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QoS based enhanced lossless contention MAC protocol for ultraviolet network

Cheng Li, Jianhua Li, Jingyuan Wang, Jiyong Zhao, Guige Gao, Ke Wang, Yang Su, and Zhiyong Xu

Open Access Open Access

Abstract

Ultraviolet (UV) communication, with its excellent characteristics of non-line-of-sight propagation, high confidentiality, and flexible networking, has gradually gained traction in the field of research. The UV media access control (MAC) protocol is relatively lacking at present, and the UV lossless contention MAC (UVLLC-MAC) protocol designed by our team earlier is limited by the predictability of communication network topology; hence, it is not applicable to multinode and multi-data networks. In order to be applicable to multinode network and satisfy the quality of service (QoS) for various data, an enhanced UVLLC-MAC (eUVLLC-MAC) protocol is proposed based on the binary exponential backoff (BEB) and UVLLC protocols. A two-dimensional Markov chain is established to analyze the network performance, and the throughput and delay expressions of the UV network are derived systematically. Subsequently, the effects of reset probability, maximum backoff order, and priority types on network performance are analyzed, and the protocol parameters are optimized to obtain the best network performance. Finally, it is observed that compared with the BEB and UVLLC-MAC protocols, the network under the eUVLLC-MAC protocol can obtain better performance in throughput, packet loss rate and delay comprehensively, which demonstrates the effectiveness of the proposed protocol. Additionally, the eUVLLC-MAC protocol can provide guidance for multinode and multi-data UV networking.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Ultraviolet (UV) communication, with its excellent characteristics of non-line-of-sight (NLOS) propagation, high confidentiality, and flexible networking, has gradually assumed significant importance in research studies. The application scenarios of UV communication are mainly short distance secure communication and networks, including military network, emergency services, disaster recovery and other complex electromagnetic environments. However, owing to the particularity of UV transmission, the media access control (MAC) protocol is relatively lacking. In recent years, scholars have tried to design efficient MAC protocols for UV communication by referring to the related networking mechanism of ad hoc networks in radio communication. Currently, research on UV access mechanism at home and abroad is divided into two categories: the access protocol based on time-division multiplexing (TDM) and random access protocol based on contention [1]. The TDM protocol has obvious disadvantages, such as low bandwidth utilization, low throughput, and large delay; thus it is especially not suitable for systems with many network nodes [2]. Similarly, the random access protocol introduces complex mechanisms of contention detection and collision avoidance, which leads to unsatisfactory performance of the UV communication network [3].

Considering the characteristics of the abovementioned protocols synthetically, the UV lossless contention MAC (UVLLC-MAC) protocol has been designed creatively by our team [4]. Based on the superposition of optical power, the logical relationship between the node operating status and channel state is fully utilized to solve the problem of terminal access collision. The complexity of its design and implementation is greatly reduced because the intricate contention detection and collision avoidance mechanisms are simplified. However, the UVLLC-MAC protocol is limited by the predictability of the communication network topology and has poor scalability to other UV network models, especially, when there are a large number of nodes in the network, and priorities cannot be allocated according to the number of nodes. In absence of such considerations, channel resources will be completely occupied by nodes with high priority, resulting in “throughput starvation” at nodes with low priority.

In ad hoc networks, the binary exponential backoff (BEB) algorithm is usually adopted to resolve collision problems when there are many nodes in the network [5,6]. In the traditional BEB algorithm, the backoff window is reduced to the minimum value when the data is sent successfully and is doubled when the data transmission encounters a collision [7]. The limited delay cannot be guaranteed, and the size of the backoff window changes dramatically in this algorithm, which leads to the intensification of communication collisions. In particular, there is no quality of service (QoS) guarantee for data services with delay requirements. Chen improved the traditional BEB algorithm and prioritized the data types [8]. The backoff windows of different types of data have different backoff algorithms. However, the protocol has limitations on data types and is not extensible. Sun analyzed the impact of data retransmission times on the network performance on the basis of the BEB algorithm [9]. Lesser retransmission times leads to a high packet loss rate, whereas a large number of retransmission times leads to a high network access delay.

The main contributions of this study are as follows: 1) In order to be applicable to UV multinode networking and satisfy the QoS with respect to various data, an enhanced UVLLC-MAC (eUVLLC-MAC) protocol is proposed based on the BEB algorithm and UVLLC protocol. 2) A two-dimensional Markov chain is established to analyze the network performance, and the throughput and delay expressions of the UV network are derived systematically. 3) The effects of reset probability αpri, maximum backoff order a, and priority types pri on network performance are analyzed, and the protocol parameters are optimized to obtain the best network performance. 4) It is observed that compared with the BEB and UVLLC-MAC protocols, the network under the eUVLLC-MAC protocol can obtain better throughput, packet loss rate, and delay performance, which fully proves the effectiveness of the proposed protocol.

The remainder of this paper is organized as follows. Section 2 describes the eUVLLC-MAC protocol, which consists of the enhanced BEB (eBEB) optical bus modules. Section 3 presents the two-dimensional Markov chain to derive the throughput and delay expressions of the protocol in detail. Section 4 is devoted to the simulation results to verify the effectiveness of the eUVLLC-MAC protocol. Finally, conclusions and future scope of study are summarized in Section 5.

2. Preliminaries

In the UV network, different data services that are transmitted between terminals often have different requirements for network delay. For example, the data of transmission parameter setting requires a short delay and must be transmitted in the shortest time. However, for the data that perceive the surrounding environment, the delay requirements are not overly strict. Therefore, it is of great practical significance to design an appropriate MAC protocol to satisfy the QoS for data services according to the requirements of different data for network delay.

An eUVLLC-MAC protocol is proposed to ensure the QoS requirements of various data in UV multinode networks. The protocol includes the eBEB optical bus modules. The eBEB module is used to avoid the same priority collisions and resolve the contention issue of the UV nodes. The optical bus module is used to determine the UV communication-channel state and ensure the QoS for data with high priority.

2.1. eBEB module

Referring to the backoff mechanism of the BEB algorithm [7], BW0, BW1, BW2,…, BWa represent $a + 1$ types of backoff window, with the backoff window $B{W_p} = {2^p}B{W_0}$ for the backoff order $p(p = 0,1,2\ldots ,a)$. It can be calculated that: $B{W_{\min }} = {2^0}B{W_0}$ and $B{W_{\max }} = {2^a}B{W_0}$, where BW0 is the initial size of the backoff window. Each terminal node randomly selects the backoff value from the backoff window, and the backoff timer of each terminal operates independently. When the channel is monitored as busy or idle, the backoff timer pauses or begins accordingly. When the timer hits 0, the node tries to send data.

In IEEE 802.11e, the Enhanced Distributed Channel Access (EDCA) algorithm defines 8 service priorities and 4 access priorities, and Dedicated Short Range Communication /Wireless Access in Vehicular Environment (DSRC/WAVE) and IEEE 1609.3 also use this setting [10–12]. Similar to the setting in the EDCA, $pri(pri = 0,1,2\ldots ,PRI)$ represents the priority of different types of data, and a smaller pri corresponds to a higher data priority. As an improvement upon the traditional BEB algorithm, αpri is defined as the reset probability of the backoff order p being reset to the minimum order 0 when the data with priority pri is sent successfully. In the eUVLLC-MAC protocol, the size of the backoff window is doubled when the data transmission encounters a collision, and the window is reset to the minimum window BWmin with the reset probability αpri when the data is sent successfully. Every type of data follows an independent backoff process. Notably, the reset probability of the data with high priority is greater than that of the data with low priority, ${\alpha _1} \ge {\alpha _2} \ge \ldots \ge {\alpha _{PRI}}$, guaranteeing the QoS for data with high priority.

2.2. Optical bus module

Based on the superposition of optical power, the use of the optical bus is proposed in the UV communication channel. When a node is required to send data, the UV light-emitting diode begins to communicate, while in the absence of data to be transmitted, it is in the silent state. The state of the optical bus is jointly determined by the operating status of each terminal node, and there is an “AND/OR” superimposition logic of the UV power, as shown in Fig. 1. In the communication channel, if one or more terminal node works, the optical bus is in the light state. If all the terminal nodes do not work, the optical bus is in the silent state.

 figure: Fig. 1.

Fig. 1. Access logic diagram of the UV nodes.

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The general frame structure of the eUVLLC-MAC protocol is shown in Fig. 2. The access arbitration segment, including the data priority section, which is the key part of the optical bus module, can be used to effectively resolve the problem of access collisions in a multi-data network. On–off keying (OOK) modulation is adopted in the UV nodes, and the light and silent states of the nodes represent bit 0 and bit 1 of data information, respectively. Competing nodes send bits information of the priority sections in a descending order. A node can effectively perceive the working state of other nodes within its effective communication range. When the bit information sent by a node is 1 (silent) and the current bit value of the priority section of other nodes is 0 (light), the node exits the access contention in the next slot and continuously monitors the status of the communication channel until the next access contention. When the bit information sent by a node is 0 (light), other nodes have no influence on the access of the current node to the UV communication channel, thereby ensuring transmission of data with high priority.

 figure: Fig. 2.

Fig. 2. Algorithm timing diagram.

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2.3. Algorithm workflow

The algorithm workflow based on the eUVLLC-MAC protocol is shown in Fig. 3:

 figure: Fig. 3.

Fig. 3. Workflow of the eUVLLC-MAC protocol.

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Step 1. Determine the data type to be sent and assign a priority pri.

Step 2: The backoff process of the current data starts from the backoff order at the end of the backoff process of the previous similar data type. Assuming that the backoff order of the previous similar data type returns to the order p, the initial backoff order of the current new data is p and the initial backoff value is rand (0, BWp−1).

Step 3. The node monitors the channel for backoff and is ready to send data when the backoff timer reaches 0. Check whether there are access collisions. If not, the data is sent smoothly. If yes, compare data priorities. The data with higher priority is successfully sent, but the transmission of the data with lower priority fails. Go to Step 4.

Step 4. If the data doesn't succeed in the access contention and the backoff order p is less than a, the backoff order increases by 1 and the backoff window doubles. If the backoff order p is equal to a, the backoff order remains the same. Subsequently, the backoff value is selected again from the new backoff window, and the backoff is performed again.

Step 5. When the data transmission is successful, the backoff order of the UV node returns from p to 0 with a probability αpri, and the backoff order is kept unchanged with a probability 1−αpri.

Considering nodes A, B, C, and D as examples, the data priority is data A > data B. Figure 2 shows the operation process of the eUVLLC-MAC protocol. First, each node randomly selects a backoff value from the respective backoff window and continuously monitors the channel during the backoff time. In the third timeslot, the backoff timers of nodes A and B are simultaneously 0 and ready to send the data. Furthermore, the other nodes change into monitoring mode, and the timer stops counting. Subsequently, data A and B compare their priorities based on the optical bus module. The first bit of the arbitration segment of data A is 0 (Light) and that of data B is 1 (Silent). According to the superposition principle of the optical bus module expounded in Section 2.2, the channel status is determined to be 0 (Light), and data B withdraws from the contention collision. In addition, the backoff window doubles, and the backoff value is re-selected. Data A wins the contention and is sent successfully, and the backoff order of this data type returns to 0 with the probability αpri. Meanwhile, the timers of the remaining nodes start again. At the 18th timeslot, the backoff timer of node D hits 0. No other node participates in the access contention at this time, hence, data D is sent directly.

In the eUVLLC-MAC protocol, the backoff mode provides a staggered peak for the multi-priorities, avoiding the collision of the identical data priorities. Additionally, the QoS of data with delay requirements can be guaranteed in the following two ways: 1) Data with high priority resets the backoff order to 0 with a higher probability αpri after being successfully sent. Therefore, data with a high priority has a smaller backoff window and a relatively short queuing delay and 2) When the backoff timers of different data are simultaneously 0 and the access collision occurs, the data with the higher priority will be sent first without loss based on the optical bus module.

3. Network performance analysis

3.1. Prediction of neighbor nodes

In the UV network, the distribution of the terminal nodes is governed by the Poisson point process, P(λ). For any terminal node, all nodes within the communication range are its competing nodes, and the distribution probability of the number of neighbor nodes is represented by the following equation:

$$P(n = k) = \frac{{{\lambda ^k}{e^{ - \lambda }}}}{{k!}},\quad k = 0,1,2, \cdots .$$
The coverage area of the UV nodes is approximately circular, and the communication radius is r. Hence, the expectation of the number of neighbor nodes is given by $\lambda = \pi {r^2} \cdot \mathrm{\rho }$, where ρ is the density of the terminal nodes in the network.

3.2. Modeling and performance analysis

The UV network has the following settings: 1) Full duplex working modes are adopted for the UV terminal nodes. When a node sends data, other nodes within the communication range can receive it. Therefore, the communication mode can be regarded as a broadcast communication; 2) UV communication channel is set as a single optical wavelength channel, that is, multiple network nodes share a single optical wavelength channel, and each node accesses the channel based on the contention; and 3) All nodes are in the channel-monitoring state before data transmission.

3.2.1. State transition probability

A two-dimensional Markov chain is used to analyze the proposed protocol. Figure 4 illustrates the state transition diagram of the Markov chain based on the backoff process for a single node. Let (p, q) express the transmission state of the node: p is the backoff order of the node and represents the time of doubling the backoff window; and q is the backoff value randomly selected by the node, $0 \le q \le B{W_p} - 1$. The transmission state space of the node is: $\Gamma = \{{(p,q)| 0 \le p \le a,0 \le q \le B{W_p} - 1} \}$. Let [x(t), y(t)] represent the backoff state of the node at time t; the transition probability is given by the following equation:

$$P\{{{p^\prime },{q^\prime }| p,q} \}= P\{{x(t + 1) = {p^\prime },y(t + 1) = {q^\prime }| x(t) = p,y(t) = q} \}.$$
Because this is a recurrent finite Markov chain, there are stable states. Hence, the two-dimensional stochastic process [x(t),y(t)] is a discrete two-dimensional Markov chain. To simplify, let ${s_{p,q}} = \mathop {\lim }\limits_{t \to \infty } P\{ x(t) = p,y(t) = q\}$ express the steady state probability of the Markov chain.

 figure: Fig. 4.

Fig. 4. State transition diagram of the Markov chain.

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For a particular node, the probability of being in the sending state at a certain time is τ, and the probability of encountering an access collision while sending data is η. Evidently, the collision probability is equal to the probability that at least one of the n−1 nodes transmit data at the same moment.

$$\eta = 1 - {(1 - \tau )^{n - 1}}.$$
From Eq. (1), it can be deduced that:
$$\eta = \sum\limits_{k = 1}^\infty {\frac{{{\lambda ^k}{e^{ - \lambda }}}}{{k!}}} [{1 - {{(1 - \tau )}^{k - 1}}} ]= 1 - {e^{ - \lambda }} - \frac{{{e^{ - \lambda \tau }}}}{{1 - \tau }} + \lambda {e^{ - \lambda }}.$$
In the new protocol, the backoff window will be doubled until it reaches the maximum backoff window BWmax when the data fails to send, and the backoff window will be reset to the minimum backoff window BWmin with the reset probability αpri when the data is successfully sent.

It can be observed in Fig. 4:

$$\left\{ {\begin{array}{l} {P\{ p,q| p,q + 1\} = 1\quad \quad p \in [0,a],q \in [{0,B{W_p} - 2} ]}\\ {P\{ 0,q| 0,0\} = \frac{{1 - \eta }}{{B{W_0}}}\quad \quad p = 0,q \in [{0,B{W_0} - 1} ]}\\ {P\{ p,q| p,0\} = \frac{{(1 - \eta )({1 - {\alpha_{pri}}} )}}{{B{W_i}}}\quad p \in [1,a - 1],q \in [{0,B{W_p} - 1} ]}\\ {P\{ a,q| a,0\} = \frac{{(1 - \eta )({1 - {\alpha_{pri}}} )+ \eta }}{{B{W_a}}}\quad p = a,q \in [{0,B{W_a} - 1} ]}\\ {P\{ p,q| p - 1,0\} = \frac{\eta }{{B{W_p}}}\quad \quad p \in [1,a],q \in [{0,B{W_p} - 1} ]}\\ {P\{ 0,q| p,0\} = \frac{{(1 - \eta ){\alpha_{pri}}}}{{B{W_0}}}\quad \quad p \in [1,a],q \in [{0,B{W_0} - 1} ]} \end{array}} \right..$$
In Eq. (5), the first term represents the probability that the backoff state shifts one step to the left at the backoff order p; the second term represents the probability that the backoff order remains unchanged when the data is successfully sent at backoff order 0; the third term represents the probability that the backoff order remains unchanged when the data is sent successfully at the backoff order p; the fourth term represents the probability that the backoff order remains unchanged when the data is sent successfully at the maximum backoff order a; the fifth term represents the probability that the data transmission fails, and the backoff order is added by one at the backoff order p-1; and the sixth term represents the probability that the backoff order is reset to 0 when the data is sent successfully at the backoff order p.

The following can be obtained from the state transition diagram of the Markov chain,

$$\left\{ \begin{array}{l} s_{0,0}^{(pri)} = s_{0,0}^{(pri)} \cdot (1 - \eta ) + \sum\limits_{p = 1}^a {s_{p,0}^{(pri)}} \cdot (1 - \eta ){\alpha_{pri}}\quad p = 0\\ s_{p,0}^{(pri)} = s_{p,0}^{(pri)}\cdot(1 - \eta )(1 - {\alpha_{pri}}) + s_{p - 1,0}^{(pri)} \cdot \eta \quad p \in [1,a - 1]\\ s_{a,0}^{(pri)} = s_{a,0}^{(pri)}\cdot[{\eta + (1 - \eta )(1 - {\alpha_{pri}})} ]+ s_{a - 1,0}^{(pri)} \cdot \eta \quad p = a \end{array} \right..$$
Based on the expressions of Eq. (6), the following can be obtained:
$$\left\{ \begin{array}{l} s_{p,0}^{(pri)} = \frac{\eta }{{\eta + (1 - \eta ){\alpha_{pri}}}}s_{p - 1,0}^{(pri)} = {\left[ {\frac{\eta }{{\eta + (1 - \eta ){\alpha_{pri}}}}} \right]^p}s_{0,0}^{(pri)}\quad p \in [1,a - 1]\\ s_{a,0}^{(pri)} = \frac{\eta }{{(1 - \eta ){\alpha_{pri}}}}s_{a - 1,0}^{(pri)} = \frac{\eta }{{(1 - \eta ){\alpha_{pri}}}}\cdot{\left[ {\frac{\eta }{{\eta + (1 - \eta ){\alpha_{pri}}}}} \right]^{a - 1}}s_{0,0}^{(pri)}\quad p = a \end{array} \right..$$
Taking ${U_\eta } = \frac{\eta }{{\eta + (1 - \eta ){\alpha _{pri}}}}$ simplifies Eq. (7) to the following:
$$\left\{ \begin{array}{l} s_{p,0}^{(pri)} = {U_\eta }^p\cdots_{0,0}^{(pri)}\quad p \in [1,a - 1]\\ s_{a,0}^{(pri)} = \frac{{\eta \cdot U_\eta^{a - 1}}}{{(1 - \eta ){\alpha_{pri}}}}s_{0,0}^{(pri)}\quad p = a \end{array} \right..$$
From the data presented in Fig. 4, the following can be obtained:
$$s_{p,q}^{(pri)} = \frac{{B{W_p} - q}}{{B{W_p}}}\cdot\left\{ {\begin{array}{l} {\sum\limits_{n = 1}^a {s_{n,0}^{(pri)}} \cdot(1 - \eta ){\alpha_{pri}} + s_{0,0}^{(pri)} \cdot (1 - \eta )\quad p = 0}\\ {s_{p - 1,0}^{(pri)}\cdot\eta + s_{p,0}^{(pri)}\cdot(1 - \eta )({1 - {\alpha_{pri}}} )\quad p \in [1,a - 1]}\\ {s_{a - 1,0}^{(pri)}\cdot\eta + s_{a,0}^{(pri)}\cdot[{(1 - \eta )({1 - {\alpha_{pri}}} )+ \eta } ]\quad p = a} \end{array}} \right..$$
For any state $s_{p,q}^{(pri)}$, all states whose backoff values are greater than q are transferred to $s_{p,q}^{(pri)}$ at the backoff order p. For special orders 0 and a, multiple state transitions must be considered.

Substituting Eq. (6) into Eq. (9), the following can be obtained:

$$s_{p,q}^{(pri)} = \frac{{B{W_p} - q}}{{B{W_p}}}\cdots_{p,0}^{(pri)}\quad p \in [0,a],q \in [{0,B{W_p} - 1} ].$$
As $s_{p,q}^{} = \mathop {\lim }\limits_{t \to \infty } P\{ x(t) = p,y(t) = q\}$ expresses the steady state probability of the Markov chain, the sum of the probability is 1.
$$\sum\limits_{p = 0}^a {\sum\limits_{q = 0}^{B{W_p} - 1} {s_{p,q}^{(pri)}} } = 1.$$
That is,
$$\sum\limits_{p = 0}^a {\sum\limits_{q = 0}^{B{W_p} - 1} {s_{p,q}^{(pri)}} } = \sum\limits_{p = 0}^a {s_{p,0}^{(pri)}} \sum\limits_{q = 0}^{B{W_p} - 1} {\frac{{B{W_p} - q}}{{B{W_p}}}} = \frac{1}{2}\sum\limits_{p = 0}^a {s_{p,0}^{(pri)}} ({1 + B{W_p}} )= 1.$$
By substituting Eq. (8) into Eq. (12), $s_{0,0}^{(pri)}$ can be obtained:
$$s_{0,0}^{(pri)} = \frac{2}{{\sum\limits_{p = 0}^{a - 1} {U_\eta ^P} ({1 + B{W_P}} )+ \frac{{\eta \cdot U_\eta ^{a - 1}}}{{(1 - \eta ){\alpha _{pri}}}}({1 + B{W_a}} )}}.$$

3.2.2. Transmission probability

The probability that the data with priority pri is sent is obtained as:

$$\begin{aligned} \tau (pri) & = \sum\limits_{p = 0}^a {s_{p,0}^{(pri)}} \\ & \textrm{ = }s_{0,0}^{(pri)}\textrm{ + }\sum\limits_{p = 1}^{a - 1} {{{\left[ {\frac{\eta }{{\eta + (1 - \eta ){\alpha _{pri}}}}} \right]}^p}s_{0,0}^{(pri)} } \textrm{ + }\frac{\eta }{{(1 - \eta ){\alpha _{pri}}}} \cdot {\left[ {\frac{\eta }{{\eta + (1 - \eta ){\alpha _{pri}}}}} \right]^{a - 1}}s_{0,0}^{(pri)} .\\ & = \frac{{s_{0,0}^{(pri)}}}{{1 - {U_\eta }}} \end{aligned}$$
The proportion of the data with priority pri is βpri in the system, and the average transmission probability of the system can be expressed as:
$$\tau = \sum\limits_{pri = 1}^{PRI} {{\beta _{pri}}} \sum\limits_{p = 0}^a {s_{p,0}^{(pri)}} = \sum\limits_{pri = 1}^{PRI} {\frac{{{\beta _{pri}}\cdots_{0,0}^{(pri)}}}{{1 - {U_\eta }}}} .$$

3.3. Network performance

3.3.1. Throughput

The network throughput S is defined as the ratio of the payload transmitted in a timeslot to the timeslot length [13]:

$$S = \frac{{E(\textrm{the payload transmitted in a timeslot})}}{{E(\textrm{a timeslot length})}} = \frac{{{P_s}{P_{tr}}E(P)}}{{({1 - {P_{tr}}} )\sigma + {P_s}{P_{tr}}{T_s} + ({1 - {P_s}} ){P_{tr}}{T_c}}} ,$$
where E(P) is the average length of data frames and Ptr is the probability that at least one data has been sent at any timeslot, which can be obtained as:
$${P_{tr}} = \sum\limits_{k = 1}^\infty {\frac{{{\lambda ^k}{e^{ - \lambda }}}}{{k!}}} [{1 - {{(1 - \tau )}^k}} ]= 1 - {e^{ - \lambda }} - {e^{ - \lambda \tau }} + \lambda {e^{ - \lambda }}(1 - \tau ) .$$
Ps is the probability of successful data transmission under the condition that data is transmitted by the nodes. Owing to the superposition mechanism of the optical bus module, data with high priority will always be sent successfully when contention occurs; therefore, Ps is 1.

The timeslot includes the idle time of the channel with probability 1−Ps, the successful transmission time of the data frame with probability PsPtr, and the collision time of the data frame with probability (1−Ps)Ptr. σ is the width per unit timeslot and Ts and Tc are the time required when data transmission succeeds and fails, respectively.

3.3.2. Network delay

The average delay Delpri of data with priority pri is the time expectation that the data waits to be sent until the transmission succeeds.

$$De{l_{pri}} = {E_{pri}}{E_t} ,$$
where Et is the average length of the timeslot and the denominator of Eq. (16).
$${E_t} = ({1 - {P_{tr}}} )\sigma + {P_s}{P_{tr}}{T_s} + ({1 - {P_s}} ){P_{tr}}{T_c} .$$
Epri is the average number of timeslots required for successful transmission of the data with priority pri:
$${E_{pri}} = \sum\limits_{p = 0}^a {{H_P}} {b_{pri,p}},$$
where bpri,p is the probability that the data with priority pri is sent successfully at the backoff order p and Hp is the expectation of the time the data waits to be sent at the backoff order p, which can be expressed as
$${H_P} = \sum\limits_{q = 0}^p {\frac{{B{W_q} + 1}}{2}} .$$
The choice of backoff order is only related to the last backoff order of the previous similar data type. Let Bpri,p represent the probability of selecting the backoff value from the backoff order p when the data with priority pri arrives:
$${B_{pri,p}} = \left\{ {\begin{array}{l} {{s_{0,0}}\cdot\frac{{B{W_0} + 1}}{2} + \sum\limits_{i = 1}^a {{s_{i,0}}} \cdot\frac{{B{W_i} + 1}}{2}\cdot{\alpha_{pri}}\quad p = 0}\\ {{s_{p,0}}\cdot\frac{{B{W_p} + 1}}{2}\cdot({1 - {\alpha_{pri}}} )\quad p \in [1,a]} \end{array}} \right..$$
The probability of sending data with priority pri successfully at the backoff order p is obtained as
$${b_{pri,p}} = \sum\limits_{i = 0}^p {{B_{pri,i}}} \cdot{\eta ^{p - i}}(1 - \eta )\quad p \in [0,a - 1].$$
Substituting Eqs. (20)−(23) into Eq. (18), the delay expression of the data with priority pri can be obtained:
$$De{l_{pri}} = {E_t} \cdot \sum\limits_{p = 0}^a {\sum\limits_{q = 0}^p {\frac{{B{W_q} + 1}}{2}} } \cdot{b_{pri,p}}.$$

4. Simulation and analysis

The UV NLOS communication model is illustrated in Fig. 5. Based on our previous simulation model [14], the UV communication radius for OOK is derived as

$${R_{OOK}} = \sqrt[{^\alpha }]{{ - \frac{{\eta \lambda {P_t}}}{{hc\xi {R_b}\ln ({2{P_e}} )}}}},$$
where the loss exponent α and loss factor ξ in are related to the transceiver elevation angles. The UV propagation parameters are set, as listed in Table 1, and the communication distance of the node can exceed 200 m. In the simulation, the communication radius of the UV node is set as 200 m, which is consistent with real-world situations. A square area of side length of 1000 m is chosen for the experimental simulation, and the number of UV nodes in the square area is 30.

 figure: Fig. 5.

Fig. 5. UV Non-line-of-sight communication model.

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Table 1. UV propagation parameters

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According to the settings of each group of protocol parameters, 1000 network topology diagrams are generated by the Monte Carlo method, as shown in Fig. 6. Dashed lines indicate that adjacent nodes are within communication range and the topology diagrams can be divided into three categories: (a) fully connected network, (b) two network subsets and (c) more than two network subsets. The conditions for forming the category (a) and (b) topologies are strict relatively in UV practical networking. So the network performance is calculated and analyzed based on the category (c) in a simulation time of 500 s. The key simulation parameters are listed in Table 2.

 figure: Fig. 6.

Fig. 6. UV network topology diagrams.

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Table 2. Simulation parameters

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The effects of reset probability αpri, maximum backoff order a and priority types pri on network performance are analyzed respectively in the eUVLLC-MAC protocol, and the algorithm parameters are optimized to obtain the best network performance. Then, the changing trends in the network performance, including throughput, delay and packet loss rate packet under the BEB, the eUVLLC-MAC and UVLLC-MAC protocols are studied, with subsequent comparisons of the differences. The effectiveness of the proposed protocol is thus verified fully via both simulations and analysis. The network delay includes transmission delay, propagation delay, and queuing delay [2]. And queuing delay accounted for the main part in the delay. Therefore, queuing delay is approximated as network delay in the performance analysis.

4.1. Reset probability

Figures 7 and 8 show the throughput and average delay of each priority data versus data generation probability p for different reset probabilities αpri, respectively. The maximum backoff order is 3, and number of priority types is 2. It is observed that the changing trends of the throughput and delay with respect to p are approximately identical for the two types of priority data. As the data generation probability increases, the increasing number of data in the network leads to increasing throughput. Meanwhile, data contention also leads to a gradual increase of queuing delay for each priority data. In the eUVLLC-MAC protocol, data with a higher priority has a higher reset probability, resulting in a smaller backoff window on average, which ensures that it occupies more channel resources. Therefore, data with a higher priority has a higher throughput and smaller delay. In Figs. 7(a) and 8(a), the throughput of data with priority 1 (2.48×104 bit/s) increases by 150.51% compared with that of data with priority 2 (0.99×104 bit/s) and the corresponding delay decreases by 58.91% from 64.55 ms to 26.53 ms when p is 0.6. In addition, the delay fluctuation of the data with high priority is smaller than that of the data with low priority, ensuring stable transmission of important services.

 figure: Fig. 7.

Fig. 7. Throughput versus data generation probability.

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 figure: Fig. 8.

Fig. 8. Delay versus data generation probability.

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In horizontal comparison, when the reset probabilities of different priority data differ greatly, the channel resource occupancy gap is larger. In Fig. 8, the delay of data with priority 1 is reduced by 58.91% compared with that of the data with priority 2 with α1 = 0.8, α2 = 0.2, while the reduction is only 49.44% (from 54.10 ms to 27.35 ms) with α1 = 0.6, α2 = 0.4 when p is 0.6. Therefore, the strict data delay requirement can be met by increasing the reset probability of the data with high priority and widening the reset probability gap among data with different priorities in practical applications.

4.2. Maximum backoff order

Figures 7, 8, 9, and 10 illustrate the throughput and average delay of each priority data versus p for various backoff orders (maximum backoff order a = 3, 5, 8). The reset probability is: α1 = 0.8 and α1 = 0.2, and the number of priority types is 2. When the maximum backoff order is larger, the size of the backoff window is larger and the queuing delay of the data with low priority is longer, resulting in lower throughput and higher network delay. Figures 8(a) and 10(a) indicate that the delay of the data with priority 2 increases by approximately 51.24% from the maximum backoff orders 3 (64.55 ms) to 5 (97.65 ms), whereas this percentage increases to 72.45% from the maximum backoff orders 5 (97.65 ms) to 8 (168.40 ms) when p is 0.6. For data with high priority, the optical bus module and high reset probability guarantee the smooth transmission of data even if the maximum backoff order increases. Therefore, the change of maximum backoff order has negligible influence on important data services.

 figure: Fig. 9.

Fig. 9. Throughput versus data generation probability.

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 figure: Fig. 10.

Fig. 10. Delay versus data generation probability.

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4.3. Priority types

Figures 11 and 12 illustrate the throughput and average delay of each priority data versus p for three typesof priority data, respectively. The maximum backoff order a is 3. It is observed that the changing trends of the throughput and average delay with respect to p are approximately identical to the network performances of the two types priority data. Data with high priority occupy more channel resources, so the throughput is higher and the average delay is lower.

 figure: Fig. 11.

Fig. 11. Throughput versus data generation probability.

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 figure: Fig. 12.

Fig. 12. Delay versus data generation probability.

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By horizontally comparing the results from the two sets of reset probabilities in Figs. 11 and 12, it can be deduced that the smaller the reset probability gap of various priority data is, the more similar the network performance of various priority data is. When the reset probability changes from α1 = 0.8, α2 = 0.5, and α3 = 0.2 to α1 = 0.6, α2 = 0.5, and α3 = 0.4,, the throughput ratio of the data with priority 3 to data with priority 1 increases from 0.34 to 0.46, while the ratio of the average delay decreases from 0.29 to 0.24 when p is 0.6.

4.4. Comparison with the BEB and UVLLC-MAC protocols

Figures 13, 14, and 15 illustrate the comparison of the network performances for the three MAC protocols. Figure 12 indicates that the network throughput of the UVLLC-MAC protocol is significantly higher than that of the BEB and eUVLLC-MAC protocols. Because there is no backoff mechanism in the UVLLC-MAC protocol, data is sent immediately after it is generated to maximize channel utilization. However, it is the lack of backoff mechanism that dramatically increases the number of collisions with the same priority data when p increases. Consequently, the throughput of the UVLLC-MAC protocol gradually decreases after the peak, and the packet loss rate increases rapidly, as shown in Fig. 14. Therefore, it cannot be applied to multinode and multi-data networks.

 figure: Fig. 13.

Fig. 13. Throughput versus data generation probability for the three MAC protocols.

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 figure: Fig. 14.

Fig. 14. Packet loss rate versus data generation probability for the three MAC protocols.

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 figure: Fig. 15.

Fig. 15. Delay versus data generation probability for the three MAC protocols.

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Compared with the BEB mechanism, the eUVLLC-MAC protocol has higher throughput (increased by approximately 12.56% on average), lower packet loss rate (decreased by 18.20%), and lower latency (decreased by 13.01%) owing to the application of the optical bus module. Moreover, data with high priority can be sent preferentially when multi-packet collisions occur, ensuring QoS of important services.

5. Conclusions and future scope

In order to satisfy the QoS for various data and increase applicability of the UV communication in UV multinode networking, the eUVLLC-MAC protocol is proposed based on the BEB algorithm and UVLLC protocol. A two-dimensional Markov chain is established to analyze the network performance, and the throughput and delay expressions of the UV network are derived systematically. Subsequently, the effects of reset probability αpri, maximum backoff order a, and priority types pri on network performance are analyzed, and the protocol parameters are optimized to obtain the best network performance. Finally, the eUVLLC-MAC protocol is compared with the BEB and UVLLC-MAC protocols. It is observed that UVLLC-MAC protocol cannot be applied in multinode and multi-data networks owing to unacceptable packet loss rate caused by same-priority data collisions. Compared with the BEB mechanism, the eUVVLLC-MAC can achieve higher throughput (increased by approximately 12.56% on average), lower packet loss rate (decreased by 18.20), and lower delay (13.01%) due to the introduction of the optical bus module, which validates the utilization of the proposed algorithm.

Because a fixed priority is set for each data service, there is no flexibility to changing the data priority when the network scenario changes. The next course of action in this field is to introduce flexible priority settings in order to improve the MAC protocol in UV networking.

Funding

National Natural Science Foundation of China (61975238, 62171463).

Acknowledgments

This work was supported by the National Natural Science Foundation of China (62171463&61975238).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. C. Li, Z. Y. Xu, J. H. Li, J. Y. Wang, Y. M. Lin, and J. Y. Zhao, “Performance of the UV Multinode Network Under the Lossless Contention MAC Protocol,” IEEE Photonics J. 14(2), 1–7 (2022). [CrossRef]  

2. M. Chen, Y. L. Xiao, S. T. Wang, and H. T. Li, “Analysis of TDMA time slot allocation algorithm in ultraviolet Ad Hoc network,” Opt. Commun. Technol. 7, 8 (2016).

3. Y. Li, J. Ning, Z. Y. Xu, S. V. Krishnamurthy, and G. Chen, “UVOC-MAC: a MAC protocol for outdoor ultraviolet networks,” Wirel. Netw. 19(6), 1101–1120 (2013). [CrossRef]  

4. C. Li, J. H. Li, Z. Y. Xu, and J. Y. Wang, “Research on the lossless contention MAC protocol and performance of ultraviolet communication network,” Opt. Express 29(20), 31952–3196 (2021). [CrossRef]  

5. F. Firyaguna and M. M. Carvalho, “Performance of polling disciplines for the receiver-initiated binary exponential backoff MAC protocol,” Ad Hoc Netw. 31, 1–19 (2015). [CrossRef]  

6. H. T. Zhao, S. Zhang, and E. Garcia-Palacios, “Cross-layer Framework for Fine-grained Channel Access in Next Generation High-density WiFi Networks,” China Commun. 13(2), 55–67 (2016).

7. N. Wei, M. Abolhasan, B. Hagelstein, P. L. Ren, and W. Xin, “A New Trellis Model for MAC Layer Cooperative Retransmission Protocols,” IEEE T. Veh. Technol. 66(4), C1–C4 (2017). [CrossRef]  

8. C. Y. Chen, Y. Fu, S. M. Jiang, and X. S. Zheng, “MAC layer channel backoff algorithm for wireless multimedia sensor networks,” Transducer and Microsy. Technol. 32(10), 134–138 (2013).

9. X. H. Sun and L. Dai, “Performance Optimization of CSMA Networks With a Finite Retry Limit,” IEEE T. Wirel. Commun. 15(9), 5947–5962 (2016). [CrossRef]  

10. H. Zhang, W. Tian, and J. Liu, “Improving EDCA for Efficient Channel Access in Vehicular Communications,” IEEE Commun. Mag. 56(10), 72–77 (2018). [CrossRef]  

11. D. B. Rawat, R. Alsabet, C. Bajracharya, and M. Song, “On the Performance of Cognitive Internet-of-Vehicles with Unlicensed User-Mobility and Licensed User-Activity,” Comput. Netw. 137(4), 98–106 (2018). [CrossRef]  

12. G. Bansal, J. B. Kenney, and C. E. Rohrs, “LIMERIC: A Linear Adaptive Message Rate Algorithm for DSRC Congestion Control,” IEEE T. Veh. Technol 62(9), 4182–4197 (2013). [CrossRef]  

13. S. Pandit and G. Singh, “Backoff Algorithm in Cognitive Radio MAC Protocol for Throughput Enhancement,” IEEE T. Veh. Technol. 64(5), 1991–2000 (2015). [CrossRef]  

14. C. Li, J. H. Li, Z. Y. Xu, and J. Y. Wang, “Study on the k-Connectivity of UV Communication Network Under the Node Distribution of RWP Mobility Model in the Arbitrary Polygon Area,” IEEE Photonics J. 12(4), 1–12 (2020). [CrossRef]  

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (15)
Fig. 1.
Fig. 1. Access logic diagram of the UV nodes.

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Fig. 2.
Fig. 2. Algorithm timing diagram.

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Fig. 3.
Fig. 3. Workflow of the eUVLLC-MAC protocol.

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Fig. 4.
Fig. 4. State transition diagram of the Markov chain.

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Fig. 5.
Fig. 5. UV Non-line-of-sight communication model.

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Fig. 6.
Fig. 6. UV network topology diagrams.

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Fig. 7.
Fig. 7. Throughput versus data generation probability.

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Fig. 8.
Fig. 8. Delay versus data generation probability.

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Fig. 9.
Fig. 9. Throughput versus data generation probability.

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Fig. 10.
Fig. 10. Delay versus data generation probability.

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Fig. 11.
Fig. 11. Throughput versus data generation probability.

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Fig. 12.
Fig. 12. Delay versus data generation probability.

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Fig. 13.
Fig. 13. Throughput versus data generation probability for the three MAC protocols.

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Fig. 14.
Fig. 14. Packet loss rate versus data generation probability for the three MAC protocols.

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Fig. 15.
Fig. 15. Delay versus data generation probability for the three MAC protocols.

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Tables (2)

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Table 1. UV propagation parameters

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Table 2. Simulation parameters

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Equations (25)

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P ( n = k ) = λ k e − λ k ! , k = 0 , 1 , 2 , ⋯ .
P { p ′ , q ′ | p , q } = P { x ( t + 1 ) = p ′ , y ( t + 1 ) = q ′ | x ( t ) = p , y ( t ) = q } .
η = 1 − ( 1 − τ ) n − 1 .
η = ∑ k = 1 ∞ λ k e − λ k ! [ 1 − ( 1 − τ ) k − 1 ] = 1 − e − λ − e − λ τ 1 − τ + λ e − λ .
{ P { p , q | p , q + 1 } = 1 p ∈ [ 0 , a ] , q ∈ [ 0 , B W p − 2 ] P { 0 , q | 0 , 0 } = 1 − η B W 0 p = 0 , q ∈ [ 0 , B W 0 − 1 ] P { p , q | p , 0 } = ( 1 − η ) ( 1 − α p r i ) B W i p ∈ [ 1 , a − 1 ] , q ∈ [ 0 , B W p − 1 ] P { a , q | a , 0 } = ( 1 − η ) ( 1 − α p r i ) + η B W a p = a , q ∈ [ 0 , B W a − 1 ] P { p , q | p − 1 , 0 } = η B W p p ∈ [ 1 , a ] , q ∈ [ 0 , B W p − 1 ] P { 0 , q | p , 0 } = ( 1 − η ) α p r i B W 0 p ∈ [ 1 , a ] , q ∈ [ 0 , B W 0 − 1 ] .
{ s 0 , 0 ( p r i ) = s 0 , 0 ( p r i ) ⋅ ( 1 − η ) + ∑ p = 1 a s p , 0 ( p r i ) ⋅ ( 1 − η ) α p r i p = 0 s p , 0 ( p r i ) = s p , 0 ( p r i ) ⋅ ( 1 − η ) ( 1 − α p r i ) + s p − 1 , 0 ( p r i ) ⋅ η p ∈ [ 1 , a − 1 ] s a , 0 ( p r i ) = s a , 0 ( p r i ) ⋅ [ η + ( 1 − η ) ( 1 − α p r i ) ] + s a − 1 , 0 ( p r i ) ⋅ η p = a .
{ s p , 0 ( p r i ) = η η + ( 1 − η ) α p r i s p − 1 , 0 ( p r i ) = [ η η + ( 1 − η ) α p r i ] p s 0 , 0 ( p r i ) p ∈ [ 1 , a − 1 ] s a , 0 ( p r i ) = η ( 1 − η ) α p r i s a − 1 , 0 ( p r i ) = η ( 1 − η ) α p r i ⋅ [ η η + ( 1 − η ) α p r i ] a − 1 s 0 , 0 ( p r i ) p = a .
{ s p , 0 ( p r i ) = U η p ⋯ 0 , 0 ( p r i ) p ∈ [ 1 , a − 1 ] s a , 0 ( p r i ) = η ⋅ U η a − 1 ( 1 − η ) α p r i s 0 , 0 ( p r i ) p = a .
s p , q ( p r i ) = B W p − q B W p ⋅ { ∑ n = 1 a s n , 0 ( p r i ) ⋅ ( 1 − η ) α p r i + s 0 , 0 ( p r i ) ⋅ ( 1 − η ) p = 0 s p − 1 , 0 ( p r i ) ⋅ η + s p , 0 ( p r i ) ⋅ ( 1 − η ) ( 1 − α p r i ) p ∈ [ 1 , a − 1 ] s a − 1 , 0 ( p r i ) ⋅ η + s a , 0 ( p r i ) ⋅ [ ( 1 − η ) ( 1 − α p r i ) + η ] p = a .
s p , q ( p r i ) = B W p − q B W p ⋯ p , 0 ( p r i ) p ∈ [ 0 , a ] , q ∈ [ 0 , B W p − 1 ] .
∑ p = 0 a ∑ q = 0 B W p − 1 s p , q ( p r i ) = 1.
∑ p = 0 a ∑ q = 0 B W p − 1 s p , q ( p r i ) = ∑ p = 0 a s p , 0 ( p r i ) ∑ q = 0 B W p − 1 B W p − q B W p = 1 2 ∑ p = 0 a s p , 0 ( p r i ) ( 1 + B W p ) = 1.
s 0 , 0 ( p r i ) = 2 ∑ p = 0 a − 1 U η P ( 1 + B W P ) + η ⋅ U η a − 1 ( 1 − η ) α p r i ( 1 + B W a ) .
τ ( p r i ) = ∑ p = 0 a s p , 0 ( p r i )  =  s 0 , 0 ( p r i )  +  ∑ p = 1 a − 1 [ η η + ( 1 − η ) α p r i ] p s 0 , 0 ( p r i )  +  η ( 1 − η ) α p r i ⋅ [ η η + ( 1 − η ) α p r i ] a − 1 s 0 , 0 ( p r i ) . = s 0 , 0 ( p r i ) 1 − U η
τ = ∑ p r i = 1 P R I β p r i ∑ p = 0 a s p , 0 ( p r i ) = ∑ p r i = 1 P R I β p r i ⋯ 0 , 0 ( p r i ) 1 − U η .
S = E ( the payload transmitted in a timeslot ) E ( a timeslot length ) = P s P t r E ( P ) ( 1 − P t r ) σ + P s P t r T s + ( 1 − P s ) P t r T c ,
P t r = ∑ k = 1 ∞ λ k e − λ k ! [ 1 − ( 1 − τ ) k ] = 1 − e − λ − e − λ τ + λ e − λ ( 1 − τ ) .
D e l p r i = E p r i E t ,
E t = ( 1 − P t r ) σ + P s P t r T s + ( 1 − P s ) P t r T c .
E p r i = ∑ p = 0 a H P b p r i , p ,
H P = ∑ q = 0 p B W q + 1 2 .
B p r i , p = { s 0 , 0 ⋅ B W 0 + 1 2 + ∑ i = 1 a s i , 0 ⋅ B W i + 1 2 ⋅ α p r i p = 0 s p , 0 ⋅ B W p + 1 2 ⋅ ( 1 − α p r i ) p ∈ [ 1 , a ] .
b p r i , p = ∑ i = 0 p B p r i , i ⋅ η p − i ( 1 − η ) p ∈ [ 0 , a − 1 ] .
D e l p r i = E t ⋅ ∑ p = 0 a ∑ q = 0 p B W q + 1 2 ⋅ b p r i , p .
R O O K = − η λ P t h c ξ R b ln ⁡ ( 2 P e ) α ,
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