Performance Analysis for IEEE 802.11S Wireless Mesh Network in Smart Grid

Wireless Pers Commun (2017) 96:1537–1555 DOI 10.1007/s11277-017-4255-7

Performance Analysis for IEEE 802.11s Wireless Mesh Network in Smart Grid

1 1 1 1 Xiaoheng Deng • Tingting He • Lifang He • Jinsong Gui • Qionglin Peng1

Published online: 27 April 2017 Ó Springer Science+Business Media New York 2017

Abstract The bi-directional communication system is an indispensable component in smart grid (SG) for monitoring and exchanging essential information among the electrical devices. IEEE 802.11s based wireless mesh networks recently have been proposed as an important networking technology to deploy in SG for data collection and remote control purposes, as the cost of networking equipments decreases and performance increases. In this paper, we focus on analyzing the MAC layer performance for IEEE 802.11s wireless mesh networks in the smart grid based on Markov model, taking into account the impact of hidden nodes and different QoS requirements of smart grid applications. We ﬁrst develop a new Markov chain model to analyze the back-off process for different applications with hidden nodes problem. Then based on the analytical model, we derive a few MAC layer performance metrics such as MAC layer packet dropping probability, the mean throughput and the mean packet delay which contains the queuing delay. Finally, the proposed analytical model is validated via comparing the analytical results with simulation results by ns- 3 in NAN scenarios with various applications. We observe a good match between the analytical model and simulations which conﬁrms the veracity of our model.

& Xiaoheng Deng [email protected] Tingting He [email protected] Lifang He [email protected] Jinsong Gui [email protected] Qionglin Peng [email protected]

1 School of Information Science and Engineering, Central South University, Changsha 410083, China 123 1538 X. Deng et al.

Keywords Smart grid Á IEEE 802.11s Á EDCA Á Markov chain Á Performance analysis

1 Introduction

Smart grid (SG) is an intelligent power network that combines various technologies in power, communication and control [1, 2]. In SG, establishing reliable and real-time bi- directional communication system is vital for it to work efficiently. Through bi-directional communication system, customers can optimize their electricity consumption for mini- mizing utility costs. Furthermore, the control centers can make real-time power pricing and many other decisions according to energy demands to improve the resource utilization [3, 4]. According to [5], the smart grid communication infrastructure consists of three different networks, home area network (HAN), neighborhood area network (NAN) and wide area network (WAN). A HAN focuses on small-scale data communication between devices inside typical households. A NAN is defined to provide a backbone for data that are transmitted from multiple HANs as well as providing various services of its own. A WAN connects grid control centers and NAN data aggregates in large areas, and transmits data in very high-speed. Data aggregation is also one of the most important tasks in some distributed applications [6–8]. NANs directly connect all the end users in regional areas, forming an important component in power grid that affects the efficiency of the whole grid [9]. NAN collects the electricity utility data from multiple HANs and forwards it to backbone through NAN gateways. Meanwhile, it delivers control and pricing messages in the reverse direction. Some data are transmitted in a periodic manner such as periodic metering and periodic power quality data. Some other data must be transmitted in a timely manner with stringent QoS requirements, e.g., reduction of load in response to emergency initiated by the consumer is usually referred to as demand response(DR). Demand response is a change in the power consumption of an electric utility customer to better match the demand for power with the supply. It has been proven to play an important role in providing users with more personalized and intelligent information services [10]. These varieties of traffic characteristics make implementation of communication networks for smart grid NANs is a challenging issue. Recently, wireless mesh networks (WMN) technologies based on IEEE 802.11s [11, 12] standards have been proposed as a potential networking technology to be employed in the smart grid NAN, considering the cost- effective deployment, easy network maintenance and reliable service coverage. Besides, owing to the importance of supporting multimedia services in WMNs, IEEE 802.11s adopts the enhanced distributed channel access (EDCA) protocol [13] defined in IEEE 802.11e to provide medium access control (MAC) and QoS supports for WMNs, which is a representative requirement in NANs. As a QoS extension to the original IEEE 802.11 distributed coordination function (DCF) [14], EDCA defines four access categories (ACs) to provide differentiated service, cor- responding to voice (AC_VO), video (AC_VI), best effort (AC_BE) and background (AC_BK) respectively from high to low. Each AC has its own transmission queue and a set of channel access parameters to contend for transmission opportunities, including mini- mum contention window (CWmim), maximum contention window (CWmax) and Arbitrary Inter-Frame Space (AIFS). If an AC has a smaller AIFS, CWmin and CWmax, traffic in this

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AC has a better chance to access the channel earlier than those of lower service classes, and thus bring on better QoS performance. By this means, EDCA can differentiate various NAN applications. While, from [15], we realize that when the transmitter-receiver distance is larger than 0.56 times the transmission range, the hidden terminal problems will affect the RTS/CTS handshake function of EDCA in multi-hop WMNs which has a potential effect on the MAC layer performance differentiation. An EDCA based adaptive priority adjustment scheme which proposed in [16].Therefore, in this paper, taking into account the impact of hidden nodes, we focus on modeling and analyzing MAC layer performance of EDCA for supporting differentiated QoS requirements NAN applications, to determine whether IEEE 802.11s wireless mesh networks can meet the smart grid communication requirements well. Our contribution can be summarized as follows. Firstly, we present a new Markov chain model and analyze the back-off process for different applications with hidden nodes problem. Secondly, based on the back-off process analysis, we analyze a few MAC layer performance metrics of 802.11s smart grid wireless networks, such as the MAC layer packet discard probability, the mean throughput and the mean packet delay which contains queuing delay. Thirdly, we validate the analytical model via comparing the analytical results with simulation results by ns-3 in NAN scenarios with various applications. The remainder of this paper is organized as follows. Section 2 discusses the related work. In Sect. 3, we present our model for IEEE 802.11s smart grid wireless networks and analyze the back-off process for different smart grid applications with hidden node problem. Then, a few MAC layer performance metrics are derived in Sect. 4. Validations of analytical model are carried out in Sect. 5. Finally, Sect. 6 concludes this paper.

2 Related Work

Recently, there have been a number of studies on improving reliability and providing high QoS services in the IEEE802.11s wireless mesh NAN. A tree-based mesh routing scheme based on multi-gateway mesh network architecture was presented in [17]. The multi-gateway mesh routing scheme is based on a ﬂexible mesh network architecture that expands on the hybrid tree routing of the IEEE 802.11s. we proposed a distributed routing protocol EPTR, to maximize the network throughput and improve the link quality [18]. A simulation based study was described in [19] enhancing the wireless mesh network performance in the smart grid. In addition, the main issues about reliability of IEEE 802.11s in SG communication network were analyzed by Kim et al. [20, 21], and they were improved by modifying routing metric, routing mechanisms and routing maintenance mechanism in HWMP. We also presented a NAN QoS-aware routing scheme, called HWMP-NQ, for optimizing HWMP protocol to meet the QoS requirements and improve the reliability for smart grid in our previous studies [22]. But none of these works studied the MAC layer performance, such as the mean packet delay and packet dropping probability for smart grid NAN. Bianchi [23] has proposed a two-dimensional Markov chain model to analyze the saturation throughput performance of WLAN for the ﬁrst time. Then, a considerable number of works have extended the Bianchi’s Markov model to analyze the service differentiation performance of 802.11e EDCA. In order to analyze the saturation performance of EDCA, Huang and Liao modeled the behavior of the back-off entity of each AC as a two-dimensional Markov chain [24]. Based on the model of Xiao [25], Engelstad et al. [26]

123 1540 X. Deng et al. have presented a three-dimensional Markov chain model for the behavior of a back-off entity in priority i class, and the z-transform of delay was derived. Then, the mean medium access delay was obtained by calculating the ﬁrst-order moment of the z-transform. Zhu and Chlamtac [27] also have introduced a three dimensional Markov model to calculate the throughput and delay performance of EDCA under different contention parameter conditions. Although simulation and analytical results have validated the effectiveness of these models, these research works which focused on the analysis for single-hop WLANs cannot be directly applied to multi-hop wireless mesh networks due to the hidden nodes problem. The existence of multi-hop wireless networks allow for more transmission opportunities and Flexibilities [28, 29]. Therefore, Lei and Zhou et al. [30] focus on modeling and analyzing the medium access delay differentiation of EDCA under saturation condition in multi-hop WMNs. In this model, the authors fully considered the performance impact of request to send (RTS) frame collisions and data frame collisions and then put forward the pseudo states to distinguish the different back-off procedures induced by these collisions. But the characteristics of smart grid applications have not been considered in above approaches. Furthermore, in [31], Xu and Wang modeled the SG networks and presented the communication delay analysis in typical wireless mesh network deployment scenarios of SG with Voronoi diagram, which provides the delay bounds that can help design satisfactory wireless networks to meet the demanding communication requirements in the smart grid. However, their models were based on DCF rather than EDCA. Hence, taking into account the different QoS requirements of smart grid applications and the impact of hidden nodes, we ﬁrst develop a new Markov chain model to analyze the back-off process for different NAN applications with hidden nodes problem which extends the analytical work in [25]. Then based on the analytical model, we derive a few MAC layer performance metrics such as MAC layer packet dropping probability, the mean throughput and the mean packet delay which contains the queuing delay.

3 Model Analysis of IEEE 802.11s Wireless Mesh in Smart Grid

In this section, we first propose and analyze a new Markov chain for EDCA in IEEE 802.11s smart grid mesh network. Then, by considering the impact of hidden terminal problem, a new model is proposed to analyze the back-off process for different NAN applications. We first make the following assumptions: (1) Each traffic instance (back-off instance) is treated as independent; (2) At each traffic instance, packet arrivals are Poisson process with rate ki (packets/s).

3.1 Markov Chain Model Analysis

We assume that each station carries four AC ﬂows. As the Markov chain for EDCA shown in Fig. 1, for a given node with priority i ði ¼ 0; 1; 2; 3Þ class, its states can be described as i, j, k. The j in the model stands for the back off stage taking values from (0; 1; ...; LretryðiÞ) where LretryðiÞ is the retry limit and is equal to 4 or 7 according to the standard, and k is the j back-off counter taking values from (0; 1; CWi;j À 1) where CWi;j ¼ 2 CWi;0 and CWi;0 ¼ CWmin½i. The idle state represents the buffer of i class is empty. Let pi denotes the probability that a transmitted frame collides of priority i and pbi denotes the probability that a back-off instance of priority i sensing the channel busy and is thus unable to count down

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Fig. 1 Markov model for the priority i in EDCA the back off slot from one to the other. qi for the probability that the buffer is empty of priority i and pa for the probability that there is at least one frame arriving during the unit slot time. Therefore, the transition probabilities of the Markov model in Fig. 1 can be derived as follows

P½¼ði; j; kÞjði; j; k þ 1Þ 1 À pbi; for 0\k\CWi;j À 2; 0\j\LretryðiÞ

P½¼ði; j; kÞjði; j; kÞ pbi; for 0\k\CWi;j À 1; 0\j\LretryðiÞ pi P½¼ði; j; kÞjði; j À 1; 0Þ ; for 0\k\CWi;j À 1; 0\j\LretryðiÞ CWi;j ÂÃ 1 À qi P ði; 0; kÞjði; LretryðiÞ; 0Þ ¼ ; for 0\k\CWi;0 À 1 CWi;0

ð1 À piÞð1 À qiÞ P½¼ði; 0; kÞjði; j; 0Þ ; for 0\k\CWi;0 À 1; 0\j\LretryðiÞ CWi;0 pa P½¼ði; 0; kÞjidle ; for 0\k\CWi;0 À 1 Wi;0 P½¼ð idlejði; j; 0Þ 1 À p Þq ; for 0\j\L ÂÃi i retryðiÞ P idlejði; LretryðiÞ; 0Þ ¼ qi

P½¼ idlejidle 1 À pa

Let bi;j;k ¼ lim Pði; j; kÞ be the stationary distribution of the Markov chain that denotes t!/ the probability of packet with priority i where the collision encountered for jth and the back-off counter is equal to k state. Then we have

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LretryXðiÞÀ1 CW À k 1 b ¼ i;j ½ð1 À p Þð1 À q Þ b þð1 À q Þb þ p b ; i;j;k CW p i i i;j;0 i i;LretryðiÞ;0 a idle i;j bi j¼0 ð1Þ

for 0\j\LretryðiÞ; 1\k\CWi;j À 1 and the steady-state probability of the idle state can be expressed as "# LretryXðiÞÀ1

bidle ¼ qi ð1 À piÞ bi;j;0 þ bi;LretryðiÞ;0 þð1 À paÞbidle ð2Þ j¼0

j Since one can easily obtain bi;j;0 ¼ pibi;0;0, the probabilities bi;j;k and bidle can be written as

CWi;j À k 1 j bi;j;k ¼ pibi;0;0; for 0\j\LretryðiÞ; 1\k\CWi;j À 1 ð3Þ CWi;j pbi

qi bidle ¼ bi;0;0 ð4Þ pa From the fact that the sum of the steady-state probabilities of all states must be equal to 1, we can write

LXretryðiÞ CWXi;jÀ1 bi;j;k þ bidle ¼ 1 ð5Þ j¼0 k¼0

We can obtain an expression for bi;0;0 written as

L þ1 1 CW ð1 Àð2p ÞLretryðiÞþ1Þð1 À p Þ ð1 À p retryðiÞ Þð1 À p Þ ¼ i;0 i i À i i bi;0;0 2ð1 À 2piÞð1 À piÞð1 À pbiÞ 2ð1 À 2piÞð1 À piÞð1 À pbiÞ ð6Þ L þ1 2ð1 À p retryðiÞ Þð1 À 2p Þð1 À p Þ q þ i i bi þ i 2ð1 À 2piÞð1 À piÞð1 À pbiÞ pa

Note that if the system is in the saturation condition, qi ¼ 0, pa ¼ 1 and pbi ¼ pi.Ifqi 6¼ 0, pa ¼ 1 and pbi ¼ 0, them the system is in the non-saturation condition. Hence, the expression provides a uniﬁed model encompassing all channel loads from a lightly loaded non-saturated channel, to a highly congested, saturated medium.

3.2 The Back-Off Process for Different Applications with Hidden Nodes Problem

In the 802.11e EDCA, an active node randomly selects a value from its contention window to back off at the beginning of each time slot, each collision causes a double of the contention window until the maximum is reached. The expected number of back-off slot before transmitting a packet in priority i depends on the contention window length CWi;j and the collision probability pi of that priority, and we can obtain the frame success j probability for priority i class after jth retransmission is pið1 À piÞ. If we sum the expected number of slot for all steady probabilities, we obtain the average expected number of slot Ti to transmit a frame in priority i successfully as follows

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LretryXðiÞÀ1 CW L CWi;L T ¼ pjð1 À p Þ i;j þ p retryðiÞ retryðiÞ ; CW ¼ 2jCW ; 0 j L ð7Þ i i i 2 i 2 i;j i;0 retryðiÞ j¼0 From (8), we have

LretryðiÞ 1 À pið2piÞ CWi;0 Ti ¼ ð8Þ 1 À 2pi 2

We assume that niði ¼ 0; 1; 2; 3Þ is the number of stations with priority i in the carrier sense range. In IEEE 802.11e EDCA, node A’s back-off timer is suspended when another active priority node B is transmitting. If we observe on the A’s time line, B’s transmission only occupies one slot of A. Since the back-off process of A and B are independent of each other, node A may collide with B anytime in back-off slot times and the collision probability is 1 (B is same priority as A) or 1 (B is not same priority as A). Therefore, the Ti Tl probability that A collide with any of other nodes can be approximated as 1 niÀ1 Y3 1 nl pi ¼ 1 À 1 À 1 À ð9Þ T T i l¼0;l6¼i l From (9), we can get the collision probability of priority i under the non-saturation condition. Since qni is the probability that the buffer is not empty of priority i and qni ¼ 1 À qi, the probability that a priority i traffic attempts a transmission in an arbitrary slot is given by qni. Considering the fact that only busy priority traffic can actually collide with packets Ti from other busy priority traffics, so the collision probability is given by niÀ1 Y3 nl qni qnl pi ¼ 1 À 1 À 1 À ð10Þ T T i l¼0;l6¼i l

In multi-hop WMNs, the MAC layer performance of different priority trafﬁcs is not only inﬂuenced by the nodes in the carrier sense range, but also depredated by the hidden terminal considerably. The interference model with hidden terminals is shown as Fig. 2, where d, rtx, rco and rcs in model represent the distance between the transmitter and the receiver, the transmission range, the collision range and the carrier sense range

Fig. 2 The interference model 123 1544 X. Deng et al. respectively. We can see from Fig. 2, node C is hidden node and can’t hear node A’s transmission. If C transmits while A is transmitting, the node B’s receiving from A will be collided. The collision probability of a data frame is far less than that of the RTS frame in the RTS/CTS mechanism. For simplicity, we study the collision happens only during RTS packets. In order for the packets send by A to be successfully transmit to B, C must defer its transmission a period Di, where Di ¼ 2ðTRTS þ SIFSÞ , TRTS is the transmission delay of RTS frame, and SIFS is the short inter-frame space. In the multi-hop WMNs, the trans- missions from A and C will cause a collision at B in any slot in the range of sh, where sh is given by D ðT þ SIFSÞ s ¼ i ¼ 2 RTS ð11Þ h SlotTime SlotTime

We let nhiði ¼ 0; 1; 2; 3Þ denote the number of active nodes with priority i in the hidden zone. Therefore, the collision probability that a station in i priority colliding with hidden node problem can be calculated as niÀ1 Y3 nl Y3 nhk qni qnl qnksh pi ¼ 1 À 1 À 1 À 1 À ð12Þ T T T i l¼0;l6¼i l k¼0 k

Let pb denotes the probability that the channel busy. Since this means that at least one back off instance transmits during a slot time, we have Y3 q ni Y3 q s nhk p ¼ 1 À 1 À ni 1 À nk h ð13Þ b T T i¼0 i k¼0 k

Then, the pbi can be calculated as

1 À pb pbi ¼ 1 À ð14Þ 1 À qnisi

Let si be the probability that a station in priority i class transmits during a generic slot time. It is calculated by summing the steady state probabilities of states where the back-off counter is equal to 0

LXretryðiÞ LXretryðiÞ LretryðiÞþ1 1 À p s ¼ b ¼ pjb ¼ b i ð15Þ i i;j;0 i i;0;0 i;0;0 1 p j¼0 j¼0 À i

4 MAC Layer Performance Analysis for Different Applications

Based on the model and the back-off process analyzed in Sect. 3, this section focuses on the MAC layer performance analysis of smart grid based on IEEE 802.11s wireless mesh network, such as the MAC layer packet dropping probability, the mean throughput and the mean packet delay containing queuing delay.

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4.1 Throughput Analysis

In the standard EDCA, when there is no transmission on the channel, the time interval between two consecutive back-off time counter decrements is an idle time slot d, which is speciﬁed by the PHY in IEEE 802.11. However, when the channel is sensed busy, the back-off time counter decrement is suspended and thus the time interval between two consecutive back-off time counter decrements may be much larger than a time slot. We let di be the time interval between two consecutive back-off time counter decrements of priority i nodes. The time slot di consists of an idle time slot d and a busy period. The busy period includes: (1) the average time that an RTS frame transmission failed Tc;RTS, (2) the average time that a data frame transmission succeeded Ts;data. Let TMAC and TPHY denote the times required for transmission of MAC header and PHY header, a denotes the propagation delay, Tdata, Tack, TRTS and TCTS denote the transmission delay of SG data packet, the transmission delay of ACK packet, the transmission delay of RTS frame and CTS frame respectively. Then, the Tc;RTS and the Ts;data can be calculated as

Tc;RTS ¼ TRTS þ CTSTimeout ¼ AIFS þ TRTS þ SIFS þ Tack þ 2a ð16Þ

Ts;data ¼ TRTS þ TCTS þ TMAC þ TPHY þ Tdata þ 3SIFS þ Tack þ AIFS þ 4a ð17Þ

We let pt1 denotes the probability that at least one transmission occurs in a given slot time for the range of carrier sense, and pt2 denotes the probability that at least one transmission occurs in any given slot time of sh in the hidden zone. Then we can get the pt1 and pt2 as

Y3 ni pt1 ¼ 1 À ð1 À siÞ ; ð18Þ i¼0

Y3 nhi pt2 ¼ 1 À ð1 À shsiÞ ð19Þ i¼0 Therefore, the probability that a station in i priority is successful transmitting a packet in a slot time in the carrier sense range is given by

Y3 niÀ1 nl ps1ðiÞ ¼ nisið1 À siÞ ð1 À slÞ ð20Þ l¼0;l6¼i

We let ps1 and pc1 represent the probability that a successful transmission occurs in a slot time and the probability that a collision occurs in a slot time in the carrier sense range. We have

X3 ps1 ¼ ps1ðiÞ ð21Þ i¼0

pc1 ¼ pt1 À ps1 ð22Þ

Using the similar analysis as above, we can obtain the probability ps2ðiÞ that a successful transmission occurs in at least sh slots for priority i, the probability ps2 that a successful transmission occurs in at least sh slots and the probability pc2 that a collision occurs in at least sh slots in the hidden zone respectively, as follows

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Y3 nhiÀ1 nhl ps2ðiÞ ¼ nhisið1 À shsiÞ ð1 À shslÞ ð23Þ l¼0;l6¼i

X3 ps2 ¼ ps2ðiÞ ð24Þ i¼0

pc2 ¼ pt2 À ps2 ð25Þ

And we can get the probability ps that a packet from any class is transmitted successfully in a time slot

ps ¼ ps1ps2 ð26Þ We let di be the mean delay (mean slot time) between two consecutive back-off time counter decrements of priority i nodes, that is the sum of the average channel idle time and the average channel busy time. The average channel busy time consists of the busy time in the carrier sense range only, the busy time in the hidden zone only and the busy time in the carrier sense range and hidden zone at the same time. 1. The average channel idle time:

Tidle ¼ð1 À pt1Þð1 À pt2Þd ð27Þ 2. The busy time in carrier sense range:

Tb1 ¼ð1 À pt2Þpt1½ps1Ts;data þ pc1Tc;RTSð28Þ 3. The busy time in the hidden zone: Ts;data þ AIFS À SIFS À TRTS À a Tb2 ¼ð1 À pt1Þpt2 ps2 þ pc2d ð29Þ sh 4. The channel busy time in carrier sense range and hidden zone at the same time:

Tb3 ¼ pt1pt2d ð30Þ

Hence, we can derive di ¼ Tidle þ Tb1 þ Tb2 þ Tb3 ¼ð1 À p Þð1 À p Þd þð1 À p Þp ½p T þ p T t1 t2 t2 t1 s1 s;data c1 c;RTS ð31Þ Ts;data þ AIFS À SIFS À TRTS À a þð1 À pt1Þpt2½ps2 þ pc2dþpt1pt2d sh Finally, we can calculate the average throughput of priority i smart grid trafﬁcs as

ps1ðiÞps2ðiÞTdata Si ¼ ð32Þ di

4.2 MAC Layer Delay Analysis

We let Di be the MAC layer end-to-end delay for the smart grid trafﬁcs with priority i, and it can be calculated as 123 Performance Analysis for IEEE 802.11s Wireless Mesh Network... 1547

Di ¼ DsðiÞ þ DqðiÞ ð33Þ where DsðiÞ is the average MAC layer service time and DqðiÞ is the queuing delay before trying to access the channel. DsðiÞ contains the back-off time DbackðiÞ spending by the packet to access the channel and the transmission delay DtransðiÞ for the packets, so we have

DsðiÞ ¼ DbackðiÞ þ DtransðiÞ ð34Þ

According to (8), we can get the average expected number of slot Ti that transmitting a frame in priority i successfully. Therefore, the back off time DbackðiÞ can be derived as DbackðiÞ ¼ diTi ð35Þ

Transmission attempt will be LretryðiÞ before dropping a packet with priority i. Then we can LretryðiÞ determine the probability of a packet being successfully transmitted as 1 À pi . Hence, the transmission delay of packets in priority i can be computed as

LretryðiÞ DtransðiÞ ¼ Ts;datað1 À pi Þ ð36Þ In the EDCA protocol, the queuing system can be modeled as M / G /1/K model, where K is the maximum queue level of queue. The arrivals of packets in priority i follow a Poisson process with rate ki. From the MAC layer service time we analyzed before, the service rate follows an exponential distribution with rate l ¼ 1 , and the trafﬁc service i DsðiÞ ki intensity q ¼ ¼ kiDsðiÞ. denote by pnðiÞ the probability to have nðn KÞ packets in the li queue in priority i, and thus 1 À q p ¼ qn ð37Þ nðiÞ 1 À qK

Then we can obtain the qi for the probability that the buffer is empty of priority i and the pa for the probability that there is at least one frame arriving during the unit slot time 1 À q q ¼ p ¼ ðq 6¼ 1Þ ð38Þ i 0ðiÞ 1 À qK

ÀkiTs;data ÀkiSlotTime ÀkiTc;RTS pa ¼ 1 Àðpse þð1 À pbÞe þðpb À psÞe Þ ð39Þ and we can calculate the mean number of packets in the queue in priority i as

XK Qi ¼ npnðiÞ ð40Þ n¼0 Therefore the queuing delay that the time for the packet staying in the buffer is given by

Q q 1 ÀðK þ 1ÞqK þ KqKþ1 1 i 41 DqðiÞ ¼ ¼ K ð Þ ki 1 À q 1 À q ki Finally, we can get the MAC layer delay for the trafﬁcs with priority i class as

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Di ¼ DbackðiÞ þ DtransðiÞ þ DqðiÞ 1 p p 2p LretryðiÞ CW À i À ið iÞ i;0 LretryðiÞ ¼ di þ Ts;datað1 À pi Þ 1 À 2pi 2 ð42Þ q 1 ÀðK þ 1ÞqK þ KqKþ1 1 þ K 1 À q 1 À q ki

5 Model Validation and Analysis

Since the ns3 platform includes the IEEE 802.11s model which realized the EDCA mechanism in the MAC layer, we validate our model via comparing the analytical results with the simulation results by ns3-19 [32].

5.1 Simulation Environment

NAN applications are configured and differentiated according to [33] and SG Network System Requirements Specification v4.1-draft3 [34]. Requested AMI data and requested power quality data require a high reliability to stabilize the whole SG so the priorities are set to 3. While the lowest priority is set to video surveillance data since they are not as important in SG compared with other data even with a strict delay requirement, and detail parameters are shown in Table 1. The requested AMI data and requested power quality data are transported using the TCP protocol, and other applications are transported using the UDP. In simulation scenarios, nodes are laid out on the network in a grid topology with node sizes distributed from 9 to 64. The distance between each mesh STA is 200 m, and the interference range is 1:78 Â 200 m ¼ 356 m. We also add an extra mesh node into network as a gateway outside interferences to gather the traffic of the rest mesh nodes. Each mesh STA is equipped with one 802.11a transmission device with a maximum transmission rate of 54Mb/s. We let the number of transmitters in different priority equal and the packet arrive to any queue with the same rate k (packets/s). The carrier sense range is set up to 550 and 440 m to simulate different scenarios with hidden terminals and without hidden terminals respectively. We can calculate the number of hidden nodes nhi ¼ 0 ði ¼ 0; 1; 2; 3Þ when the carrier sense range is 550 m and nhi ¼ 2 when the carrier sense range is 440 m, according to the mesh topology and the distance between mesh nodes. The main simulation

Table 1 Smart grid applications setting Type of service Transmission interval Application size Priority (AC) Requirement latency

Periodic AMI 15 s 123 bytes 1 \15 s AMI management 300 s 4000 bytes 2 \1s Periodic power quality 3 s 3000 bytes 1 \3s Power management 300 s 4000 bytes 2 \1s Requested AMI On-demand 123 bytes 3 \5s Requested power quality On-demand 2000 bytes 3 \5s Video surveillance Constant 250 kB/s 0 \100 ms

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Table 2 Main simulation Parameter Value parameters Simulation time 500 s PHY Standards IEEE 802.11a k 8 (packets/s) K 255 (packets) Transmission range 250 m Length of PHY header 24 bytes Length of MAC header 28 bytes Size of ACK/CTS 14 bytes Size of RTS 20 bytes SIFS 16 lm SlotTime 9 lm a 1 lm

CWmin 15

CWmax 1024

Fig. 3 Average throughput against network size of four AC applications with and without hidden node. a Average throughput of AC3. b Average throughput of AC2. c Average throughput of AC1. d Average throughput of AC0

123 1550 X. Deng et al. parameters are shown in Table 2. For each simulation scenario, we repeat simulation for 10 runs with different random seeds and take the average.

5.2 Simulation Results and Performance Analysis

The MAC layer performance comparisons for all applications with and without hidden nodes are shown in Figs. 3, 4, and 5 by varying the network size. Figure 3 shows the comparisons of average throughput comparisons between the analytical results and simulation results for all applications with and without hidden nodes respectively. From Fig. 3, we note that the agreement between the analytical results and the simulation results is excellent for all applications whether at the presence of hidden terminals or not. With the increment of number nodes, the more the data will be generated and this also leads to an increase in the throughput. But once the network comes into saturated state, the throughput decreases because of insufficient resources. And we can see from the Fig. 3a, b, EDCA can provide stringent QoS assurance for requested and management traffics in non-saturation state. Since the periodic traffic generated every 15s and 3s, the throughput is greater than other three kinds of traffic considerably as shown in Fig. 3c. In the case of hidden nodes, the average throughput of all applications saturated earlier for the increment of collision probability, and declined following with the increase of number of nodes in the saturation state. Comparing with other applications, the throughput of video surveillance data

Fig. 4 Average MAC delay against network size of four AC applications with and without hidden node. a Average MAC delay of AC3. b Average MAC delay of AC2. c Average MAC delay of AC1. d Average MAC delay of AC0 123 Performance Analysis for IEEE 802.11s Wireless Mesh Network... 1551

Fig. 5 Average packet dropping ratio against network size of four AC applications with and without hidden node. a Average packet dropping ratio of AC3. b Average packet dropping ratio of AC2. c Average packet dropping ratio of AC1. d Average packet dropping ratio of AC0 increased slowly and saturated when the number of nodes is 36 whether with hidden terminals to guarantee the QoS of high priority applications in saturated state. The results of MAC layer delay comparisons between the analytical and simulation results for all applications are shown in Fig. 4. With the increase of the network size, the average MAC layer delay for all ﬂows increases with and without hidden nodes. The reason is that as the network size increases, the collision probability increases, and thus leads to retransmit and suffer from long queuing delay and service time for the packets which causes the increment of MAC layer delay. Besides, results indicated that the simulation results meet quite well with analytical results, which validates the accuracy of our model. Figure 5 shows the average packet dropping ratio comparisons of four applications with and without hidden nodes. Results showed that the EDCA access mechanism in IEEE 802.11s can provide prioritized QoS for different smart grid applications, and it also provides good QoS assurance for requested(AC3) and management applications(AC2). Whereas the packet dropping ratio increases signiﬁcantly with the increase in node numbers for all applications, especially with the hidden node problem. This is due to the fact that in the saturated state, each node always has packets to transmit and keeps con- tending for the channel, which greatly increases the collision probability. Besides, the packet dropping ratio of video surveillance data is highest, e.g., in the case of hidden terminal, it is even close to 70% when the network is severely congested because of 123 1552 X. Deng et al. dropping the video surveillance data while retaining higher priority data for more reliable transmission.

6 Conclusion

In this paper, we analyzed a few MAC layer performances of IEEE 802.11s wireless mesh networks based smart grid by developing a new Markov model, fully taking into account the impact of hidden nodes and different QoS requirements of smart grid applications. Firstly, we analyzed the back-off process for different applications with hidden node problem. Then derived a few MAC layer performance metrics such as MAC layer packet dropping probability, the average throughput and the average packet delay which contains the queuing delay. To validate our model and analysis, we ﬁnally evaluated the analysis by ns-3 in NAN scenarios with various applications. The simulation results matched well with the analytical results. To mitigate the impact of hidden terminal problem and to improve the performance of EDCA in 802.11s smart grid wireless mesh networks will be studied in the near future.

Acknowledgements The authors acknowledge the support of National Natural Science Foundation of China projects of Grant No. 61379058. The author Xiaoheng Deng also acknowledge the support Science and Technology Program of Hunan Province (Talent and platform) project of Grant No. 205TP2017. The research is supported in part by the Fundamental Research Funds for the Central Universities of Central South University under Grant No. 2017zzts480.

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Xiaoheng Deng received the Ph.D. degrees in computer science Central South University,Changsha, Hunan, P.R. China, in 2005. Since 2006, he has been an Associate Professor and then a Full Professor with the Department of Electrical and Communication Engineering, Central South University. He is a senior member of CCF, a member of CCF Pervasive Computing Council, a member of IEEE and ACM. He has been a chair of CCF YOCSEF CHANGSHA from 2009 to 2010. His research interests include wireless communications and networking, congestion control for wired/wireless network, cross layer route design for wireless mesh network and ad hoc network, online social network analysis.

Tingting He is a M.Sc. student in School of Information Science and Engineering of Central South University, Changsha, China. She received B.Sc. degree in information engineering from Hunan Agri- cultural University, Changsha, China, in 2015. Her major research interests are wireless mesh network, software-deﬁned network and smart grid.

Lifang He is a M.Sc. student in School of Information Science and Engineering of Central South University, Changsha, China. She received B.Sc. degree in electronic and information engineering from Kunming University of Science and Technology, Kunming, China, in 2013. Her major research interests are wireless mesh network and smart grid.

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Jinsong Gui He received the B.E. from the University of Shanghai for Science and Technology, China, in 1992, and the M.S. and Ph.D. from Central South University, China, in 2004 and 2008, respectively. He is currently an Associate Professor in the Department of Computer Sci- ence and Technology, School of Information Science and Engineering, Central South University, and a Member of China Computer Federa- tion (CCF). His research interests cover the general area of distributed systems, as well as related ﬁelds such as wireless network topology control and network security.

Qionglin Peng is currently working toward his master degree in the School of Information Science and Engineering of Central South University, Changsha, China. His research interests are in the area of routing protocol of NAN for the smart grid.

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