMaxFrameRetries (macMaxFrameRetries is an attribute defined in IEEE 802.15.4; its default value is 3) is crossed, the packet is dismissed. The time unit used by CSMA-CA is the aUnitBackoffPeriod (aUnitBackoffPeriod is a constant defined in IEEE 802.15.4 and is equal to 320 microseconds). In Figure 1, we show the flow diagram of the slotted CSMA-CA mechanism.

The 802.15.4 MAC is distinguished by the backoff mechanism and the use of two CCAs. These characteristics lead to a reduced likelihood of collisions and an improved conservation of power, and these are useful characteristics in WSN-based applications like WBANs.

3. Related Work

In this section, we highlight some state-of-the-art related work that tackled the problem of improving the standard BEB in 802.15.4 MAC to enhance its performance and serve the applications of WBAN.

In [14], the authors proposed the genetic fuzzy logic channel optimization (GFCO) approach for IEEE-802.15.4-based low-rate wireless personal area networks. GFCO employs a genetic algorithm to modify a fuzzy logic controller optimally. The main target is to adjust the contention window size to improve the probability of medium access. Through this optimization, the performance is improved in terms of throughput, packet delivery ratio, packet loss ratio, and packet delay. In evaluating their proposed technique, the authors use extensive simulations, considering two WBAN scenarios: in one scenario, a WBAN with 10 sensors was mounted on the body of a single person; while in the other scenario, 10 to 50 persons were considered to be present in a hospital ward. The authors report results that show the ability of GFCO to outperform the standard BEB in terms of the aforementioned metrics.

The authors of [15] focused mainly on improving the reliability of the 802.15.4 MAC protocol to better support data transmission in WBANs. After studying a simple two-dimensional Markov chain that models the CSMA-CA algorithm, the authors proved mathematically that the parameter macMaxCSMABackoffs is directly related to the reliability of packet transmission. Therefore, by properly tuning this parameter, transmission reliability can be improved. With this observation in mind, the value of macMaxCSMABackoffs will be set depending on the severity of the sensed physiological data (termed as the criticality index (CI); the CI lies between 0 and 1). The range of the CI is divided into five sub-ranges, each of which is assigned a different value of macMaxCSMABackoffs. A local processing unit assigns sensor nodes their CIs. Whenever a sensor node has critical packets to transmit, it sets its macMaxCSMABackoffs based on its CI. The reliability was finally studied as a function of the probability of collision, failure during CCA1, and CI. The reported results show promising improvements in transmission reliability when the macMaxCSMABackoffs parameter is properly tuned.

In [16], the authors studied the lack of support of data prioritization in 802.15.4 standard and how BEB does not recognize the levels of urgency or importance among different nodes traffics. The authors introduced the class of service traffic priority MAC (CSTP-MAC) scheme to cover that gap. In the CSTP-MAC, nodes are classified based on the different priorities of the data they are carrying. Backoff periods are computed using a set of unique backoff expressions peculiar to the data priorities. The idea behind the unique expressions is to grant nodes a non-conflicting range of backoff periods, which resolves the contention among the nodes to access the shared medium of communication.

In [17], the authors proposed the retransmission adaptive intelligent MAC (RAI-MAC) protocol to achieve fair retransmissions in WBANs. In the RAI-MAC, a coordinator node tracks the number of failed transmission attempts by each sensor node in its cluster. By learning about the number of failed transmissions, the coordinator classifies the nodes in the WBAN into priority classes. These priority classes help control the next backoff interval of all current transmitting sensors in a WBAN, which affects the retransmission priority of each node. This approach results in an adaptive adjustment of backoff intervals, which helps RAI-MAC reduce the probability of collisions and delay.

The authors in [18] studied the improvement of the backoff and CCA mechanisms in the 802.15.4 MAC protocol to better support WBAN applications. The authors pointed out that the standard specifies that the BE is confined to the interval [0, (macMinBE, macMaxBE)]; macMinBE = 2; macMaxBE = 5. In the case of recurring collisions, and since macMaxCSMABackoffs = 4, the backoff exponent will be selected from the intervals 0–7, 0–15, 0–31, 0–31, and 0–31. Therefore, in the case of frequent collisions over the wireless medium, there will be several sensor nodes selecting their BE from the interval 0–31, and they may end up selecting the same BE, which leads to more collisions. To mitigate such situations, the authors propose using distinct intervals for each backoff period and reducing the number of backoff periods to 3. As for the CCA mechanism, the authors note that waiting for two idle CCAs may lead to unnecessary delays in communications. Therefore, they propose to allow a sensor node to send its data as soon as it finds the CCA idle. The modifications of the backoff and CCA mechanisms have been modeled mathematically using Markov chains and evaluated through simulations. The targeted performance parameters were energy conservation, packet delivery ratio, throughput, and delay. The reported results show superior performance compared to the standard 802.15.4 MAC protocol.

The authors in [19] focused on the requirements of adaptive data traffic and QoS guarantees in several wireless applications like WBANs. As such, they introduced the enhanced superframe offering adaptive duty cycle (ESAD), a new superframe structure for the 802.15.4 standard to support adaptive traffic. ESAD aims at offering better throughput, reduced network delay, and the accommodation of more nodes to transmit data within a time frame. Specifically, the ESAD proposes that the active period of the standard superframe becomes adapted to the traffic requirements, which improves the utilization of the GTSs. Moreover, the slot size of each GTS is reduced in an attempt to double the total number of GTSs. Finally, the allocation of the GTSs by the personal area network coordinator is achieved based on the shortest-job-first algorithm instead of the first-come-first-served algorithm. The performance of the ESAD has been evaluated through simulations. The targeted performance parameters were as follows: delay; data transmission; GTS utilization; and the number of GTS requesting nodes. The generated results show that the ESAD is superior to the conventional 802.15.4 MAC protocol in terms of these parameters.

The authors in [20] pointed out that based on the specifications of the standard 802.15.4 MAC protocol, whenever a node detects a busy wireless medium, it increases its BE by 1 (up to macMaxBE). The next backoff period for this node will expand while the node that has attained access to the medium will have a better chance of accessing the medium in the future as its backoff period will be shorter. To fix this unfairness for WBANs, the authors proposed using a fixed value of BE during the execution of all BEB steps. This way, all nodes experience the same backoff periods in their transmission attempts, leading to equal opportunities for medium access. This proposal has been evaluated using simulations focusing on packet reception rate, average delay, and throughput. The simulations considered the typical traffics generated by five biomedical sensors in a patient monitoring system. The reported results indicate that using a fixed BE among different nodes leads to significant improvements in the performance in terms of the parameters mentioned above.

In [21], the authors introduced the traffic class prioritization-based CSMA/CA (TCP-CSMA/CA) scheme to support medium access priorities among heterogenous-natured biomedical sensor nodes (BMSNs) in intra-WBANs. The TCP-CSMA/CA provides prioritized medium access to nodes of different traffic classes to improve performance parameters like packet delivery delay, packet loss, energy consumption, throughput, and packet delivery ratio (PDR). Patients’ data are classified based on four traffic classes. Prioritizing access to the medium is made possible by allocating a distinct, minimized, and prioritized backoff period range to each traffic class in every backoff during contention. Furthermore, the BE is made to start from 1, rather than 0, to avoid having the same third, fourth, and fifth backoff ranges (as was the case with [18]). The performance of TCP-CSMA/CA in terms of the parameters mentioned above was studied via extensive simulations, which showed it to be superior to the 802.15.4 standard.

In [22], the authors proposed REO, a reliable and energy-efficient optimization algorithm that optimizes delay, reliability, and energy trade-offs based on traffic and QoS requirements. The authors refer to the delay and energy specifications of medical sensors that are commonly used in WBANs. The best packet size and data rate combination that maximizes the sensor node’s battery lifetime was investigated based on these specifications. By properly adjusting the MAC parameters to be consistent with the packet size and data rate selected, QoS requirements could be achieved. Simulation results reflect that REO can outperform comparable works in delay, energy consumption, and reliability.

In [23], the authors focused on the fact that 802.15.4 uses a fixed superframe structure without considering the different needs of the nodes. The 802.15.4 does not recognize the demands of different applications. To improve 802.15.4 in this direction, the authors proposed a content-based dynamic superframe adaptation (CDSA) scheme by which to adapt BO and SO based on the content requirements simultaneously. The network coordinator uses five QoS parameters (i.e., data rate, receive ratio, size of the network, number of collisions, and delay) to adjust the superframe and the BE dynamically to achieve the optimal solution. The superframe adjustment scheme aims at achieving higher throughput and reducing end-to-end latency. Furthermore, the nodes’ duty cycle is reduced during no activity periods. This way, the network lifetime is enhanced. Performance evaluation through simulations showed that CDSA, compared to 802.15.4 and other schemes that adjust SO and/or BO, can achieve a better packet delivery ratio and throughput, more energy savings, and lower end-to-end delay.

In light of reviewing the works above, we can make the following observations:

• These are very recent studies that prove the validity of the problem we are tackling in this paper, that is, proposing improvements to the MAC protocol as an important means of enhancing the performance in WBANs.
• These studies focus on IEEE 802.15.4 MAC, which proves that this protocol is still a potential candidate for deployment in WBANs.
• Within the limits of our review, works in the literature are mainly focusing on small-scale WBANs. This fact motivates the investigation of new MAC protocols that maintain promising performance as the WBAN grows in size; that is, studying MAC protocols in large-scale WBANs is validated.

4. Improved Adaptive Backoff Algorithm (I-ABA)

In this section, we describe the new improved adaptive backoff algorithm (I-ABA), which aims to enhance the adaptive backoff algorithm (ABA) that we introduced in [11]. We first describe ABA briefly and comment on its downside. Then, we show how I-ABA can overcome the downside of ABA and support large-scale WBANs in achieving superior performance.

4.1. Adaptive Backoff Algorithm (ABA)

ABA recognizes that the standard BEB, in response to collisions over the wireless medium, keeps updating the size of the contention window in a deterministic manner without regard for network size or how active the sensor nodes are in sending data. To resolve this shortcoming of BEB, ABA uses the probability of collision ($P_c$) as a parameter that controls how the contention window size grows or shrinks. The main idea behind this approach is to adapt the size of the contention window dynamically based on the conditions over the communication medium: with a high level of collisions (typical in large-sized networks), the contention window should grow in size; while with a low level of collisions (typical in small-sized networks), the contention window should shrink in size. The mathematical expression by which to update the size of the contention window is as follows:

$$W=P_c{W}_{max},$$

(1)

where $W$ is the contention window size, $P_c$ is the probability of collision, and $W_{max}$ is the 802.15.4’s maximum contention window (set to $2^{macMaxBE}$). $P_c$ is computed locally at each node by knowing the proportion of packets that suffered from collisions. According to Equation (1), the size of the contention window ($W$) cannot exceed $W_{max}$ (see [11,12] for full details on how the contention window its updated over time).

Our extensive simulations showed that $P_c$ is a good indicator of the size of the network. Indeed, Equation (1) manages to relate the size of the contention window to the size of the network indirectly. However, even though the achieved performance was superior to the standard BEB, the maximum contention window size we tested was limited to 256, and degradation in the performance was noticed as the size of the network exceeded 50 nodes.

4.2. The Downside of ABA and Introducing I-ABA

To better understand the downside of ABA, we conducted several experiments to find the optimal size of the contention window that will result in the best performance (in terms of the metrics that will be explained later in this paper) under different network sizes. The results of our experiments are illustrated in Figure 2. In this figure, we show the optimal value of the contention window ($W_{opt}$) compared to the contention window computed using Equation (1) with $W_{max}$ set to 256, 2048, and 4096.

It is apparent from Figure 2 that the case of $W_{max}$ = 256, which was used with ABA, is highly diverted away from the curve corresponding to $W_{opt}$. The diversion is evident for both small-scale and large-scale networks. It is also noticeable that with $W_{max}$ set to 2048 or 4096, we can achieve a boost in the performance (as we show later in this paper, with $W_{max}$ = 2048, the channel utilization increases from 30% to 65% in a network of 200 nodes). Our introduction of I-ABA relies on the observations evident in Figure 2.

In light of our understanding of what Figure 2 reflects, we generate a new curve that captures the optimal values of the contention window, where the performance is optimal, under different values of the probability of collision. The curve is shown in Figure 3 in blue. Since we are plotting contention window sizes against the probability of collision, we can apply curve fitting techniques to formulate an analytical expression of the probability of collision. By using quadratic regression, we can write the following formula:

$$h\left(P_c\right)=\left(5.18\times {P_c}^2\right)-\left(0.65\times P_c\right)+0.05.$$

(2)

Based on Equation (2), we now introduce an improvement to Equation (1) and use $h\left(P_c\right)$ to control the size of the contention window:

$$W=h\left(P_C\right)W_{max}.$$

(3)

Equation (3) is plotted in Figure 3 in orange. It is apparent that the quadratic regression helped in achieving an excellent approximation to $W_{opt}$. The importance of Equation (3) lies in its use of the main strength of ABA, that is, its use of $P_c$ as a parameter to control the contention window (Equation (1)), while achieving a performance that is close to optimal. Similar to ABA, $P_c$ can be calculated locally by the node based on the ratio of the failed frame transmissions to the total frames sent.

The flowchart that describes the I-ABA algorithm is shown in Figure 4. This is an updated version of the flowchart in Figure 1. In the following sections, we develop a mathematical model based on the Markov chain to evaluate the performance of I-ABA; then, we conduct extensive simulations to investigate the impact of using $h\left(P_c\right)$ on the network’s performance. We use MATLAB 7.6 to verify the accuracy of our mathematical model while we use user-defined tools in our simulations.

4.3. Markov-Based Mathematical Model for I-ABA

A Markov chain is a mathematical model that describes the behavior of a system that transitions between a set of states such that the probability of moving from one state to another depends only on the current state and not on past states before it. The state space of a Markov chain is the set of all possible states that a system can visit at any given time. In Figure 5, we show the Markov chain model while highlighting the new expression for $W$. It is essential to mention that modeling backoff algorithms of 802.15.4 using Markov chains are widely adopted in the literature. In creating the Markov chain in Figure 5, we highly benefited from that literature. The state transition and stationary probabilities associated with our Markov chain are similar to or borrowed from our previously published works [11]. In Figure 5, each state in the Markov model is described by a pair (i, j), where i can be 0 (backoff/CCA states), −1 (successful transmission states), or −2 (collision states). States (0, j) (with j ∈ [1, W − 1]) refer to the states wherein the node is in backoff (in which the node is involved in no activity). State (0, 0) corresponds to CAA1, and State (0, −1) corresponds to CCA2. States (−1, j), where j ∈ [0, ${\mathrm{L}}_{\mathrm{s}}$ − 1], correspond to the time period required to successfully transmit a packet. Finally, States (−2, j), where j ∈ [0, ${\mathrm{L}}_{\mathrm{c}}$ − 1], correspond to the time wasted due to a packet collision. The parameters shown in Figure 5 are defined in

Table 1. Parameters associated with the Markov chain model.

#	Parameter	Definition/Mathematical Expression
1	$N$	The size of the network
2	$L_s$	The time needed to transmit a packet successfully
3	$L_c$	The time wasted due to a frame collision
4	$\alpha$	The probability of finding the medium busy during CCA1
5	$\beta$	The probability of finding the medium busy during CCA2
6	$\tau$	The probability that a node initiates CCA1
7	$P_c$	The probability of collision
8	${\overline{T}}_{BO}$	The mean backoff time
9	${\overline{T}}_{CCA}$	The mean time spent in CCAs
10	${\pi }_{SC}$	The probability of a successful cycle
11	${\pi }_{BC}$	The probability of a busy cycle
12	${\pi }_{CC}$	The probability of a collision cycle
13	$P_{tx}$	The average Power consumed during packet transmission
14	$P_{rx}$	The average Power consumed during packet reception
15	$P_{idle}$	The average Power consumed during the backoff
16	$b_{ij}$	The probability of being at state (i,j) in the Markov chain
17	$x$	$\alpha +(1-\alpha )\beta$
18	$y$	$(1-\alpha )(1-\beta ) P_c$

.

For the performance parameters, we reuse the expressions that have been defined in previous works of ours. We note that the derivations are tedious, and to avoid redundancy, we refer the interested readers to the references mentioned above. Therefore, we find it sufficient to provide the expressions without repeating the work that has been published before.

The parameters that we will use to evaluate the performance of I-ABA are the probability of collision, channel utilization, channel idle time, channel collision time, delay, reliability, average energy consumption, average energy wasted in collisions, and fairness. In the following subsections, we define these parameters and represent them mathematically based on the Markov-based model shown in Figure 5. All mathematical expressions are generated under the assumption that we have unacknowledged saturated traffic conditions in the network.

A.

Probability of Collision

The following expression gives the probability of experiencing packet collisions:

$$P_C=1-{\left(1-\tau \right)}^{N-1}.$$

(4)

B.

Channel Utilization

The channel utilization ($U$) parameter measures how efficiently I-ABA utilizes the wireless communication channel to transmit packets successfully. Based on the Markov model in Figure 3, we can express $U$ in the following manner:

$$U=NL\tau \left(1-\alpha \right)\left(1-\beta \right){\left(1-\tau \right)}^{N-1}.$$

(5)

C.

Channel Idle Time

The channel idle time ($T_{idle}$) parameter measures the percentage of time in which the wireless communication channel is free of transmissions or collisions. $T_{idle}$ is indicative of the percentage of time in which all nodes are either in backoff or CCA stages; therefore, the access protocol should lower its value. In Table 1, we have defined $\alpha$ to be the probability of finding the medium busy during CCA1. As such, we can define $T_{idle}$ to be the complement of $\alpha$. Therefore, $T_{idle}$ is mathematically expressed as follows:

$$T_{idle}=1-\alpha .$$

(6)

D.

Channel Collision Time

The channel collision time ($T_{collision}$) parameter measures the percentage of time in which the wireless communication channel is busy due to collisions. Collisions prevent nodes from utilizing the wireless channel. We should aim to lower $T_{collision}$ to minimize the portion of time the wireless channel is wasted with useless activities. Based on (5) and (6), we can express $T_{collision}$ as follows:

$$T_{collision}=1-U-T_{idle}=\alpha -NL\tau \left(1-\alpha \right)\left(1-\beta \right){\left(1-\tau \right)}^{N-1}.$$

(7)

E.

Delay

We define delay ($D$) to be the meantime needed to transmit a packet successfully, and it is defined as follows:

$$D={\displaystyle \frac{1}{{\pi }_{SC}}}{\overline{T}}_{BO}+{\displaystyle \frac{{\pi }_{BC}}{{\pi }_{SC}}}{\overline{T}}_{CCA}+\left(1+{\displaystyle \frac{{\pi }_{CC}}{{\pi }_{SC}}}\right)\left(2+L\right).$$

(8)

F.

Reliability

Reliability ($R$) refers to the probability of delivering a packet successfully. Computing R requires knowledge of the number of successfully transmitted packets ($n_s$), the number of medium access failures ($n_{af}$), and the number of collision failures ($n_{cf}$). The full details of finding these numbers are found in our previous work in [11]. Therefore, $R$ can be expressed as follows:

$$R={\displaystyle \frac{n_s}{n_s+n_{af}+n_{cf}}}.$$

The mathematical derivation of the metric leads to the following expression:

$$R={\displaystyle \frac{1}{1+\frac{\left(1-x\right)x^{m+1}}{\left(1-x^{m+1}\right)\left(1-x-y\right)}+\frac{y^{n+1}}{{\left(1-x\right)}^{n+1}-y^{n+1}}}}.$$

(9)

G.

Average Energy Consumption

The average energy consumed while sending unacknowledged traffic can be computed using the following expression:

$$\begin{gathered} E_{tx}=P_{tx}\left(\sum _{j=0}^{L_s-1}{b}_{-1,j}+\sum _{j=0}^{L_c-1}{b}_{-2,j}\right)+P_{idle}\left(b_{{-1,L}_s}+b_{{-2,L}_c}\right) \\ +P_{rx}\sum _{j=L_s+1}^{L_s+L_{ack}}{b}_{-1,j}+P_{idle}\sum _{j=L_c+1}^{L_c+L_{ack}+1}{b}_{-2,j}. \end{gathered}$$

(10)

H.

Average Energy Wasted in Collisions

It is essential to monitor the level of collisions over the wireless medium. Since nodes consume energy while transmitting packets, collisions result in loss of data and wastage of energy. The average energy wasted due to packet collisions ($E_c$) is computed as follows:

$$E_c=P_{tx}L\left(1-{\left(1-\tau \right)}^{N-1}\right){\left(1-\alpha \right)\left(1-\beta \right)b}_{\mathrm{1,1}}.$$

(11)

I.

Fairness

It is crucial to investigate how fair I-ABA is in granting nodes an equal opportunity to access the wireless medium. We examine the fairness of I-ABA using the fairness index (Jain’s formula) introduced in [24]:

$$fairness index={\displaystyle \frac{{(\sum x_i)}^2}{N\sum {x_i}^2}}.$$

(12)

$N$ is the number of nodes in the network, and $x_i$ is the medium share of the ith node. For I-ABA to be fair, it should achieve a fairness index that is close to 1. A fairness index of less than 1 (and more towards zero) indicates that the protocol favors some nodes over others in accessing the wireless medium.

5. Performance Evaluation and Verification of the Mathematical Model

In this section, we evaluate the performance of I-ABA by implementing the algorithm in Figure 4 using two different tools developed independently: one is Java-based while the second is C-based. Two of the authors developed each tool independently. The purpose of creating these two separate implementations was to ensure the accuracy and reliability of our results by comparing outputs from different programming environments. The primary advantage of utilizing user-defined tools is to streamline future extensions, expedite development, and facilitate troubleshooting. We also use MATLAB to generate data based on the mathematical model we have developed. The data generated by MATLAB are used to verify the data generated by the two user-defined tools. Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13 show how the data generated by the two tools for I-ABA compare to what MATLAB generated using the Markov-based model. In these figures, the curves related to the Java-based simulator, the C-based simulator, and MATLAB are denoted as IABA_J, IABA_C, and IABA_T. These figures clearly show that both simulation tools are generating data that are comparable to a high degree. This enhances confidence in both the design of the simulation tools and the results they generate, especially since the tools were developed independently by two different software developers. To better quantify how close the simulations results are to the MATLAB results, we compute the coefficient of variation of the root-mean-square deviation RSMD (CV(RMSD)) for the performance parameters in Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13. CV(RMSD) is a good measure of accuracy between two sets of data, and it is defined as follows:

$$CV\left(RSMD\right)={\displaystyle \frac{\sqrt{\frac{{\sum }_{i=1}^n{(V_{theo}-V_{sim})}^2}{n_{sample}}}}{\overline{V}}},$$

where $V_{theo}$ is the predicted theoretical value by the Markov-based model, $V_{sim}$ is the simulated value, $\overline{V}$ is the average of the observed values, and $n_{sample}$ is the total number of the sample values used. An accurate theoretical model should achieve low values for CV (RMSD).

Table 2. CV(RMSD) values.

Performance Metric	J_Sim/C_Sim	J_Sim Theoretical	C_Sim Theoretical	Average
Probability of Collision	0.16%	0.61%	0.68%	0.48%
Channel Utilization	0.06%	3.17%	3.20	2.14%
Channel Idle Time	0.13%	4.84%	4.86%	3.27%
Channel Collision Time	0.27%	16.23%	16.41%	10.97%
Transmission Delay	0.03%	0.48%	0.48%	0.33%
Reliability	0.1%	0.18%	0.26%	0.18%
Energy	0.12%	11.90%	11.78%	7.93%
Energy Collision	1.98%	8.02%	6.03%	5.34%

shows the CV(RMSD) values for all parameters in Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13. The table shows the difference between the two simulation tools (J_Sim/C_Sim), the Java-based simulator and MATLAB (J_Sim/Theoretical), and the C-based simulator and MATLAB (C_Sim/Theoretical). It is fairly evident in this table that the CV(RMSD) values are fairly small, which proves that the simulation tools are generating highly comparable results and that both tools closely match what MATLAB is generating. However, it is essential to highlight a relatively high CV(RMSD) value of around 16% for the channel collision time parameter between the simulation results and the MATLAB results. The discrepancy between the theoretical and simulation models for this metric can be explained by the fact that the theoretical value is calculated as C = 1 − U − T, where the error is the sum of errors of U and T.

The implementations for the Java-based simulator, C-based simulator, and MATLAB are made available at GitLab (see [25,26,27]). The simulation settings and parameters are specified in

Table 3. Simulation settings and parameters.

Network Topology	Star
Traffic	Saturated and Unacknowledged
Average Power Consumption (mW)	Rx	40
	Tx	30
	CCA	40
	Sleep	0.8
Durations	Timeslot Duration	0.32 ms (80 bits)
	Frame Length ($L$)	14 timeslots
	ACK Frame Length ($L_{ack}$)	2 timeslots
	Simulation Time	320 s
802.15.4 Settings	macMaxCSMABackoffs	5
	macMaxFrameRetries	4
	macMinBE	3
	macMaxBE	5

. The simulation setup is described next.

We utilized custom-developed tools based on Java and C to evaluate the performance of the network. The Java-based tool was used for the initial development and debugging of the algorithm. The standard JDK with additional networking and data handling libraries have been used. The C-based tool was used to run extensive simulations and gather performance metrics (C was selected due to it being optimized for performance). The GNU Compiler Collection (GCC) and POSIX libraries were used for low-level network simulations and timing functions. Furthermore, Python was used for curve-fitting to derive the mathematical expression that relates the optimal contention window to the network size. The simulations were run on Linux and Windows to ensure platform independence and robustness. Each simulation was run extensively (at least 100 runs). Performance metrics were averaged over all runs to obtain the final results, and 95% confidence intervals were calculated. Since floating-point arithmetic can lead to precision errors, especially in simulations involving small time scales or energy measurements, we carefully managed precision by using double-precision floating-point numbers where necessary. To minimize rounding errors, we applied appropriate rounding techniques only during the final result presentation. To ensure reproducibility and avoid biases due to random number generation, we used fixed random seeds for simulations. We compared our results with those from the standard BEB and ABA to ensure that any performance gains observed were due to the improvements in I-ABA, not experimental biases. The results obtained from the Java and C simulations were cross-validated to check for consistency between different simulation platforms. All simulation runs were logged with detailed information about the network configuration, the number of collisions, and other relevant parameters to trace and debug any anomalies.

For validity threats, we next discuss the internal and external threats to our simulations. We identify programming bugs, model accuracy, and simplified simulation assumptions as potential internal threats. Programming bugs could potentially lead to incorrect results. To mitigate this situation, we conducted thorough code reviews, unit testing, and cross-validation between the Java and C implementations to minimize the risk imposed by errors on our results. For model accuracy, it is apparent that inaccurate models fail to mimic real-world scenarios and, as such, lead to invalid and potentially misleading results. To deal with this, we ensured that the simulation parameters (e.g., network size, node behavior, collision detection, etc.) closely match those used in real-world WBAN deployments. We validated our model against known results from established backoff algorithms like BEB and ABA. For simplified simulation assumptions, there is always the risk of oversimplifying the simulation or experimental environment to the extent that it no longer reflects a practical situation (for example, the use of a uniform node distribution or deterministic patterns). To mitigate this, we used randomized inputs and varied simulation parameters across multiple runs. This randomness helps mimic the unpredictability of real-world environments. We also identify the applicability to real networks and environmental factors as potential external threats to our simulations. These threats are legitimate and can be better mitigated through actual deployment and experimentation on real sensor nodes, which is beyond the scope of this study and is left for future investigation.

Our simulations compare the performance of I-ABA to ABA, standard BEB, and the optimal channel utilization performance that was determined based on experiments. Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20 and Figure 21 show the simulation results.

In Figure 14, we consider the probability of collision over the wireless medium as the size of the network increases. The figure clearly shows that as the network size increases and becomes as high as 350 nodes, the standard BEB performs poorly, leading to high collision probabilities. However, compared to the standard BEB and ABA, I-ABA can maintain a slow increase in the probability of collision as the size of the network increases. As the size reaches 340 nodes, the collision probability is around 40%, while it is 49% and 95.2% for ABA and the standard BEB, respectively. I-ABA is also able to remained closer to the optimal protocol compared to ABA. At 340 nodes, the probability of collision is 28.2% with the optimal protocol.

In Figure 15, we depict the performance in terms of channel utilization. It is evident again that the standard BEB channel utilization deteriorates with the increase in network size. At 340 nodes, BEB hits a channel utilization of 13.3%, which is extremely poor. For I-ABA and ABA, the channel utilization is 61.1% and 57.6%, respectively. Again, I-ABA is closer to the optimal protocol that achieves a channel utilization of 63.7% at a network size of 340 nodes.

The performance in terms of channel idle time is illustrated in Figure 16. As shown, the standard BEB is far from the optimal case that maintains the channel idle time percentage at around 24.5%. BEB decreases the channel idle time percentage to 12.8% as the network size reaches 340 nodes. I-ABA, however, supports a channel idle time of 19.8% at a network size of 340 nodes. ABA, on the other hand, hits a channel idle time of 17.8%. These results show again that I-ABA is still closer to the optimal case compared to ABA and BEB.

In Figure 17, we examine channel collision time, a parameter that should be lowered as it indicates how long the wireless medium was busy with useless activity. The figure shows the rapid increase in channel collision time with BEB. It reaches a percentage as high as 74% at 350 nodes. I-ABA and ABA significantly reduce channel collision time to 19% and 24.6%, respectively, at 340 nodes. Consequently, I-ABA is still superior to the other techniques in reducing channel collision time.

Figure 18 focuses on the transmission delay. As the size of the network increases, the delay with the standard BEB increases rapidly to reach 11.4 ms at 340 nodes. In the meanwhile, I-ABA achieves a delay of 2.5 ms at the same network size. It is lower than the delay with ABA (2.65 ms) and closer to the optimal protocol (2.4 ms).

In Figure 19, the performance in terms of reliability is illustrated. It is interesting to note that I-ABA achieves high reliability at high network sizes. This reliability is as high as 57.8% at a network size of 340 nodes. This reliability is superior to both the standard BEB (3%) and ABA (46.2%) at the same network size.

In Figure 20, we show the performance in terms of the average energy consumption. The performance of both I-ABA and ABA is quite comparable. However, both techniques manage to reduce energy consumption compared to the standard BEB. At a network size of 340 nodes, BEB consumes average energy of 46 W.s., while I-ABA and ABA consume around 33 W.s.

Figure 21 depicts the performance in terms of the average energy wasted in collisions. Again, I-ABA and ABA performance are comparable and much better than the standard BEB. At a network size of 340 nodes, BEB consumes an average energy of 7.47 W.s., while I-ABA and ABA consume 1.17 and 1.56 W.s., respectively.

Finally, Figure 22 reflects how fair the techniques under the scope of this paper are. The figure clearly shows that I-ABA, ABA, and the standard BEB can achieve a fairness index close to 1. It indicates that these medium access controls are fair and guarantee an equal opportunity for every node in the network to access the wireless medium.

Table 4. Performance comparison between I-ABA, ABA, and standard BEB at a network size of 340 nodes.

		Technique
		Standard BEB	ABA	I-ABA
Performance Metric	Probability of Collision	95.2%	49%	40%
	Channel Utilization	13.3%	61.1%	57.6%
	Channel Idle Time	12.8%	17.8%	19.8%
	Channel Collision Time	74%	24.6%	19%
	Transmission Delay	11.4 ms	2.65 ms	2.5 ms
	Reliability	3%	46.2%	57.8%
	Average Energy Consumption	46 W.s.	33 W.s.	33 W.s.
	Average Energy Wasted in Collisions	7.47 W.s.	1.56 W.s.	1.17 W.s.

summarizes the data that have been collected at a network size of 340 nodes and provides a comparison between I-ABA, ABA, and the standard BEB.

Based on the performance evaluation of I-ABA, we now provide a general comparison between I-ABA and the related works that were covered in Section 3. The comparison is provided in

Table 5. Comparison between I-ABA and related works.

Reference	Network Size	Application	IEEE 802.15.4 MAC Parameter Tuning	Large-Scale WBAN	Performance Metrics						Comments
					Reliability	Probability of Collision	Transmission Delay	Power or Energy Consumption	Fairness	Channel Efficiency
[14]	50 nodes	WBAN	✗	✗	✓	✓	✓	✗	✗	✓	Aims at optimizing CW
[15]	5 nodes	WBAN	✓	✗	NA	NA	NA	NA	NA	NA	Scalability is not considered
[16]	14 nodes	WBAN	✗	✗	✓	✗	✓	✓	✗	✓	Scalability is considered in a multi-hop scenario; WBAN is studied for a single-hop star topology with up to 14 nodes
[17]	5–30 nodes	WBAN	✗	✗	✗	✗	✓	✓	✗	✓	PAN coordinator controls backoff behavior of nodes based on the number of failed transmissions
[18]	12 nodes	WBAN	✗	✗	✓	✓	✓	✓	✗	✓	Scalability is not considered beyond 12 nodes
[19]	2–40 nodes	General	✓	✗	✗	✗	✓	✗	✗	✓	Boost in performance focuses on efficient GTS allocation; Scalability is not considered
[20]	5 nodes	WBAN	✗	✗	✓	✗	✓	✗	✗	✓	Scalability is not considered
[21]	14 nodes	WBAN	✗	✗	✓	✓	✓	✓	✗	✓	Scalability is not considered
[22]	6 nodes	WBAN	✓	✗	NA	NA	NA	NA	NA	NA	Scalability is not considered
[23]	1–20 nodes	WBAN	✓	✗	NA	NA	NA	NA	NA	✓	Scalability is not considered
I-ABA	340 nodes	WBAN	✗	✓	✓	✓	✓	✓	✓	✓	Scalability is a main goal

. The comparison criteria are based on the network topology, network size, application area, whether the work relies on 802.15.4 parameter tuning, the applicability to large-scale WBANs (as was defined in Section 1), and performance metrics. Also, the table provides noteworthy comments about each work. While different works use different performance evaluation metrics, the metrics provided in the table are the ones we have evaluated in this paper. These metrics are compared to show how comprehensive and distinguished our evaluation is compared to other works. Also, since this work targets supporting large-scale WBANs, the table examines whether each performance metric has been evaluated against the network size. As a result, the works that lack such evaluation are given the description “not applicable” (NA) in the respective table cell. Furthermore, for convenience, and since different works assess how efficient their techniques are in utilizing the wireless channel using different (but comparable) metrics, channel efficiency is used in this table to refer to channel utilization, channel idle time, channel collision time, throughput, or goodput; that is, any work that supports one or more of these metrics is assumed to have evaluated channel efficiency (of course, against network size). All works, including I-ABA, assume a single-hop star topology (with the exception of [16], as explained shortly). Finally, power or energy consumption refers to whether there has been any power or energy analysis (including consumption and wastage due to collisions) conducted in the work.

Based on Table 5, we can see that our work is distinguished by designing a new technique that focuses on scalability. I-ABA is the only technique in this table that supports single-hop WBANs that are composed of hundreds of nodes. Furthermore, the table shows that our performance evaluation is comprehensive and covers an important set of performance metrics; none of the surveyed works covers all of the listed metrics. The only exception is reference [16], which studies networks composed of 100 nodes. However, the evaluated topology is multi-hop, and the targeted application is non-medical; the same reference uses a single-hop WBAN of 14 nodes to evaluate the performance. For references [14,17,19], which evaluate the performance with network sizes 50, 30, and 40 nodes, respectively, it is not clear how the performance will behave when the network size reaches hundreds of nodes, as is the case with I-ABA. Furthermore, reference [17] relies on the PAN coordinator in its operation, which poses a single point of failure, and reference [19] targets the efficient allocation of GTS while GTS is not used in I-ABA. It is also worth noting that I-ABA requires no parameter tuning for 802.15.4 MAC, while several works rely on that [15,19,22,23]; that is, I-ABA requires no changes to the default parameters of 802.15.4 MAC and imposes minimal changes to its mechanism (as evident when comparing Figure 1 and Figure 4). Finally, it is worth mentioning that the proposal in [14] follows the same approach as in both ABA and I-ABA in terms of optimizing the size of the contention window (CW) based on the conditions over the wireless medium that lead to collisions. However, as stated earlier, the work in [14] does not consider large-scale WBANs.

6. Conclusions

This paper proposes a new backoff algorithm, called the Improved Adaptive Backoff Algorithm (I-ABA), for IEEE 802.15.4 MAC protocol. This technique improves the Adaptive Backoff Algorithm (ABA) that the authors proposed in previous works. I-ABA is designed for deployment in large-scale wireless body area networks (WBANs), that is, WBANs composed of hundreds of sensor nodes. By conducting experiments to identify the optimal values for the size of the contention window, I-ABA uses quadratic regression to create a function of the probability of collision that approximates the aforementioned optimal data. I-ABA is modeled using the same Markov-based model of ABA.

Two simulation tools (based on Java and C) were developed independently by two software developers to study the performance of I-ABA. The data generated by the simulation tools were compared to the data generated by MATLAB based on the Markov chain model. After comparing the simulators’ data with MATLAB data and verifying their accuracy, extensive simulations were conducted to study the performance of I-ABA in terms of the probability of collision, channel utilization, channel idle time, channel collision time, delay reliability, average energy consumed, average energy wasted due to collisions, and fairness. Our simulations results showed that I-ABA performance is superior to the standard BEB and ABA. The primary conclusion is that I-ABA is successful in achieving promising performance in large-scale WBANs.