research article a real-time and efficient mac protocol...

Research ArticleA Real-Time and Efficient MAC Protocol forSmart Grid Wireless Communications

Qiang Liu,1 Danqi Chen,2 Fangping Gao,2 and Guoli Pang2

1 Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China2Department of Disaster Information Engineering, Institute of Disaster Prevention, Sanhe, Hebei 065201, China

Correspondence should be addressed to Fangping Gao; [email protected]

Received 2 March 2014; Revised 4 June 2014; Accepted 11 June 2014; Published 26 June 2014

Academic Editor: Yung-Fa Huang

Copyright © 2014 Qiang Liu et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Communication and information technologies play crucial roles in the smart grid system. Wireless communications offer manyunique features to utilities. Real-time capability and high efficiency under heavy load are vital capabilities for smart grid wirelesscommunications. However, the existing medium access control (MAC) protocols for low-rate and short-range wireless transferin the literature mainly aim to achieve the objectives of low energy consumption and self-configuration and rarely address theserequirements under heavy traffic intensity. This paper presents a real-time, efficient, and lightweight MAC (RE-MAC) protocolto support smart grid applications, based on priority node polling and a hybrid scheme. The upper bounds of packet delay aredetermined using the embedded Markov chain method, and the simulation results demonstrate that the protocol can achievepredictable, real-time, and efficient performance.

1. Introduction

Over the last few years, the smart grid has gained wideattention for its potential to address the challenges in the tra-ditional power grid, such as increasing load demands, quicklyaging components, domino-effect failures, renewable energysources, and improving grid security [1, 2]. Communicationand information technologies play crucial roles in the smartgrid system. Wireless communications offer many uniquefeatures to utilities [3, 4]. For example, wireless networkscan accommodate condition-monitoring applications due totheir ability to work in extreme environmental conditions.

Wireless technologies can be widely applied to the smartgrid, including power generation, power delivery, and powerutilization [5]. In contrast to wired networks, wireless net-works support flexible addition and removal of devices andreduce installation costs. In addition, wireless nodes can bemounted on mobile devices and high-voltage equipment andcan fulfill monitoring and control tasks [6]. In detailed sce-narios, condition-monitoring of transformers, circuit break-ers, and power lines in substations is a very importanttask, includingmonitoring temperature, voltage, and current.

Wireless networks make monitoring these parameters moreeasy and efficient. However, when domino-effect failuresoccur, a great deal of data emerge, andwireless networksmusttolerate the heavy load and transfer information in real time.

However, many challengesmust be overcome to use wire-less communications in the smart grid, including networkperformance, suitability, and security [7]. The length of thecommunication delay is the most important requirementfor supporting smart grid applications, and these delayrequirements range from 8ms to more than 1 s. It is difficultto satisfy the delay requirement over a wireless network evenfor less challenging delay requirements, such as 500ms forphase measurement [8]. However, the efficiency of wirelesscommunications over shared media is a key metric whenprocessing the heavy and dynamic load in emergencies.

Medium access control (MAC) protocols play a vital rolein message delay and communication efficiency characteris-tics. However, fewMAC protocols allow for a real-time smartgrid. In general, the MAC protocols of wireless networks forlow-rate and short-distance applications consider the energyefficiency as an important aspect. However, higher energyefficiency typically results in a noticeable message delay.

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2014, Article ID 291927, 8 pageshttp://dx.doi.org/10.1155/2014/291927

2 International Journal of Distributed Sensor Networks

MAC protocols for low-rate and short-distance applica-tions can be categorized into contention-based, schedule-based, and hybrid schemes. In contention-based MAC pro-tocols, nodes compete to acquire the channel for randomaccess, which may result in unpredictable delays arising fromcollisions. To mitigate unpredictable delays, the RT-MACprotocol maximizes spatial channel reuse by avoiding thefalse blocking problem of RTS/CTS exchange within onesource and sink node pair [9]; however, this protocol stillsuffers from the interference of multistream communica-tions. TheMaxMAC protocol utilizes additional wake-ups toachieve a low delay and high throughput according to therate of incoming packets [10]. ENCO imposes an approximatevalue of the optimum contention window size to minimizethe channel access delay [11]. QoS-MAC for IEEE 802.15.4implements QoS support based on the IEEE 802.15.4 unslot-ted carrier sense multiple access with collision avoidance(CSMA/CA) scheme by utilizing differentiated service fordata traffic with different priorities. The QoS-MAC protocolis designed for smart grid distribution monitoring [12]. DRXis another MAC protocol for smart grid applications, andit is based on delay-estimation and data-prioritization stepsthat are performed by the application layer, in addition to theMAC layer parameters responding to the delay requirementsof the smart grid application and the network condition [13].Although many protocols based on contention can mitigatedelays, it remains difficult to eliminate the effect caused bycollisions.

Currently, schedule-based MAC protocols generally sup-port deterministic delays. WRT-Ring is a distributed real-time MAC protocol and operates in the slotted virtual ringnetwork [14]. Based on a control signal that circulates into thevirtual ring and CDMA, WRT-Ring supports real-time andgeneric applications. Because the control signal distributeswhile traveling, addressing the urgent alarm transmission iscomplicated. Point coordination function (PCF) is one of thetwo medium access mechanisms in IEEE 802.11, and PCF isa polling scheme that provides a shorter delay in mediumaccess applications than the distributed coordination func-tion (DCF) mechanism, even under heavy loads [15]. Time-division multiple access (TDMA) is an important schedule-based MAC protocol. A tree-based TDMA protocol, whichis based on a tree topology and the TDMA scheme [16],has been designed for home area networks in the smartgrid; however, TDMA-based protocols lack the flexibility torespond to fluctuations in the traffic load.

Hybrid schemes are developed to overcome the draw-backs of a single scheme by combining multiple schemes.IEEE 802.15.4 works as a hybrid of CSMA/CA and TDMAwhen using a superframe structure and guaranteed timeslot. Because of the limited number of available slots andcongestion of the contention access period under intensivedata exchanges, this scheme does not appear to be applicablefor high-performance, time-critical smart grid applications[17]. WirelessHART is also based on a CSMA/CA andTDMA-based hybrid scheme regarded as a paradigm shifterin the process control industry [18]. WirelessHART satisfiesthe strict timing requirements and high security concernsfor industrial control using time synchronization, channel

Gateway dataGateway node polling

ListeningDevice node polling reply

Time

SleepingRegular device data

Urgent device data

Gateway nodeDevice node i

Device node i + 1

Device node N

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

· · ·

tn

𝜇i 𝜏i Si tn+1

𝜇i+1 𝜏i+1 Si+1

...

Figure 1: Timeline of the RE-MAC protocol.

hopping, and mesh networking. However, CSMA/CA andTDMA suffer from low efficiency under heavy loads andload changes, respectively. EQ-MAC provides QoS supportby combining a hybrid medium access scheme with servicedifferentiation for cluster-based single-hop sensor networks[19]; however, it still suffers from congestion because it usescontention-based medium access for control messages.

Applications for smart grid wireless communications,such as condition monitoring, must exhibit high real-timecapability, high efficiency under heavy loads, and low com-plexity. Furthermore, the gateway nodes of such applicationsmust have an unlimited power supply. We study the wirelessmedium access in this scenario and present a real-time,efficient, and lightweight MAC protocol: RE-MAC.

2. Lightweight, Real-Time Hybrid Scheme

Agateway nodemust communicatewith several device nodes(the sensor and actuator nodes) for condition-monitoringapplications in the smart grid.The sensor nodes send regularand urgent data to the gateway node, which then transmitscontrol commands to the actuator nodes. These applicationsrequire real-time ability, even under heavy loads, and thegateway node is powered by an unlimited power supply.Tailored to this type of scenario, the lightweight pollingscheme, priority node scheme, and hybrid MAC methodform a promising hybrid scheme.

RE-MAC is a hybrid scheme of the polling scheme andTDMA. The polling scheme provides high efficiency evenunder high traffic, and TDMA is used to transmit emergencydata during the sleeping period. First, the nodes are dividedinto clusters. Each cluster has one gateway node and severalsensor and actuator nodes in a star topology. The gatewaynode has an unlimited power supply; thus, the energy con-sumption of wireless communications can be ignored for thegateway node.Thenodes in a cluster utilize the hybrid schemeto share the channel, as shown in Figure 1. Consideringthe importance of the control commands and configurationdata transmitted by the gateway node, the gateway nodeis prioritized over the other nodes and transmits data firstduring each polling period. Figure 2 shows a flow chart of theRE-MAC protocol. Initially, all of the device nodes turn ontheir radios to listen, and the gateway node begins to transmitits data, if any exist. Then, the gateway node sends a polling

International Journal of Distributed Sensor Networks 3

All of device nodes turn on to listen

Gateway node has data to transmit

Gateway node transmits the data

Gateway node sends a polling packet to device

Is this device

Other device nodes receive the reply of device

Yes No

hasdata to transmit

Devicereply for the polling packet

Devicetransmits the data

goes to sleep

Other device nodes go to sleep

The device node sleeps until the slot for sending urgent

The device node transmits urgent device data if any exists

The device node sleeps until the polling for next device node

Yes

No

Yes

No

node i

node i

node i?

node i

Device node i

and i = i + 1

Device node i

node i sends the

device data for this node is available

Figure 2: Flow chart of the RE-MAC protocol.

packet containing the length of the sleeping duration to acertain device node, such as device node 𝑖 in Figure 2. Thatnode sends a reply that indicates whether it has data to besent and, if so, the length of the data. Then, the device nodesends its data, if any, and goes to sleep. If the device nodehas no data, it goes to sleep directly for the sleeping duration.On the other hand, the other device nodes listen and receivethe reply packet from the polled device node and obtain thelength of the data to be sent by the polled device node. Thus,the other device nodes will sleep for a period that includes thedata transmission period for the polled node and the sleepingduration. When the sleeping period is complete, the gatewaynode will poll the next device node.

Each device node owns two queues, one for regular devicedata and the other for urgent device data.When a device nodeis polled to transmit data, it will send regular device data.During the sleeping period, the device node can wake up andsend urgent device data to the active gateway by the TDMA

(1) 𝑖 = 0; N = Number of device nodes;(2) if has data to transmit then(3) Transmit the data;(4) Send a polling packet containing the length of

the sleeping duration 𝑠𝑖to device node 𝑖;

(5) Receive the reply packet of device node 𝑖;(6) if the reply packet indicates device node 𝑖 has

data to transmit then(7) Receive the data of device node 𝑖;(8) Begin the sleeping duration(9) Receive urgent data in the slot for device

node 1;(10) Receive urgent data in the slot for device node 2;(11) ⋅ ⋅ ⋅

(12) Receive urgent data in the slot for device node N;(13) 𝑖 = (𝑖 + 1)%𝑁;(14) Goto Step 2;

Algorithm 1: Gateway node processing of RE-MAC.

(1) Turn on the radio to listen;(2) Receive the polling packet with the sleeping

duration 𝑠𝑖;

(3) if the polling packet is for this device node then(4) Send the reply for the polling packet;(5) if this device node has data to transmit then(6) Transmit the data;

Set the length of sleeping for this node with 𝑠𝑖;

(7) Else(8) Wait to receive the reply for the polling packet;(9) Get the data length 𝑙

𝑖from the reply packet;

(10) Set the length of sleeping for this node with 𝑠𝑖

and 𝑙𝑖;

(11) Go to sleep(12) if this is slot for urgent data of this node then(13) Transmit urgent data;(14) End of the sleeping duration;(15) Goto Step 1;

Algorithm 2: Device node processing of RE-MAC.

method as shown in Figures 1 and 2. Each device node hasone slot for transmitting urgent device data in each sleepingperiod, and these slots follow the duration of regular devicedata one by one, as shown in Figure 1.The device node sleepsuntil the slot for sending urgent device data for this node isavailable, and then that device node sends the urgent data, ifany exist, and goes to sleep. If the device node has no urgentdevice data, it goes to sleep directly.

Algorithm 1 describes the gateway node processing of RE-MAC in detail. During one polling period, the gateway nodewill send its data first and then poll device nodes to receive thedata; finally, the gateway node will receive the urgent devicedata by the TDMAmethod.

Device node processing of RE-MAC is shown asAlgorithm 2. The device node will receive the polling packetand obtain the sleeping duration for the polling packet. If this


node is the polled node, it will transmit its data. Otherwise, itwill wait to receive the reply for the polling packet from thepolled node and obtain the transmitted data length from thereply packet. Finally, the device node will send urgent data bythe TDMAmethod.

We illustrate the RE-MAC protocol with an example.There are 10 device nodes from DN 1 to DN 10 and onegateway node, GN, in a cluster. At the beginning, all 10 of thedevice nodes turn on their radios to listen. GN transmits itsdata if any exists.Then, GN sends a polling packet containingthe length of the sleeping duration 𝑠

1to DN 1. DN 1 receives

the polling packet and returns a reply with the length of data𝑙1to be sent. If DN 1 has data to be sent, it transmits the data

to GN at once. Then, DN 1 goes to sleep for 𝑠1. The other

device nodes receive the polling packet to DN 1 and the replypacket of DN 1, set the sleeping period referring to 𝑠

𝑖and 𝑙𝑖,

and then go to sleep. During the sleeping period, DN 1 to DN10 send urgent device data to GN one by one using TDMAslots at the beginning of the sleeping period. At the end of thesleeping period, all of the device nodes wake up to listen. GNbegins pollingDN2, with the same protocol as for pollingDN1. After polling DN 10, GN polls DN 1 to access the wirelesschannel.

In summary, there are three types of data for this RE-MAC hybrid scheme: gateway data, urgent device data, andregular device data. We utilize the priority node schemeand TDMA scheme in each sleeping period to provide real-time processing capability for the gateway node and devicenodes, respectively. RE-MAC is also highly efficient for devicenodes. The device nodes work under a polling scheme andTDMA; therefore, device nodes using the RE-MAC protocolgain better transmission efficiency and energy efficiency thanCSMA/CA protocols, which suffer contention, especiallyunder a heavy load. In addition, device nodes will go to sleepwhen there is no work to do within the polling duration,which will greatly reduce the energy consumption of devicenodes and extend the life time of device nodes.

3. Theoretical Analysis

We analyze the performance of priority node polling for RE-MAC and then verify the theoretical results and investigatethe entire protocol using simulations.

We assume that a cluster includes𝑁+1 nodes, where onenode is the gateway node and the other 𝑁 nodes are device(sensor and actuator) nodes. The gateway node polls devicenodes in cyclic order 1, 2, . . . , 𝑁, such that node𝑁 is followedby node 1. Each node has two queues of the first-come-first-serve type, and the capacity of each queue is unlimited. Theservice of all nodes is of the gating type, namely, the nodesends only those packets that were waiting in the queue whenthe transmission began. For the device nodes, the arrivingpackets of node i (𝑖 = 1, 2, . . . , 𝑁) follow a Poisson processwith an arrival rate 𝜆

𝑖; the service time for each node to

transmit packets is independent of the other nodes with ageneral distribution, and the distribution function is 𝐻

𝑖(𝑥).

𝐺 expresses the queue of the gateway node; the input is aPoisson process with an arrival rate 𝜆

𝐺; the service time

has a general distribution; and the distribution function is

𝐻𝐺(𝑥). From node 𝑖 to node 𝑖 + 1, the polling time has a

general distribution and the distribution function is𝜇𝑖(𝑥); the

sleeping time has a negative exponential distribution; and thedistribution function is 𝑠

𝑖(𝑥). 𝜐𝑖(𝜏) and 𝜐

𝐺(𝜏) are the number

of packets of node 𝑖 and gateway arriving within 𝜏 duration,respectively. In the equilibrium state, when the polling arrivesat node 𝑖, the probability of node 𝑘 (𝑘 = 1, 2, . . . , 𝑁, 𝐺)

having 𝑗𝑘packets waiting is 𝑔

𝑖(𝑗1, 𝑗2, . . . , 𝑗

𝑁, 𝑗𝐺). We define

the generation function as follows:

𝐺𝑖(𝑥1, 𝑥2, . . . , 𝑥

𝑁, 𝑥𝐺)

=

+∞

∑

𝑗1,𝑗2,...,𝑗𝑁,𝑗𝐺=0

⋅ ⋅ ⋅∑𝑥𝑗1

1𝑥𝑗2

2⋅ ⋅ ⋅ 𝑥𝑗𝑁

𝑁𝑥𝑗𝐺

𝐺𝑔𝑖(𝑗1, 𝑗2, . . . , 𝑗

𝑁, 𝑗𝐺) .

(1)

In the device nodes, assume that the instant of the start ofservice at one of the device nodes is . . . , 𝑡

𝑛, 𝑡𝑛+1, . . ., as shown

in Figure 1; then ⋅ ⋅ ⋅ < 𝑡𝑛< 𝑡𝑛+1

< ⋅ ⋅ ⋅ . 𝑇 is defined as thesequence {𝑡

𝑛}. Define random variables 𝜀

𝑛(𝑖) as the number of

packets in node 𝑖 at instant 𝑡𝑛and 𝛿𝑛as the node identifier of

the polling arriving at instant 𝑡𝑛.Thus, at instant 𝑡

𝑛, the system

state is (𝛿𝑛, 𝜀𝑛(1), 𝜀𝑛(2), . . . , 𝜀

𝑛(𝑁), 𝜀

𝑛(𝐺)) and the state space

of the system is 𝐼 = {(𝑖, 𝑘1, 𝑘2, . . . , 𝑘

𝑁, 𝑘𝐺) : 𝑖 = 1, 2, . . . , 𝑁,

𝑘𝑖= 0, 1, 2, . . ., 𝑗 = 1, 2, . . . , 𝑁, 𝐺}. Thus, the transition prob-

ability of the state (𝛿𝑛, 𝜀𝑛(1), 𝜀𝑛(2), . . . , 𝜀

𝑛(𝑁), 𝜀

𝑛(𝐺)) becomes

an aperiodic, irreducible finite Markov chain. Therefore, wehave the following limiting probability:

lim𝑛→∞

Pr {𝛿𝑛= 𝑖, 𝜀𝑛 (𝑘) = 𝑗𝑘; 𝑘 = 1, 2, . . . , 𝑁, 𝐺}

= 𝑔𝑖(𝑗1,𝑗2, . . . , 𝑗

𝑁, 𝑗𝐺) .

(2)

The necessary and sufficient condition for existence of theequilibrium state is given by

𝑁

∑

𝑖=1

𝜌𝑖+ 𝜌𝐺< 1, 𝜌

𝑖= 𝜆𝑖ℎ𝑖, 𝜌

𝐺= 𝜆𝐺ℎ𝐺, (3)

where ℎ𝑖and ℎ

𝐺are the mean service time of a packet in the

device node 𝑖 and in the gateway node, respectively. 𝜌𝑖and

𝜌𝐺are the traffic intensity of node 𝑖 and gateway, respectively.

The above equation yields the equilibrium condition that thetotal traffic intensity must be less than one.

In (2), 𝑔𝑖(𝑗1, 𝑗2, . . . , 𝑗

𝑁, 𝑗𝐺) expresses the probability that

𝑗𝑘packets are waiting at device node 𝑘 (𝑘 = 1, 2, . . . , 𝑁)

when the gateway node polls device node 𝑖 inequilibrium state, namely, considering the statespace 𝐼 = {(𝑖, 𝑘

1, 𝑘2, . . . , 𝑘

𝑁, 𝑘𝐺) : 𝑖 = 1, 2, . . . , 𝑁,

𝑘𝑖

= 0, 1, 2, . . ., 𝑗 = 1, 2, . . . , 𝑁, 𝐺}. In addition,𝑔𝑖(𝑗1, 𝑗2, . . . , 𝑗

𝑁, 𝑗𝐺) is the transition probability from

state (𝑖 − 1, 𝜀𝑖−1(1), 𝜀𝑖−1(2), . . . , 𝜀

𝑖−1(𝑁), 𝜀

𝑖−1(𝐺)) to state

(𝑖, 𝜀𝑖(1), 𝜀𝑖(2), . . . , 𝜀

𝑖(𝑁), 𝜀

𝑖(𝐺)). There are two cases for the

state transition, for all 𝑗𝑘≥ 0, the first case is 𝑔

𝑖(𝑗1, 𝑗2, . . . ,

𝑗𝑁, 𝑗𝐺) > 0 (𝑖 = 1, 2, . . . , 𝑁) and the second case is 𝑔

𝑖(𝑗1, 𝑗2,

. . . , 𝑗𝑁, 𝑗𝐺) = 0 (𝑖 = 1, 2, . . . , 𝑁). In the first case, the Markov

chain is ergodic and the system can be assumed to be instatistical equilibrium. In the second case, all the states areeither transient or recurrent null.


We define 𝐹𝐺(𝑥) as the service time of the gateway node

data at any one instant 𝑡𝑖, and there are 𝑥 packets in the

gateway node. During the period from 𝑡𝑛to 𝑡𝑛+1

, the servicetime for the gateway node is 𝐹

𝐺(𝜀𝑛(G)). Therefore, at instant

𝑡𝑛+1

, the gateway node and device nodes own the followingnumbers of packets:

𝜀𝑛+1 (𝐺) = 𝜐𝐺 (𝜇𝑖 (𝑛) + 𝜏𝑖 (𝑛) + 𝑠𝑖 (𝑛)) + 𝜐𝐺 (𝐹𝐺 (𝜀𝑛 (𝐺))) ,

𝜀𝑛+1 (𝑖) = 𝜐𝑖 (𝜏𝑖 (𝑛) + 𝑠𝑖 (𝑛)) ,

𝜀𝑛+1

(𝑗) = 𝜀𝑛(𝑗) + 𝜐

𝑗(𝜇𝑖 (𝑛) + 𝜏𝑖 (𝑛) + 𝑠𝑖 (𝑛))

+ 𝜐𝑗(𝐹𝐺(𝜀𝑛 (𝐺))) ,

(4)

where 𝜇𝑖(𝑛), 𝜏

𝑖(𝑛), and 𝑠

𝑖(𝑛) are the polling time, service

time, and sleeping time for device node 𝑖 from 𝑡𝑛to 𝑡𝑛+1

,respectively. When the system attains the state of statisticalequilibrium, the probability distribution generation functionof Pr (𝑖 + 1, 𝜀

𝑛+1(1), 𝜀𝑛+1(2), . . . , 𝜀

𝑛+1(𝑁), 𝜀

𝑛+1(𝐺)) is

𝐺𝑖+1(𝑥1, 𝑥2, . . . , 𝑥

𝑁, 𝑥𝐺)

= 𝐸[

𝑁

∑

𝑘=1

𝑥𝜀𝑛+1(𝑘)

𝑘⋅ 𝑥𝜀𝑛+1(𝐺)

𝐺]

= 𝑈∗

𝑖(𝐴) ⋅ 𝑆

∗

𝑖(𝐵) ⋅ 𝐺𝑖

× (𝑥1, 𝑥2, . . . , 𝐻

∗

𝑖(𝐵) , . . . , 𝑥𝑁, 𝐻

∗

𝐺(𝐴)) .

(5)

In the above equation, 𝑈∗𝑖(𝑠) and 𝑆∗

𝑖(𝑠) (𝑖 = 1, 2, . . . , 𝑁)

are the Laplace-Stieltjes transform of the polling time andsleeping time probability distribution, respectively, when thegateway node polls from device node 𝑖 to 𝑖 + 1; 𝐻∗

𝑖(𝑠)

is the busy period probability distribution Laplace-Stieltjestransform of the device node queue with a Poisson input;and𝐻∗

𝐺(𝑠) is the busy period probability distribution Laplace-

Stieltjes transform of the gateway node queue with a Poissoninput. 𝐴 and 𝐵 are as follows:

𝐴 = ∑

𝑘 ̸= 𝑖

𝜆𝑘(1 − 𝑥

𝑘) + 𝜆𝐺(1 − 𝑥

𝐺) ,

𝐵 =

𝑁

∑

𝑘=1

𝜆𝑘(1 − 𝑥

𝑘) + 𝜆𝐺(1 − 𝑥

𝐺) .

(6)

Thus, 𝐺𝑖(𝑥1, 𝑥2, . . . , 𝑥

𝑁, 𝑥𝐺) is described in functional

equation form using the recursive formula of (5); however,the explicit representation of𝐺

𝑖(𝑥1, 𝑥2, . . . , 𝑥

𝑁, 𝑥𝐺) cannot be

derived. The mean queue length in node 𝑗 at the start-of-service instant at node 𝑖 is denoted by 𝑔

𝑖(𝑗); then, we have

𝑔𝑖(𝑗) = lim

𝑥1,𝑥2,...,𝑥𝑁,𝑥𝐺→1

𝜕𝐺𝑖(𝑥1, 𝑥2, . . . , 𝑥

𝑁, 𝑥𝐺) /𝜕𝑥𝑗

𝐺𝑖 (1, 1, . . . , 1, 1)

. (7)

From (5), we obtain 𝐺𝑖(1, 1, . . . , 1, 1) = 𝑘 as a constant

when 𝑖 = 1, 2, . . . , 𝑁. Therefore, for (5), we can performdifferential operations with respect to 𝑥

𝑗, 𝑥𝑖, and 𝑥

𝐺. When

𝑥𝑙→ 1 (𝑙 = 1, 2, . . . , 𝑁, 𝐺), the following expressions are

obtained:

𝑔𝑖+1(𝑗) = 𝜆

𝑗𝜇𝑖+ 𝜆𝑗𝑠𝑖+ 𝑔𝑖(𝑗) + 𝜆

𝑗ℎ𝑖𝑔𝑖 (𝑖) + 𝜆𝑗ℎ𝐺𝑔𝑖 (𝐺) ,

𝑔𝑖+1 (𝑖) = 𝜆𝑖𝑠𝑖 + 𝜆𝑖ℎ𝑖𝑔𝑖 (𝑖) ,

𝑔𝑖+1 (𝐺) = 𝜆𝐺𝜇𝑖 + 𝜆𝐺𝑠𝑖 + 𝜆𝐺ℎ𝑖𝑔𝑖 (𝑖) + 𝜆𝐺ℎ𝐺𝑔𝑖 (𝐺) ,

(8)

where 𝜇𝑖and 𝑠𝑖are the mean polling time and mean sleeping

time for device node i, respectively. With the third equationin equation set (8), we obtain the expression for𝑔

𝑖(𝐺) because

𝑔𝑖+1(𝐺) = 𝑔

𝑖(𝐺) in the equilibrium state. Then, we substitute

the expression for 𝑔𝑖(𝐺) into the first equation of equation

set (8) and accumulate the first equation with respect to 𝑖 =𝑗+1, . . . , 𝑖−1, 𝑖 and the second equation with respect to 𝑖 = 𝑗.When device nodes are symmetric, namely, 𝜆

𝑖= 𝜆, 𝜇

𝑖= 𝜇,

𝑠𝑖= 𝑠, ℎ

𝑖= ℎ, 𝜌

𝑖= 𝜌, 𝑔

𝑖(𝐺) = 𝑔(𝐺), and 𝑔

𝑖(𝑖) = 𝑔, we obtain

the mean queue length of the device nodes as follows:

𝑔 =𝑁𝜆𝜇 + 𝑁𝜆𝑠 − 𝜆𝑠𝜌

𝐺− 𝜆𝜇

1 − 𝜌𝐺− 𝑁𝜌 + 𝜌𝜌

𝐺

. (9)

The mean queue length of gateway node is

𝑔 (𝐺) =(1 − 𝜌

𝐺− 𝜌 + 𝜌𝜌

𝐺) 𝜆𝐺𝜇 + (1 − 𝜌

𝐺) 𝜆𝐺𝑠

(1 − 𝜌𝐺) (1 − 𝜌

𝐺− 𝑁𝜌 + 𝜌𝜌

𝐺)

. (10)

Then, we can obtain the mean cyclic time of polling as

𝑇cyclic = 𝑁 ⋅ [𝜇 + 𝑠 + ℎ𝑔 + ℎ𝐶𝑔 (𝐺)]

=𝜇 + 𝑠 + 𝜇𝜌


𝐺

⋅ 𝑁.

(11)

We ignore the radio propagation delay here because thenodes are relatively close to each other. A device node willwait for one cycle time to transmit a packet in the worst case,and thus, the mean upper bound of the device node packetdelay is given by

𝑇upper bound dn =𝜇 + 𝑠 + 𝜇𝜌


𝐺

⋅ 𝑁 + ℎ. (12)

The gateway node has a higher priority than the devicenode, and it will have the opportunity to send packets at everyservice start instant. Therefore, the mean upper bound of thegateway node data packet delay is given by

𝑇upper bound gn =𝜇 + 𝑠 + 𝜇𝜌


𝐺

+ ℎ𝐺. (13)

4. Simulation Results

In this section, we present simulation results to verify thetheoretical results and illustrate the advantage of the RE-MAC algorithm compared to wirelessHART and DRX.

The mean upper bounds of regular device data packetdelay and gateway data packet delay are obtained from(11)–(13). To verify these analytical results, we established


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

2

4

6

8

10

12

14

Total traffic intensity

Mea

n cy

clic t

ime (

s)

N = 5, analysis resultN = 5, simulation result

N = 10, analysis resultN = 10, simulation result

Figure 3: Verification of the mean cyclic time.

the RE-MAC simulation scenario based on ns-2 as follows.Systems with five or 10 device nodes were applied. The totaltraffic intensity was set to the range of 0.05 to 0.80, and thestepwas 0.05.Thedata inputs of the device nodes and gatewaynode have symmetrical distributions, the data packet lengthsare all 400 bits, the polling packet length is 32 bits, the linkrate is 250Kbps, the mean value of the sleeping time is 0.2 s,and the simulation running time is 200 s. Figure 3 illustratesthat the simulation results of the mean cyclic time agree withthe theoretical analysis, thus verifying that the theoreticalanalysis is correct. The simulation results indicate that atleast 99.0063% of the packet delays satisfied the mean upperbounds of the packet delay.

We developed a wirelessHART (wHART) simulationscenario and added the urgent device data to RE-MACand wirelessHART. The regular device data and the urgentdevice data utilize the contention access period slots andcontention-free period slots, respectively, and the gatewaydata use the contention-free period for the wirelessHARTsimulation. In addition, we developed a DRX simulationscenario and set the delay threshold to 0.4 second for theregular device data and the gateway data. Figure 4 illustratesthat the gateway data delays are all less than 200ms when thetotal traffic intensity is less than 0.35, and RE-MAC, DRX,and wirelessHART all present good real-time performance.However, the gateway data delay of DRX and wirelessHARTincreases rapidlywhen the total traffic intensity is greater than0.4 and 0.7, respectively. Figure 5 shows that the urgent devicedata delays are all less than 200ms when the total trafficintensity is less than 0.35, and RE-MAC and wirelessHARTboth present good real-time performance. With the growthof the total traffic intensity, the urgent device data delays ofRE-MAC show a slow rise; however, the data delays of DRXincrease quickly when the total traffic intensity is greater than0.4.

According to the regular device data delay results shownin Figure 6, the RE-MAC data delay slowly increases with

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

5

10

15

20

25

30


Dat

a pac

ket d

elay

(s)

N = 5, gateway data delay, RE-MACN = 10, gateway data delay, RE-MACN = 5, gateway data delay, wHARTN = 10, gateway data delay, wHARTN = 5, gateway data delay, DRXN = 10, gateway data delay, DRX

Figure 4: Gateway data delay.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

5

10

15

20

25

30


Dat

a pac

ket d

elay

(s)

N = 5, urgent device data delay, RE-MACN = 10, urgent device data delay, RE-MACN = 5, urgent device data delay, wHARTN = 10, urgent device data delay, wHARTN = 5, urgent device data delay, DRXN = 10, urgent device data delay, DRX

Figure 5: Urgent device data delay.

total traffic intensity growth, and the data delay of DRX andwirelessHART rapidly rises when the total traffic intensity ismore than 0.4 and 0.5 for𝑁 = 5 and𝑁 = 10, respectively. RE-MAC is based on a polling scheme, and the polling schemecould provide this traffic-adaptive ability. In addition, usingthe priority node method and TDMA, RE-MAC exhibitsbetter efficiency than DRX and wirelessHART under heavyload conditions.



Dat

a pac

ket d

elay

(s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

5

10

15

20

25

30

35

40

N = 5, regular device data delay, RE-MACN = 10, regular device data delay, RE-MACN = 5, regular device data delay, wHARTN = 10, regular device data delay, wHARTN = 5, regular device data delay, DRXN = 10, regular device data delay, DRX

Figure 6: Regular device data delay.

5. Conclusion

This paper presented a real-time, efficient, and lightweightMAC protocol, RE-MAC, based on priority node polling anda hybrid scheme. The mean upper bounds of the gatewaydata packet delay and regular device data packet delay weredetermined.The gateway data and regular device data presentoutstanding real-time performance, even under heavy traffic.Additionally, the urgent messages of the device nodes can betransmitted in real time using TDMA scheduling.

Disclosure

This paper is original and has been written by the statedauthors who are all aware of its content and approve itssubmission. It is not under consideration for publicationelsewhere.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

The authors would like to thank the anonymous reviewers forseveral valuable comments and suggestions, which enabledthe authors to significantly improve this paper.This work wassupported in part by the Science and Technology ProgramProject of Hebei Province under Grant no. 12270325 and theSpecial Fund of Fundamental Scientific Research BusinessExpense for Higher School of Central Government (projectsfor creation teams) under Grant no. ZY20120104.

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