ARM: an Asynchronous Receiver-initiated Multi-channel MAC Protocol with Duty Cycling for WSNs

Jinbao Li1,2, Desheng Zhang1,2, Longjiang Guo1,2,3, Shouling Ji3 and Yingshu Li3 1 School of Computer Science and Technology, Heilongjiang University, Harbin, Heilongjiang, China, 150080

2 Key Laboratory of Database and Parallel Computing of Heilongjiang Province, Harbin, Heilongjiang, China, 150080 3 Department of Computer Science, Georgia State University, Atlanta, GA, USA, 30303

longjiangguo@gmail.com, jbli@hlju.edu.cn, zhang@ieee.org, sji@cs.gsu.edu, yli@cs.gsu.edu

Abstract—This paper proposes ARM, an receiver-initiated MAC protocol with duty cycling to tackle control channel sa-turation, triple hidden terminal and low broadcast reliability problems in asynchronous multi-channel WSNs. By adopting a receiver-initiated transmission scheme and probability-based random channel selection, ARM effectively solves control channel saturation and triple hidden terminal problems. Fur-ther, ARM employs a receiver-adjusted broadcast scheme to guarantee broadcast reliability for broadcast-intensive applica-tions. Via the theoretical analysis, two factors that assist ARM to handle these problems are derived. The simulation and real testbed experimental results show that via solving these three problems ARM achieves significant improvement in energy efficiency and throughput. Moreover, ARM exhibits a promi-nent ability to enhance its broadcast reliability.

I. INTRODUCTION

Recently, some multi-channel MAC protocols (mcMAC) [2, 3, 4] have been proposed to support the applications [1] in wireless sensor networks (WSNs) via parallel transmissions. A mcMAC mainly consists of channel selection and media access. Channel selection decides how to select idle channels for all the nodes efficiently in order to optimize the perfor-mance of WSNs; whereas, media access decides when and how all the nodes access channels that have been selected for them to avoid collisions. Channel selection can be generally classified as static [2] [6] [7] or dynamic [3] [4] [5]; while existing media access schemes generally fall in two basic categories: Time Division Multiple Access (TDMA) [2] [3] [5] [6] and Carrier Sense Multiple Access (CSMA) [4] [12] [13] [14]. Dynamic channel selection and CSMA with duty cycl-ing are jointly considered as suitable schemes for WSNs due to three reasons as follows. First, dynamic channel selection requires less number of channels than static schemes [4]. Second, CSMA involves no overhead of time synchroniza-tion required in TDMA [19]. Third, duty cycling is a scheme to address idle listening, which is considered as one of the largest sources of energy consumption in WSNs [1].

However, the above scheme cannot provide satisfactory performance due to three problems. (1) Control Channel Saturation (CCS), which can lead to severe collisions of con-trol packets and prevent all the channels being fully utilized. (2) Triple Hidden Terminals (THT), which can result in the fact that two node-pairs employ one channel to transmit data. (3) Existing mcMACs in asynchronous WSNs provide an ineffective supporting for broadcast, which lead to Low Re-liability of Broadcast (LRB). Above issues are verified and elaborated in Section III.

In this paper, aiming at CCS, THT and  LRB, an Asyn-chronous Receiver-initiated Multi-channel MAC protocol is proposed, called ARM, with duty cycling. Involving no overhead of time synchronization and multi-radio, ARM is tailored to overcome CCS and THT as well as LRB. The key novelty of this work is to use the receiver-initiated trans-mission to minimize loads on the CC to handle CCS together with the probability-based random channel selection  to avoid THT. Further, a simple but reliable single-hop broad-cast scheme is proposed for broadcast-intensive applications. This paper hopes to contribute in the following ways:

Makes effective solutions for CCS  and THT in WSNs context by adopting a receiver-initiated transmission scheme and a probability-based random channel selec-tion. To best of authors’ knowledge, no previous works give such solutions for these problems in WSNs context.

Proposes a duty cycling based multi-channel MAC pro-tocol ARM for WSNs, which exploits a receiver ad-justed asynchronous broadcast scheme to solve LRB. This single-hop broadcast scheme is capable of dynami-cally adapting to the objective of specific networks, which makes ARM suitable for QoS requirements.

Analyzes two factors related to channel selection and duty cycling, i.e., the probability of random channel se-lections and duty cycle by Queueing theory and Markov chain. These factors bring significant influence in per-formances of ARM’s solutions for CCS, THT and LRB.

Conducts extensive simulation to evaluate ARM’s per-formance. The simulation results show that compared with the other protocols, ARM achieves 162% more throughput ratios, 24% better energy efficiency ratios and 35% higher broadcast reliability ratios at most via effectively solutions for CCS, THT and LRB. More im-portantly, ARM is also implemented in a real testbed. The experimental results show that ARM achieves 67% more throughput ratios at most.

The rest of this paper is organized as follows. Section II describes the motivation behind this work and definitions of control channel saturation, triple hidden terminals and low broadcast reliability problems. Section III surveys related mcMACs. Section IV introduces ARM design, followed by its analysis in Section V. Section VI evaluates the ARM’s performance by comparing ARM with other MAC protocols in simulation and real testbed experiments, respectively. Section VII concludes the paper.

114978-1-4244-9328-9/10/$26.00 ©2010 IEEE

II. MOTIVATION

A. Need for solving CCS

In multi-channel WSNs,  CCS means that under certain circumstances the CC is considered as a bottleneck of net-work performance, which is verified in Fig.1 as the loads and number of channels increase in the simulation with 144 nodes. When the number of channels is larger than 4 and the loads are larger than 25, throughput of CAM-MAC [16] (details descried in Section VI) becomes stable, which is because collisions on the CC become severer. Thus, it de-grades the throughput of CAM-MAC. This becomes even worse under WSNs, where the deployment density of nodes is usually higher than general ad hoc networks and the traf-fic loads are usually bursty.

B. Need for solving THT

THT includes: (1) traditional multi-hop hidden terminal; (2) multi-channel hidden terminal [5]; (3) sleep hidden ter-minal. A instance for two new hidden terminals is given in Fig.2 where involves one CC and two DCs. Node  ,  ,  ,  , and  are awake and is sleeping. When has data for  , randomly selects an idle DC such as DC1 and puts the reser-vation information (e.g., who will occupy which channel for how long) into a  and sends to  on the CC. Then,  sends a back to to confirm this  . Next,  and  switch their channels to DC1 around time  . The awake neighbors of and (e.g.,  ,  and  ) update their channel usage in-formation by overhearing on the CC; whereas, the sleeping neighbors (e.g.,   ) still assume that DC1 is idle. During ( , ), has data for   .  randomly selects an idle DC such as DC2 and then switches to DC2 with  after a reserva-tion. Because  and as well as  are not overhearing on CC during ( , ),   ,   and   still assume that DC2 is idle. Around time  , two situations can cause packet collisions at

or   . (1) When   finishes sending data to   , has data for  . If  also selects DC2 that   and  are still occupying, then a collision may happens. In this case, is called the multi-channel hidden terminal of   and   . (2) When   wakes up,  has data for  . If  also selects DC2 that   and  are still occupying, then a collision may happens as well. In this case, is called the sleep hidden terminal of  and  . Since WSNs jointly involves multi-hop, multi-channel and duty cycling together, it will suffer from all triple hidden terminals, which will cause the severe packets collisions.

C. Need for solving LRB

Broadcast is an important traffic pattern on which many upper layer protocols depend. But, in the asynchronous mul-ti-channel scenario, it is hard to guarantee that all the neigh-bors receive broadcast packets, because of two reasons. (1) Only a small subset of neighbors is on the same channel with the sender, when it decides to send a broadcast packet. (2) In duty cycle based WSNs, the idle nodes enter sleeping state periodically, so the sleeping neighbors of a broadcast sender cannot receive the broadcast packet. Fig.3 illustrates the problem of broadcast packet loss. Among all the neigh-bors of broadcast sender  , only and can receive broad-cast packets, since   , , ,   and are not on the same channel with , while and are in the sleeping state.

III. RELATED WORK

In this section, related mcMACs are surveyed from two categories: synchronous and asynchronous.

A. Synchronous MAC Protocols

1) mcMACs for WSNs: Zhou et al. [2] proposed MMSN which is the first mcMAC that takes into account the restric-tions imposed by WSNs. Salajegheh et al. [6] proposed HyMAC for WSNs where the base station allocates specific time slots and channels to all the nodes. Jovanovic et al. [7] proposed TFMAC for WSNs where the schedules are made by all the nodes rather than the base station. Kim et al. [3] proposed Y-MAC, which schedules receivers rather than senders to achieve low energy consumption.

2) mcMACs for other networks: So et al. [5] proposed MMAC for ad hoc networks by dividing up time into mul-tiple slots, where all the nodes exchange control information on the CC for reservations of DCs  at the front of each slot and switch to DCs for data communication at the rest of the slot. Chen et al. [8] proposed MAP for ad hoc networks. MAP works in the same way to MMAC but has variable-size data time slots. Tzamaloukas et al. [9] proposed CHAT for ad hoc networks using channel hopping scheme. Under CHAT, all idle nodes switch among all channels using a common hopping sequence. Bahl et al. [10] proposed SSCH for ad hoc networks, which adopts multiple hopping se-quences for different nodes. Tzamaloukas et al. [11] pro-posed RICH-DP based on channel hopping for wireless networks, which differentiates itself with a receiver-initiated collision-avoidance scheme.

Figure 1. The verification of CCS Figure 2. The illustration of THT Figure 3. The broadcast issue

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3) Summing up: Above studies design protocols by time synchronization where let all the control information or data be sent in predetermined slots or channels. However, for larger scale WSNs, synchronization itself remains an open issue [4]. One common solution is to send SYNC packets periodically, but these SYNC packets induce considerable overhead, which consumes more energy [19].

B. Asynchronous MAC Protocols

1) mcMACs for WSNs: Le et al. [4] proposed PMC which utilizes a control theory approach to dynamically add available channel in a distributed method. Sun et al. [18] proposed RI-MAC which is a receiver-initiated single-channel MAC protocol for WSNs. Wu et al. [19] proposed TMCP, which does not require synchronization. However, this protocol is more like a topology control protocol than a MAC protocol. Zhou et al. [20] proposed CUMAC using cooperation for WSNs, but it requires a tone device on each node to notify collisions, which increases the cost of WSNs.

2) mcMAC for other networks: Wu et al. [12] proposed DCA for ad hoc networks, which uses two radios, one for control information exchanging and the other for data com-munication. Adya et al. [13] proposed MUP for wireless networks, which allows both radios to send control informa-tion and data interchangeably. Jain et al. [14] proposed RBCS for wireless networks with a receiver-based channel selection scheme via SNR comparisons at receivers. Nasipu-ri et al. [19] proposed a multi-radio MAC protocol for wire-less networks. Above four protocols are based on multi-radio scheme. Exploiting multi-radio can simplify the de-sign of protocols by dedicating one radio on the CC to con-sistently overhear the control information exchanging. However, multi-radio schemes lead to not only larger node size but also more energy consumption [16].

Luo et al. [16] exploited Distributed Information SHar-ing mechanism (DISH) and proposed CAM-MAC for ad hoc networks. When a node-pair reserves a channel, all its neighbors send cooperative packets to invalidate the reser-vation if they aware of the fact that the selected DC or re-ceiver is unavailable. Luo et al. [17] also proposed ALTU based on altruistic cooperation, which introduces some spe-cialized nodes called altruists whose only role is to acquire and share channel usage information. These two mcMACs are based on DISH. However, all the idle neighbors of the sender and its receiver will send packets for invalidation if they assume that this reservation is invalid. It involves more packet transmission than necessary and easily results in packet collisions, since many cooperative packets can be sent simultaneously. Thereby, this scheme will consume considerable energy under large scale WSNs [20].

C. Summary

All the mcMACs mentioned are summarized in Table I. It can be seen from Table I that currently there is no MAC protocol that is based on single-radio multi-channel asyn-chronous and supports broadcast and duty cycling for WSNs. The design of ARM addresses all the needs in Table I.

IV. DETAILED DESIGN OF ARM

In ARM, wireless bandwidth is divided into one dedicat-ed Control Channel (CC) for control packets only and Data Channels (DC) for control packets and data packets.

A. Unicast Scheme

1) Overview: In Fig.3, a message transmission includes five steps. (1) When sender  in sleeping period has a mes-sage for receiver that is also in sleeping period, wakes itself up passively to listen on the CC. (2) When wakes up to receive a message, initiates a possible transmission by sending a broadcast AnNounCement ( ) packet on the CC including a DC ID number, say  , selected by based on a certain scheme (discussed in next Subsection). Then, switches to the DC with ID number and listens for possi-ble incoming packets. (3) After receiving an  from , switches to the DC with ID number and sends a  after a random delay, which is to avoid the collisions caused by the fact that multiple senders may send their s simulta-neously. (4) After receiving a  , sends a  to to confirm this transmission. (5) After  receives this  , employs the & method for data transmission. Finally, they switch back to the CC to enter sleeping period when this communication is over. Other situations described as follows. (1) When does not receive an from within a predetermined time, sends an on the CC just like waking up, which is to avoid the deadlock. (2) When switches to a DC and waits for a predetermined time, if there is no or  for , enters to sleeping period based on its duty cycle (addressed in Section V.B).

2) Channel Selection Scheme: When wakes up to re-ceive packet, selects a DC and then puts its ID number in an   . should select the “best” DC based on some Channel Usage Information (CUI) that can be obtained by eavesdropping on the CC. This Eavesdropping based Chan-nel Selection (ECS) is an effective scheme in ad hoc net-works and is adopted by most of mcMACs [5] [12] [13] [16] [17]. However, THT make ECS is inefficient in WSNs, and is not suitable for ARM. Thus, it is no better choice than the random selection, when duty cycling and single-radio are employed and traffic loads are heavy. Thereby, to avoid THT, ARM uses probability-based random scheme to select DCs. By this scheme, when a node is ready to receive, it randomly selects a DC  (No matter this DC  is idle or busy) with probability  , and enters to sleeping period with 1 to conserve energy. is elaborated in Section V.

Figure 4. The unicast scheme of ARM

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Figure 5. The broadcast scheme of ARM

B. Broadcast Scheme

By adjusting all the potential receivers, ARM utilizes a simple but reliable receiver adjusted scheme to solve LRB.

1) Overview: Under ARM, Broadcast Channel (BC) is a dedicated DC for broadcast. When a sender has a broadcast packet to send, it switches to the BC, and then senses the BC. If the BC is idle, it repeatedly sends this broadcast packet for

continuous time intervals, which are defined as the aver-age length of time that a node sends a broadcast packet. Al-though nodes are asynchronous in ARM, every neighbor node (potential receivers, including all sleeping nodes) ad-justs itself to switch to the BC in every 1 time intervals. Thus, every neighbor of the broadcast sender can receive the broadcast packet during time intervals. This is because the length of neighbor’s hopping intervals (i.e.,  1) is shorter than the length of sender’s continuous broadcast packet transmission (i.e., ). Fig.5 gives an example of this scheme. When   has a broadcast packet to send,   first switches to the BC, and then  repeatedly sends a broadcast packet in  5 time intervals. Every 1 4 time in-tervals, other nodes such as and adjust themselves to switch to the BC to receive possible broadcast packets. The-reby, all the neighbors of the sender can receive this packet. ARM utilizes this broadcast scheme to achieve high reliabil-ity, which is validated in Section VI.A.4).

2) Broadcast Parameter: is significant to the broad-cast performance of ARM. The larger is, the more times a broadcast sender transmits the same packet repeatedly with, the longer latency of broadcast incurs, the more energy the sender consumes, while the smaller hopping frequency other potential receivers have, the less energy other nodes con-sume. A trade-off between energy and latency has to be achieved. Under ARM, to achieve a balance of energy con-sumption between a sender and all its receivers, the default setting of is the value that can make all the energy, with which a sender sends a broadcast packet, is equal to all the energy, with which all its receivers receive a broadcast packet. More importantly,  can be dynamically changed in order to make ARM suitable for QoS requirements as well. For instance, if the objective of the networks is to minimize broadcast latency as less as possible, regardless of energy cost, can be set to 2. Thus, after every one time interval, all the nodes have to switch to the BC to check whether there is a broadcast packet to receive. The optimal is based on specific applications of WSNs.

V. PERFORMANCE ANALYSIS

Two parameters bring significant influence on ARM’s performance, which are: (1) Probability , with which a receiver randomly selects a DC and communicates with the sender; (2) Duty cycle , with which idle nodes enter to the sleeping state periodically. Subsection A and B are to decide the optimal values of and , respectively.

A. The Probability

In ARM, the optimal p is set to the ratio of the number of Average available DCs (denoted as  ) and the number of total available DCs (denoted as ). So, represents the probability that a node randomly selects a DC  which is not occupied by other nodes. Usually, is limited by the hard-ware design standards or the reality of wireless spectrum availability, which are not determined by MAC protocols. Assuming that is given, can be obtained by analyzing  .

can be easily obtained, if the number of average occupied DCs (denoted as  ) is given. is derived as follows.

In a networks, denoted as   , the routing layer of   (which consists of the routing layers of all the nodes) pays a cost to the MAC layer of  for the messages that are re-layed from the routing layer to the MAC layer. Let de-notes the average rate at which the MAC layer of earns. In other words, denotes the sum of all the nodes’ MAC layers earning rate in  . Let denotes the average amount of money that the routing layer of pays to MAC layer for every message. Let denotes the average rate at which the messages of routing layer arrive to the MAC layer. Under the network stabilization condition, it is self-explaining that

.                                               1

Next, Eq. 1 is used to obtain the number of average oc-cupied DCs ( ) when becomes stable. Assuming that at the MAC layer, the total number of packets belonging to the same message at routing layer is independent and geometri-cally distributed with parameter  , i.e. with mean 1/ .

Theorem 1: Under the network stabilization condition:

1/ .                                             2

Proof: If the cost rule is set as that routing layer of pays $1  per time-unit only when one packet is sending on a DC. Then, the earn rate ( ) of the MAC layer is equal to the number of the packets sending on all DCs, which is equal to the number of occupied DCs, i.e. . Further, the average amount ( ) of money, which the routing layer pays to the MAC layer, is equal to the average number of packets belonging to the same message at the routing layer, i.e. 1/ .

is independent with the cost rule, so is not varying. Based on 1 , ,  1/ , Eq. 2 is valid. ▇

Based on Theorem 1, the average number of occupied DCs ( ) can be obtained under the network stabilization condition. Thereby, the average number of available DCs ( ) can be obtained by   , since is given. Finally,

/ / .                                  

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B. The Duty Cycle

Under duty cycling, the duty cycle  is defined as the ra-tio of wake-up time and wake-up time plus sleeping time, but the optimal (denoted as ∗ ) is hard to find. So, we transfer seeking ∗ to seeking optimal (denoted as   ∗ ), which is maximum sleeping time. The following model and simplifications are made for analyzing ARM. (1) The net-works consist of stationary nodes sharing common media in one hop. (2) Time is divided up into small slots, and each slot length (denoted as  ) is equal to the time of a packet sending at MAC layer. (3) Messages of routing layer arrive to the MAC layer by a Poisson process with rate  .

1) State Diagram: The state diagram of nodes is shown in Fig.7. All states fall into 5 main categories, i.e. Sleeping State ( ), Transmitting State ( ), Receiving State ( ), Hopping State ( ), and Listening State ( ). In addition,

consists of 7 substates, which are: TryA state ( ) where a node tries to send an ; TryR state ( ) where a node tries to send a ; Back-Off state ( ) where a node is backing off before sending a packet; WaitA state ( ) where a node is waiting for an ; Waking state ( ) where a node is wake-up for a possible on a DC; state where a node as a Sender is Listening on channel for two slots Unconditionally due to THT; state where a node as a Receiver is Listening on channel for two slots Unconditionally for the same reason. All state symbols are in Table II. The state occupancy time depend on , and all lengths of time in Fig.7 are represented by times of  . The different slots in the same states are denoted as [state name, slot number]. In Fig.7, denoted as low case letters, i.e. a, the transition probabilities for the state diagram are derived as follows.

P , 1 | , e , 1 .                  3

P , 1 | , 1 , 1 .                             4

P , 1 | , 0 e .                                                           5

Eq. 3 is the decrement of backoff counter, which means no message arrives and happens with probability  e . Eq. 4 represents the probability of messages arriving, and Eq. 5 gives the probability of waking up and trying to send  .

P , | , 1 e e , 1 . 6

P , 1 | , 1 1 e e , 1 . 7

P , 1 | , 1 1 1 e e .    8

Eq. 6 and Eq. 7 model the probabilities that either only one or multiple nodes try to transmit a packet in  , respec-tively. Eq. 8 gives the probability that retry limit reached.

P , | , 1.                                9

P , 1 | , 1.                               10

P , 0 | , 1 1.                              11

Eq. 9 - 11 model the process that a receiver switches to a DC unconditionally listening for two slots due to THT.

P , | , 0 1 .                         12

P , 1 | , 0 .                           13

Eq. 12 and Eq. 13 give the probability of either only one or multiple senders trying to transmit a in this slot, re-spectively. can be solved via , which is the probability that only one sender chooses the least slot in all backing off slots it can choose. Thereby, the winner is the only one try-ing to transmit a in a coming slot. Therefore,

  1 ∑ ∙ ,                   14

where is the expected number of receivers. Assuming that all the senders choose receivers with equal probability,

∑ 1 ∙2

1,                         15

where is the number of average waking up nodes on the CC. Since the number of average occupied DCs (denoted as

) is already obtained in previous subsection, in the long run,

  ∙ 2 1 ,                                   16

where is the duty cycle and is the number of neighbors of a node, which both are given.

P , | , 1 , 0 1.                 17

P , 1 | , , 0 1.                   18

P , | , 0 .                            19

P , 1 | , 1.                          20

Figure 6. The state diagram for ARM node

TABLE II. STATE SYMBOL

Symbols Meanings S maximum number of Sleep slotsA maximum number of wait slots for an D maximum time of resenDU maximum number of wake-Up slotsB maximum number of Back off slotsDC Data Channel CC Control Channel

tryA try to transmit an tryR try to transmit a

AnNounCement packet 1st packet Mth packet

Average number of packets in a Message

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Eq. 17 - 18 give the probabilities that after listening for one slot on a DC, the node receives a and continues to listen. Eq. 19 - 20 model the process that no sender sends

 to the node in this wake-up period, and then the node goes back to the CC to enter sleeping period.

P , | , 1.                          21

P ,  1 | , 1.                      22

P ,  1 | ,  1 1.                    23

P , | ,   1.                       24

When the node is in , , it implies that this node al-ready knows a sender has packets to it. Based on assump-tions, this transmission is not inferred by other senders from now. The node goes to , to transmit a , and then goes to ,  1 to receive the 1st data packet, and then moves to ,  1 to transmit the 1st and so on, until the last is sent out. The node switches to the CC to enter sleeping period. Eq. 21 - 24 model this process.

P , | , 1 , 1 .        25

P , 1 | , , 1 .       26

P , | , 0 1 .                       27

Eq. 25 - 26 give the process that a node waiting for receives the or continues to wait, respectively. Eq. 27 represents that probability that the node goes to , to prevent a possible deadlock. is the probability that no

is sent by intended receivers on the CC. Let , denotes the steady-state probability of , , and then

is equal to 1 , .

P , | , 1.                            28

P , 1 | , 1.                              29

P , 0 | , 1 1.                             30

Eq. 28 - 30 model the process that a sender receives re-ceiver’s  , and switches to a DC to listen in two slots.

P , 1, | , 01, 1 .       31

Eq. 31 represents probability of the 1st time randomly backing off for avoiding collisions. State , 1, means backing off ( ) slot at 1st backing off.

P , 1, 1 | , 1, 1,   1 .    32

P , 1 | , 1,0 1.                            33

Eq. 32 is the decrement of backoff counter, which happens with probability 1. Eq. 33 gives the probability of the node trying to send with the 1th time.

P , | , 1 ,   1 .          34

P , 1, | ,1

, 1 , 1 . 35

P , | , 1 .                          36

Eq. 34 gives the probability that a sender sends a . Eq. 35 models the process of a sender backing off th time.

Eq. 36 represents the probability that the backing off limit reached and a sender switches to the CC to sleep.

P , | , 1.                       37

P ,  1 | , 1.                   38

P ,  1 | ,  1 1.                 39

P , | ,   1.                    40

Eq. 37 - 40 model the process related to Eq. 21 - 24 .

2) Steady-state Probability: , represents the steady-state probability of , 1 . Denoting , by

, all steady-state probabilities can be represented with and transition probabilities, e.g. , , . The prior of , is a state which can transfer to   , with the transition probability, e.g. , 1 is the only prior to , 2 . The steady-state probability of , can be represented as the sum of all the priors’ steady-state probabilities multiply-ing by related transition probabilities, e.g.,

P , 1 ∑ , ∙ 1 1 ∙ . 41

Thus, all the steady-state probabilities can be expressed by transition probabilities and . Since all the transition proba-bilities are given and all the steady-state probabilities can be represented by alone, using normalization condition (i.e., the sum of all steady-state probabilities is equal to 1), is solvable. Then, all steady-state probabilities are solvable.

3) Optimal Duty Cycle: All states can be put into 5 cate-gories. Each category represents one kind of given energy consumption model, i.e.,  , , ,  and

, respectively. The steady-state probabilities are de-noted as , , ,  and , we have

∑ , ,

, , , ,         

∑ ,, ,  ∑ ,   ,   ,

 ∑ ,, ,  ∑ ,   ,   ,

∑ , ∑ ,   ,

 ∑ ∑ , , ∑ , .                          42

Next, the expectation of energy consumption of a node in one slot, denoted as , can be represented as

∑ , , , , ∙ .        43

Similarly, if the average length of a message is denoted as , then the expectation of data a node transmits in one

slot, denoted as , is

∑ ,   ∙ E / .                 44

The ratio of and represents energy efficiency, denoted as / . Assuming all the parameters of ARM are given except for which is the maximum num-ber of sleeping slots. If is varied, is also changing. The optimal number of sleeping slots (denoted as ∗) can obtain the maximum   . Thereby, ∗ / ∗ can be ob-tained which is the optimal duty cycle for ARM.

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VI. PERFORMANCE EVALUATION

In this section, simulation and testbed experiments are conducted to examine the effectiveness of ARM.

A. Simulation Experiments

Three metrics, aggregate MAC throughput, energy con-sumption, and broadcast reliability, are utilized to verify the effects of ARM. In each group, different Total Number of Channels (TNC) and network loads are considered except for the last one where the broadcast Packet Arrival Rate (PAR) and the Number of Broadcast Nodes (NBN) are con-sidered. Network loads are varied via changes of the Num-ber of CBR (NCBR, Constant Bit Rate) streams in the net-work. In all simulations, TNC is set to 4 when NCBR is va-rying, and NCBR is set to 30 when different TNCs are used.

The configurations of the simulation for unicast are as follows. Total 289 nodes, whose radio communication ranges are set to 40m, are uniformly deployed in a square area of size 200m 200m with a node density of 38. The traffic model is many to many. The payload size is set to 32 Bytes, and the channel bandwidth is set to 250 Kbps. ARM with OPtimal Duty Cycle (ARM-OPDC) is compared with four MAC protocols described as follows: (1) RI-MAC [18]; (2) MMSN [2]; (3) PMC [4]; (4) CAM-MAC [16]. Further, two varieties of ARM-OPDC are also involved to justify the value of the optimal duty cycle from the analysis: first va-riety utilizes the duty cycle of 25% (ARM-25%); the second exploits the duty cycle of 50% (ARM-50%).

1) Evaluation on Throughput: Aggregate throughput is computed as the total amount of all useful data successful delivered via the MAC layer in the network per unit time.

The throughput is explored when different TNCs are used in Fig.7 (a). Compared with others, three ARMs have similar or little lower throughput when TNC is small. This is because under ARM, all transmissions start on DCs that the receiver randomly selected, and the sender has to switch to that DC, and then makes a handshake with the receiver. This scheme will pay considerable cost if TNC is small, since all senders will handshake with receivers on such few DCs. When more channels are available, ARMs, PMC and CAM-MAC allow more nodes to transmit on different DCs simul-taneously. ARM-50% has better throughput than ARM-25% and ARM-OPDC, but as TNC is larger than 7, the dif-ference becomes smaller. When NCBR is increasing, throughput changes are shown in Fig.7 (b). It is observed that aggregate throughputs of all protocols increase with NCBR, because if more node-pairs are involved in data communication, more parallel transmissions will occur. However, the results show that under heavy loads, ARMs perform progressively better than other MAC protocols, which illustrates that ARMs significantly benefit from the receiver-initiated scheme and random channel selection when degrees of CCS and THT increase with loads.

2) Evaluation on Energy Consumption: The energy consumption is computed as the energy consumed to suc-cessfully deliver a useful data byte.

(a) Throughput vs. TNC (b) Throughput vs. NCBRFigure 7. Throughput evaluation

As TNC increases, energy consumption changes are ob-served in Fig.8 (a). Results show that all energy consump-tions decrease with the rise of TNC, but ARMs perform bet-ter than others, since they conserve energy by duty cycling. Further, ARM-OPDC outperforms ARM-25% and ARM-50%, which validates the analysis of the optimal duty cycle. The energy consumption is measured by varying loads in Fig.8 (b) where energy consumptions increase when loads rise. ARMs maintain relatively low energy consumption because of their duty cycle schemes. ARM-OPDC achieves better energy efficiency than ARM-25% and ARM-50%.

3) Evaluation on Broadcast Reliability: The broadcast reliability is computed as the ratio of the average number of packets received by neighbors of the broadcast sender, and the total number of packets sent by the broadcast sender.

Fig.9 (a) plots broadcast reliability changes when NBN is set to 35 and PAR is varying. It is observed that the relia-bilities of all protocols decrease with the rise of arrival rate, but ARM-OPDC outperforms others when PAR is larger than 20. This is because ARM-OPDC benefits from the lightweight of its broadcast scheme. The broadcast reliabili-ty is measured by setting PAR to 25 and changing NBN in Fig.9 (b). All the reliabilities generally drop when NBN be-comes larger. However, ARM-OPDC has a higher reliability when NBN is bigger than 30. This is also due to the lightweight of ARM, which is not largely affected by loads.

(a) Energy vs. TNC (b) Energy vs. NCBRFigure 8. Energy consumption evaluation

(a) Reliability vs. PAR (b) Reliability vs. NBNFigure 9. Reliability evaluation

0 1 2 3 4 5 6 7 8 92.0

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Sun, O. Gurewynchronous Duty CWireless Sensor NWu, John A. Stankmmunications in WZhou, et al. Handlannel MAC in LFOCOM, 2010.

a) Throughput vs. TFigure 11

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VIII. CONCLUSIO

ported by the N(61070193, 60

ical Research 9), the China Science and (2008RFQXG

tion (No.LRB0h of Heilongjiae Heilongjiangng Scholar, the208) and Innov

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