O EURASIP Journal on Wireless Communications and Networking

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RESEARCH Open Access

Analysis of superframe adjustment and beacon transmission for IEEE 802.15.4 cluster tree networks

Bih-Hwang Lee1*, Muhammad Udin Harun Al Rasyid1 and Huai-Kuei Wu2

Abstract

Wireless sensor networks based on the IEEE 802.15.4 standard are able to achieve low-power transmissions in the low-rate and short-distance wireless personal area network (PAN). A cluster tree network consists of several clusters; each cluster has a coordinator, known as cluster coordinator, and several device nodes. In the cluster tree topology of IEEE 802.15.4, a PAN coordinator periodically transmits beacon frames to its coordinator nodes as well as a coordinator node periodically transmit beacon frames to their device nodes. The main challenge in the cluster tree network is the collisions between beacons or even between beacon and data frames, which degrades the network performance. In order to decrease collisions, this article proposes the superframe adjustment and beacon transmission scheme (SABTS) by assigning the accurate values of beacon order and superframe order for the PAN coordinator, cluster coordinators, and device nodes, and deciding the precise time for the beacon transmission of PAN and coordinator nodes. A Markov chain model for the cluster tree network is developed with taking into account packet retransmission, acknowledgement, and defer transmission. Both analytical and simulation results show that SABTS performs better than IEEE 802.15.4 standard in terms of the probability of successful transmission, network goodput, and energy consumption.

Keywords: Wireless sensor network, IEEE 802.15.4, Personal area network, Cluster tree topology, Markov chain

Introduction

Wireless sensor networks based on the IEEE 802.15.4 standard have been designed to specify the physical layer (PHY) and medium access control (MAC) sublayer for low power consumption, short transmission range, and low-rate wireless personal area network (LR-WPAN) [1]. The IEEE 802.15.4 standard has three kinds of topology: star, peer-to-peer, and cluster tree topologies, which can operate on beacon- and non-beacon-enabled modes. The beacon-enabled mode has the most unique features of IEEE 802.15.4, while the beacons are used to synchronize the attached devices, to identify the personal area network (PAN), and to describe the structure of the superframe.

A cluster tree network consists of several clusters; each cluster has a coordinator, known as cluster coordinator,

* Correspondence: bhlee@mail.ntust.edu.tw

1NationalTaiwan University of Science and Technology, 43, Keelung Rd., Section 4, Taipei 106, Taiwan

Fulllist of author information is available at the end of the article

and several device nodes. A PAN coordinator serves as root to form the first cluster and initiates the network. The PAN coordinator and coordinator nodes broadcast beacon frames to their neighboring devices to complete the whole cluster networks. In a cluster tree topology, the PAN coordinator periodically transmits beacon frames to its coordinator nodes as well as the coordinator nodes periodically transmit beacon frames to their device nodes. However, if the coordinator nodes send beacon frames at the same time, collisions will happen among these beacon frames. Consequently, the children nodes in the cluster cannot synchronize and communicate with their coordinators. The main challenge in the cluster tree network of IEEE 802.15.4 beacon-enabled mode is the collisions between beacons or even between beacon and data frames, which degrades the network performance [2-4]. In other words, it is a crucial challenge on the cluster scheduling and collision avoidance (CA) in a cluster tree network.

Springer

© 2012 Lee et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

To solve the aforementioned problem, a time division beacon scheduling (TDBS) and superframe duration (SD) scheduling mechanisms are proposed [2]. The idea of TDBS is to manage beacon frame transmission from coordinator nodes in a non-overlapping way while the idea of SD scheduling is to decide the duty cycle of router nodes. A multi-dimensional scheduling (MDS) is proposed to avoid beacon collision in LR-WPAN, which uses the clean channel searching scan to change the time offset to transmit a new beacon frame during the inactive period [3]. MDS can minimize the possibility of beacon collisions, but the power consumption of the PAN coordinator is more than that of IEEE 802.15.4 standard due to the process of channel searching scan during inactive period. Therefore, in order to improve the network performance by decreasing beacon collisions as well as the collisions between beacon and data packets, this article proposes the superframe adjustment and beacon transmission scheme (SABTS) which is based on the IEEE 802.15.4 slotted carrier sense multiple access with CA (CSMA/CA), to assign the accurate values of beacon order (BO) and superframe order (SO) for the PAN coordinator, cluster coordinators and device nodes, and to decide the precise time for beacon transmission of PAN and coordinator nodes.

A number of mathematical analysis models have been proposed to analyze the performance of IEEE 802.15.4 based on the Markov chain model without considering packet retransmissions [5-11]. Several modified Markov chain models including packet retransmissions have been investigated but not consider the defer transmission [12-15], while the authors of [16-18] improve the Markov chain models by considering the defer transmission. An analytical model based on Markov chain for multi-hop cluster network has been studied without taking into account the acknowledgement (ACK) to confirm the successes of data packet transmission, the defer transmission, and packet retransmission [19]. Lastly, we propose an analytical model based on Markov chain for SABTS cluster tree network with taking into account packet retransmission, ACK, and defer transmission by modifying the Markov chain model from [17]. The major contribution of this article is to model the channel

access for a cluster tree network to obtain network goodput and energy consumption based on the proposed Markov chain.

Overview of IEEE 802.15.4

In the beacon-enabled mode of IEEE 802.15.4, each node employs two system parameters: BO and SO, which define beacon interval (BI) and SD, respectively, i.e., BI = aBaseSuperframeDuration x 2BO and SD = aBaseSuper-frameDuration x 2SO, for 0 < SO < BO < 14. aBaseSuper-frameDuration denotes the minimum number of symbols in an active period, which is fixed to 960 symbols. The active period of each superframe consists of three parts: beacon, contention access period (CAP) and contention free period (CFP), while the active period is further equally divided into 16 time slots called aNum-SuperframeSlots. The length of one slot is equal to aBaseSlotDuration x 2SO symbols, where aBaseSlotDura-tion is the minimum number of symbols in a slot and equal to 60 symbols. Figure 1 shows an example of the superframe structure. In IEEE 802.15.4 standard, BO and SO shall be equal for all superframes on a PAN. All devices shall interact with the PAN only during the active portion of a superframe.

In CAP, each node performs the CSMA/CA algorithm before transmitting data frame or MAC command frame. Each device maintains three parameters: the number of backoff (NB), contention window (CW), and backoff exponent (BE). NB denotes the required NB while attempting to transmit data; CW denotes the number of backoff periods that need to be clear before committing transmission; and BE denotes how many backoff periods a device need to wait before trying to access the channel. The initial value of NB, CW, and BE are equal to 0, 2, and macMinBE, respectively, where macMinBE is equal to 3.

In the located boundary of the next backoff period, a device takes delay for random backoff between 0 and 2be - 1 unit backoff period (UBP), where UBP is equal to 20 symbols (or 80 bits). A device performs clear channel assessment (CCA) to make sure whether the channel is idle or busy, when the number of random backoff periods is decreased to 0. The value of CW will be

Beacon

Beacon

Inactive Period

1 I 2 | 3 |4 I 5 I 6 | 7 I 8 | 9 10 | 111 12 13 I 14 | 15 SD = aBaseSuperframeDuration * 2SO symbols - Active Period -►

BI = aBaseSuperframeDuration * 2 symbols

Figure 1 An example of the superframe structure.

decreased by one if the channel is idle; and the second CCA will be performed if the value of CW is not equal to 0. If the value of CW is equal to 0, it means that the channel is idle after twice CCA; then a device is committed the data transmission. However, if the CCA is busy, the value of CW will reset to 2; the value of NB is increased by 1; and the value of BE is increased by 1 up to the maximum BE (macMaxBE), where the value mac-MaxBE is equal to 5. The device will repeatedly take random delay if the value of NB is less than the value of macMaxCSMABackoff, where the value of macMaxCS-MABackoff is equal to 4; and the transmission attempt is decided to be failure if the value of NB is greater than the value of macMaxCSMABackoff.

Description of SABTS

SABTS aims to assign the accurate values of BO and SO for the PAN coordinator, cluster coordinators and device nodes, and to decide the precise time for the beacon transmission of PAN and coordinator nodes. In order to guarantee the data transmission from its coordinator nodes, the BI of the PAN coordinator should be the round function to the interarrival time (INTV) of data packets. Let us denote BOPAN be the BO for the PAN coordinator, which can be obtained by Equation 1, where Ncoord denotes the number of coordinator nodes; Rs, Bs, and Ns denote symbol rate, aBaseSlotDuration, and aNumSuperframeSlots, respectively, e.g., Rs, Bs, and Ns are equal to 62,500 symbols/s, 60 symbols, and 16 slots, respectively. To reduce the beacon collisions between the parent and children coordinators, the different BO between coordinators at different depth can be obtained by Equation 2, where BOcoord is the BO for coordinator. The PAN coordinator might often be powered; therefore, the SO for the PAN coordinator (SOPAN) can be set to its BOPAN as shown in Equation 3. For the SD, if we assume there is no CFP, the SD of coordinator (SDcoord) only consists of CAP and beacon as defined in Equation 4, where EstimatedCAPcoord and ¿beacon denote the estimated CAP for coordinator and the length of beacon, respectively, e.g., ¿beacon is equal to 190 symbols.

BOPAN —

Ncoord X INTV x Rs Bs x Ns

BOcooid — BOPAN _ 1 SOPAN — BOPAN

SDcoord — EstimatedCAPcoord ^ LBeacon

EstimatedCAPcoord is equal to the BI of coordinator (BIcoord) divided by the number of coordinator nodes (Ncoord), as shown in Equation 5. By using Equations 4

and 5, SDcoord can be obtained by Equation 6. Therefore, the value of SO for coordinator (SOcoord) can be obtained by Equation 7. BO and SO for device nodes (BOdev and SOdev) are decided by its coordinator node, which are equal to BO and SO of its coordinator node as shown in Equation 8.

EstimatedCAPcoord —

BIcooid Ncooid

BsxNsx 2BOcoo'd

Ncooid

SDcooid — Bs x Ns x 2SOcoord BsxNsx 2BOcoord

Ncooid

-+ 190

SOcoord —

Ncooid

BOdev — BOcoord ; SOd ev — SOcoord

Based on the aforementioned description, SABTS can be resumed by flowchart as shown in Figure 2. In this article, we consider the cluster tree topology with one PAN, three coordinator nodes, and nine device nodes as shown in Figure 3. Figure 4 shows an example of the superframe adjustment and precise time for beacon transmission for the cluster tree topology of Figure 3,

Figure 2 The flowchart of SABTS.

Figure 3 The selected cluster tree topology.

while INTV of each device node is equal to 0.1. As shown in Figure 4, we get the different starting time of beacon transmission among coordinator nodes to avoid beacon collisions. Furthermore, the coordinator nodes and device nodes can save energy consumption during inactive periods. By using SABTS, we get the values of BO and SO for PAN to be equal to 4; the value of BO for each coordinator node and device node is equal to 3; and the value of SO for each coordinator node and device node is equal to 1.

In order to reduce the collisions of the beacon transmissions among coordinator nodes, SABTS adjusts the beacon starting times of PAN and coordinator nodes. Let us denote TxOffsetPAN and TxOffseti to be the beacon starting times of PAN and the ith coordinator node, respectively. TxOffsetPAN starts at the beginning of superframe, then TxOjjseti is adjusted by Equation 9, where SDcoordi_1 denotes the SD of the (i - 1)th coordinator node.

TxOjfseti = <

TxOffsetPAN H--ît02- , i = 1

TxOjjseti-i + + SDcoold._i, ^

2<i<NCoord

Analysis of SABTS

In this section, the Markov chain model for SABTS in the case of the acknowledged uplink data transmission is analyzed to obtain the stationary probabilities, whose state transition diagram is shown as Figure 5. Let bjk be the stationary probability at the stochastic state (s(t) = i, c(t) = j, and r(t) = k), where s(t) c(t), and r(t) represent backoff stage, backoff counter, and number of retransmissions, respectively, shown as Equation 10, where bi,-1,k> bi,-2 k, and bi,-3,k are the stationary probabilities for the first CCAi, the second CCA2, and packet transmission, respectively, at the ith backoff stage and the kth retransmission. Let bSi,k and bCi,k be the stationary probabilities of the successful transmission and collision at the states of Sikk and Q k shown as Equations (11) and (12), respectively, where m and R are the maximum NB

Figure 4 An example of SABTS for three coordinator nodes.

stage and retransmissions, i.e., they are equal to 4 and 3, respectively.

bijk = limP{s(t) = i, c(t) = j, r(t) = k}

for ie(0, m), je(—3, wi-1), ke(0, R) (10)

bs,t = lim P{Ss(t) = Si, r(t) = k), ie(0, m), ke(0, R)

tH V 7

bc,t = limP{Cs(t) = Ci, r(t) = k} , ie(0, m) , ke(0 , R)

tH V 7

The parameters used in the Markov chain model are explained as follows. An IDLE state means that a device node has no packet to transmit. Let wi = 2BEi be the backoff window at the ith backoff stage of a device, where BEi = 3, 4, 5, 5, and 5 for 0 < i < m. Let us denote q to be the probability that packet arrives during the active period, which can be obtained by Equation 13, where Ldata, Rb, and SDT are packet length (in bits), data rate (i.e., 250 kbps), and the SD time (in seconds),

respectively; where SDT is equals to R, and jnTv is the number of packets in SDT.

INTV x Rb x SDT

The MAC sublayer should transmit packet if the remaining CSMA/CA steps, i.e., two CCA analyses, frame transmission, and any ACK, can be completed before the end of CAP. Conversely, if the current CAP has not enough slots to transmit data packets, it should defer transmission until the beginning of the CAP in the next superframe. Let us denote d to be the probability of defer transmission, which can be obtained by Equation 14, where Ttxcca, T„ Tad<, and Txack are the CCA transmission time, packet transmission time, time to wait for ACK, and time to transmit ACK from receiver to transmitter node, respectively.

*2Ttxcca Ttx Tack Ttxack

Let a and ji be the probabilities that CCAX and CCA2 are busy, respectively. CCA1 busy means that the tagged

node at one of the CCA1 states while at least one of the other nodes at packet transmission state, while CCA2 busy means that the tagged node at one of the CCA2 states while at least one of the other nodes at packet transmission state. Let us denote Pcoll to be the probability of the collision of packet transmission, i.e., the tagged node at packet transmission state while at least one of other nodes in the packet transmission state at the same time. Let us also denote Pfaili and Pfail2 to be the probabilities of fail transmission due to the maximum number of retransmissions after collisions and due to no channel to use after reaching the maximum backoff stage at the maximum retransmission stage, respectively.

To analyze the Markov chain model, several state transition probabilities are evaluated as shown from Equations 15 to 23. Equation 15 states the probability that the backoff counter is decreased after each slot. Equation 16 gives the probability of finding busy channel either in CCA1 and CCA2. Equation 17 states the probability of picking a backoff state in the next retransmission stage after the collision of packet transmission when having enough time to send packet in the remaining active period and channel idle in both CCA1 and CCA2. Equation 18 states the probability of entering the IDLE state after the collision of packet transmission while reach the maximum retransmission stage after finding the remaining active period to be enough to send packet and channel idle in both CCA1 and CCA2. Equation 19 gives probability that the remaining CAP is not enough to send packet and need to defer and pick backoff state in the next superframe. Equation 20 states the probability of successful packet transmission and picking new random backoff at the first backoff stage. Equation 21 states the probability of entering the IDLE state if the node has no data packet to transmit after successful packet transmission. Equation 22 states the probability of entering the IDLE state due to channel access failure. Equation 23 states the probability of going to the first backoff stage from the IDLE state if the node has data packet to transmit.

P(i, j, k\i, j + 1, k) = 1, for ie(0, m), je(0, wt - 2),

ke(0, R) (15)

wt — j

P(i, j; k | i - 1; 0,k) = [(1 - d)(a) + (1 - d)(1 - a)f!\ wi

= wL-i(1 - d)[a +(1 - a)fl: wi

ie(1; m); je(0; Wi - 1); ke(0; R)

P(0; 0; k|i; 0; k - 1) = (1 - d)(1 - «)(1 - £)(P«oJl) ;

k e(1; R) (17)

P(/DL£|i; 0;R) = (1 - d)(1 - a)(1 -p)(Peo„)(1 - q)

P(0; j; k|i; 0; k) = (d); k^ (0; R) (19)

P(0; j; 0|i; 0; k)

= ^ (1- d)(1- a)(1 - Jg)(1-PCo«)(q); w0

i e (0; m); j e (0; Wi - 1); k e (0; R) (20)

P(/DL£|i; 0; k )

= (1 - d)(1 - a)(1 - ^)(1 - PCoii)(1 - q);

i e (0; m); k e (0; R) (21)

P(IDLE\m; 0;R) = (1 - d)[a +(1 - a)$(1 - q)

P(0; j; 0|IDL£) =W0-(q); je(0; Wi - 1) (23)

By using Equation 16, the stationary probability bjk can be obtained by Equation 24. From Equation 17, b0,o,k can be obtained by Equation 25, where Y and X are the probabilities of entering the next backoff stage and the collision of packet transmission in a certain backoff stage, respectively. Similarly, bir0,k can be obtained by Equation 26. Finally, the steady-state probabilities to perform random backoff, CCA1, CCA2, packet transmission, successful of packet transmission, collision of packet transmission, and idle can be obtained from Equations 27 to 33, respectively. Since the sum of probabilities in the Markov chain must be equal to one, we have Equation 34. By using Equations 27 to 34, we can get the value of b0,0,0 easily by using excel spreadsheet.

Wi — j

bi,j,k =-bi—1,0,k (1 — d)[a +(1 — a)p]

= WW-1 bi,0,k (24)

bo, 0, k —(1 - d)(1 - a)(1 - fipJE m—0bi, 0; k-1 + (1 - d)[a +(1 - a)6]b m, 0, k—1

— (1-d)(1-a)(1-p)PcouYJm 0bi,0,k-1 + Y bm,0,k-

P[CCA2] — £ ^Lbi,-2;

((1 - d)(1 - «)(i - fiPjz, m^y

" Ym"1 k

(1-d)(1-a)(1-p)Pcoii

1 - Z 1 — Y

b0,0, 0 [((1 - d)(1 - a)(1 - 0)PcoiU)k + Zk

— b0, 0, ^Xk + Zk)

i -2 k

— (1 - d)(1 - a)£k

— b0;0;0 (11--((XX++z" - 1 x (1 - d)(1 - a)

— b0, 0, 0 V U (1 - d)(1 - a)

P[packet transmission]

i—0Z, k—0bi -3 k

where Y — (1 - d)[a +(1 - a)6];Z — Ym+1; U — (1-|); and X — (1 - d)(1 - a)(1 - 6)PcollU for simplicity.

bi,0 ,k — bi-1, 0,k (1 - d)[a +(1 - a)6]

— ((1 - d)[a +(1 - a)6])%, 0,k

— Yi b0,0,k

— Y%,0 , 0(Xk + Zk) for ie(0, m) , ke(0 , R)

— (1 - d)(1 - a)(1 - m—0TR—0Yib0fi,k

— b0 ,0 ,0 I 1—+ z)— 2XZ

k— 1Z

1 -(x + Z) —y V1 -Y;(1 d)

x (1 - a)(1 - 6) — b0,0,0 VU (1 - d)(1 - a)

x (1 - 6) (30)

P[rand°mbackoff] — £ i—R—0bi,j,k = £ :„£ R—0 W k

— W0 b0 0 0 1 -(X + Z) - 2XZ 2 0 '0 0 l 1 - (X + Z)

1 (2Y)R + 4Y3+4Y4

1 - (2Y)

— y b0 , 0, 0 VQ

P[successful of packet transmission]

i—0!^ k—0bSik

— (1 - d)(1 - a)(1 -6)(1 - PcoU)YZ0T.l0Yib0,0,k

— b0 , 00 (i-pc + z) -2XZy

x (1 - a) (1 - 6) (1 - Pcoii )

—0 k—0 '1 - Z^

(1 - d

— b0 , 0,0 VU (1 - d) (1 - a) (1 - 6) (1 - Pcoii ) (31 )

where V = ((X++ZR - 2XZ and Q — 1-+ 4Y3 + 4Y4

for simplicity.

P[CCA1] — £"oYLoh-1

— (1 - d)£ m £ L 0Yib0,0, k

1 -(X + Z)R

1 - (X + Z) — b0,0,0 VU (1 - d)

a - Z ,1-Y

(1 - d) (28)

P[collision of packet transmission]

i—0 k—0bCi k — (1 - d)(1 - a)(1 - 6)Pco^J2R^0Yib0,0,k

— b0 ,0 ,0 X I 1 (X, + - 2XZ

1 - (X + Z)

— b0 ,0 ,0 X V

P[IDLE] = (1 - q)Y,„Em^s» + (1 -q)Y.,.obc,;R + (1 - q)d^,J>i.w + (1 - q)Yb„AR + (1 - q)P[IDLE]

=(1 - q) [XLEL^+X=J>C„+d x;>,,+Y b„„]

(1 - q)

(1 - q)

1 -(x+z); - 2XZ

1 -(X + Z) I

1 - Z 1 — Y

(1 - d)(1 - a)(1 - £)(1 - PœU)

+ (X2 + Z2)X + d ( 1—Y ) + Z(X2 + Z2)

b0,0,0 [VU (1 - d)(1 - a)(1 - £)(1 - PCoii) + (X2 + Z2)(X + Z) + d U ]

i=0l^>=0 2^k=0bi'j'k + Z,i=0Z^k=0bi'-1 + i=0l^k=0bi'-2k + Z,i=0Z^k=0bi'~3'k + Z,i=»Z,fc=0bS'

+ £ m »£ L 0bCi;k + P[IDLE] = 1

Let and fa be the conditional probabilities that a tagged node will be at one of the CCA1 states after backoff and at one of the CCA2 states after sensing channel idle in the CCA1, which can be obtained by Equations 35 and 36, respectively. Let us denote t to be the probability that a tagged node can transmit a packet, i.e., the tagged node is in one of the CCA1 states and senses the CCA2 is idle, while the other nodes do not in the CCA1 state, which can be expressed by Equation 37, where Nch is the number of children nodes of certain coordinator nodes. Therefore, the previous mentioned probabilities of a, |3, Pcoll, Pfail1, and Pfail2 can be expressed by Equations 38 to 42, respectively.

i 0 k 0bi -1 k

i=0/^=0bi;-1* + 2^i=02^=0 2^=0b< /1 - (X + Z)R

w,- 1 R i=0 j=0 k=0bi j k R+1 ^

1 - (X + Z)

1 - Z 1- Y

(1 - d)

1 -(X + ^ - 2XZ v 1 -(X + Z) )

VU(1 - d)

(1 - d)+W0f1 -(2Y )R;X + 4Y 3 + 4Y 4

1 - Y)y 2 \ 1 - (2 Y)

V0 [u(1 - d)+W Q'] where V' = 1—iX^ZZT - 2XZ and Q' = 1—i^YT + 4Y3 + 4Y4 for simplicity.

i=0 k=0bi -2 k

i=0l^k=0bi'-1k + Z,i=0Z.,jM>bi'-2;k + Z^i=0Ï^H> Z^kJ'M

1 -(X + Z) , 1 -(X + Z)

1 - Z 1 - Y

(1 - d)(1 - a)

1 -(X + Z) ^ 1 -(X + Z) ^

V'U(1 - d)(1 - a) V' [U(1 - d)(2 - a)+W Q']

1 - Z 1- Y

(1 - d)(2 - a) +

W0 1 -(2Y )R + 4Y 3 + 4Y 4 2 1 - (2Y) ,

T = 01 (1 - Nch-1(1 - a) (1 - ß)

((Ni-D GNTV) )

a = 01 (1 — (1 — t)

ß = 02 1 - (1 - T)

((«ci-1)(îN?V ))

Peon = Nch T (1 -(1 - T)((Nh-1)(inTv)))

Pfam = £"0 = bo, 0, 0 + ZR) X

PsuePAN =(1 - Pdropeoord)( 1 - PdropPAN)

Based on the aforementioned analyses, the number of successful packets received by PAN (NrecvPAN) and the network goodput (G), can be expressed by Equations 49 and 50, respectively, where Ndev, Nbeacon, and rsim are the number of device nodes in network, the number of observed BIs of PAN, and the observed simulation time (in seconds), respectively.

NreevPAN =

Ndev PsuePAN Tsi INTV

Pfaii2 = bm,o ,r(1 - d)(a + (1 - a)ß) = bo ,o , o(Ym)(XR + ZR)(1 - d)(a -

(1 - a)ß)

NreevPAN Ldata Nbeaeon BIPAN

Let us denote Pdr to be the probability of a packet being dropped due to collision retransmission, which can be expressed by Equation 43. Because the probability of collision increases as the value of INTV decreases, we define Pjntv be the fraction time of the total number of data packets and ACK packets to the CAP time of the superframe as expressed by Equation 44, where interframe space (IFS) is the minimum period between two successive frames transmitted from device [1]. Let us denote Pdropcoord and Psuccoord to be the probabilities of packet dropped and successful transmission from device node to its coordinator, respectively, which can be obtained by Equations 45 and 46. Similarly, let us denote

PdropPAN and PsucPAN be the probabilities of packet

dropped and successful transmission from coordinator node to the PAN coordinator, respectively, which can be obtained by Equations 47 and 48.

Pdr = £ L1 (Peo")k

PINTV =

Pdropeoord —

IFS + ACKy-*-1 INTV x SDT )

Pfaill + Pfail2 + Pdr, if PiNTV < 1 1 , if PiNTV = 1

Psuccoord — 1 Pdropcoord PdropPAN = (Pdropcoord)

Basically, the total energy consumption of a cluster tree network consists of the energy consumptions by device nodes, coordinator node, and the PAN coordinator, denoted by Edev, Ecoord, and EPAN, respectively. Let us denote PWidle, PWsleep, PWtx, and PWrx to be the power consumptions for idle, sleeping, transmitting a packet, and receiving a packet, respectively. Let us also denote Lcca, Lbeacon, and Lack to be the lengths of CCA, beacon, and ACK transmissions, respectively. Moreover, let us denote DCdev, DCcoord, and DCPAN to be the duty cycles of device nodes, coordinator nodes, and the PAN coordinator, respectively.

The energy consumptions of a cluster tree network are analyzed as follows. The energy consumption of device nodes consist of seven parts as shown in Equation 51, i.e., the seven parts of energy consumptions are in order for backoff, CCA transmission, data packet transmission, idle, receiving beacon from its coordinator, receiving ACK, and sleeping, respectively, where dnode is the distance between device nodes (or coordinator nodes) and its coordinators (or the PAN coordinator). Similarly, the energy consumption of coordinator nodes can be obtained by Equation 52, which consists of 10 parts as in order for backoff, receiving data packet transmission from its children node, transmitting ACK to its children nodes, transmitting CCA, transmitting data packet, receiving ACK from its coordinator (i.e., PAN coordinator), idle, transmitting beacon, receiving beacon, and sleeping, respectively. The energy consumption of the PAN coordinator can be obtained by Equation 53, which consists of five parts as in order for idle, transmitting beacon, receiving data packet, transmitting ACK, and sleeping. Finally, the total energy consumption of a cluster tree network, Etotal, can be obtained by Equation 54.

Edev — Ndev Tsi

SDdev BIpAN

i=0Z^j=0 l^k=0bi'j'k

INTV Rb

+ 1 ^ Psuccoord dnode] + (PWidle P[IDLE ^^

2 PWtxLcca J n ,7

i_ k=0 (bi' + bi;

INTV Rb

, PWrx Lbeacon l P'Wrx Lack + ~ + 1 t-» ™-,-rr r ""~ P succoord

Rb BIcoord \INTV Rb

bipan) PWs,eep(1 - DCdev)

BIdev \ BIpAN

Ecoord = Ncoord Tsi

SDcoord\m 17 \ , ( H n PWrx Ldai

Nch PWidle —-2^i=0Z^j=0 Z^k=0bi,j,^ + (Nch Psuccoord

+ I Nch dnode Psuccoord j^r^x ~Lâ ^

2 PWtx L,

INTV Rb

INTV Rb

-R^Psuccoord dnode^2i=0£R=0 (bi,-1,k + bi,-2,k

PWtx Ldata P P d \

P succoord P sucPAN dm)de I

INTV Rb

PWrx -ack n N

"TT" P sucPAN

+ [PWidie P[IDLE

ÎPWrx -be

V Rb Bit

SDcoord

BIpAN )

+ I PWsleep (1 - DCcoord)

y yINTV Rb

L beacon dnode Rb BIcoord) BIcoord

EpAN = Tsi

PWidie P[IDLE

SDpan\ BIpAN )

Rb BIpan)

+ ^jNjTV Rta PsucpAN Nde^j + ^INTV -R^ PsucpAN dnode Nde L+PWsiee^(1 -DCpAN )

Etotai = Edev + Ecoord + EpAN

Simulation and analysis results

In this section, simulation experiments are performed by using the extended network simulator NS-2 to validate the analysis and performance evaluation. We consider a cluster topology with 1 PAN coordinator, 3 coordinator nodes, and 9 device nodes as shown in Figure 3, where the distance between nodes (dnode) is equal to 10 m. The packet arrival rate follows the Poisson distribution with the INTV of data packets from 0.1 to 1, where packets have the same length of 560 bits. To simulate the performance of power consumption, we consider the radio parameters of Chipcon's CC2420 2.4 GHz for the IEEE 802.15.4 RF transceiver [20], where the transmitting power PWtx, the receiving power PWrx, the idle power PWaie, and the sleeping power per time unit PWsleep are 31.32 mW, 35.28 mW, 712 ^W, and 144 nW, respectively [16]. The BO and SO settings follow the proposed SABTS algorithm, but they are fixed for IEEE 802.15.4 standard, i.e., BO = SO = 6. Table 1 summarizes the simulation parameters. We compute the probabilities of collision of packet transmission and entering the next backoff stage in a certain backoff stage. We also

compare the analytical (ana) and simulation (sim) results between the proposed algorithm (SABTS) and IEEE 802.15.4 standard (Std) for network goodput, total network energy consumption, and the probability of successful packet transmission arriving at PAN.

Figure 6 shows the probabilities of collision of packet transmission and entering the next backoff stage in a certain backoff stage, denoted as X and Y, respectively, against the INTV of data packets by analytical model. The probabilities of X and Y of SABTS are lesser than those of IEEE 802.15.4 standard. Normally, the lesser probabilities of X and Y, the higher probability of successful packet transmission, which implies the lesser energy consumption needed for packet transmission, i.e., SABTS should have higher network goodput and lesser energy consumption than those of IEEE 802.15.4 standard.

Figure 7 shows the probability of successful transmission arrives at the PAN coordinator (PsucPAN) against the INTV of data packets by analytical and simulation. SABTS obtains higher probability of successful transmission arriving at the PAN coordinator than that of IEEE

Table 1 The simulation parameters

Parameter Value

Channelbandwidth 250 kbps

Packet length (¿data) 560 bits

UBP 80 bits

MAC header 2 UBP

ACK length (Lack) 88 bits

dnode 10 m

PWtx 31.32 mW

PWrrx 35.28 mW

PWidle 712 |_iW

PWsleep 144 nW

BO = SO (Std.) 6

802.15.4 standard because the length of active period and the beacon transmission time are managed appropriately. The probability of successful transmission of IEEE 802.15.4 standard decreases more as traffic load increases because the heavy collision occurs either between beacons or between beacon and data frame.

Figure 8 shows the network goodput against the INTV of data packets. The network goodput obtained by simulation is very close to that obtained by analysis model. It is obvious the network goodput of SABTS is higher than that of IEEE 802.15.4 standard especially when the traffic load increases. The probability of collisions of transmitting beacons and data packets can be decreased, because the beacon transmission time and active period length are accurately managed by SABTS. In the light traffic load (i.e., INTV is equal to 1 and 0.9), the network good-put of SABTS is almost same as those of IEEE 802.15.4 standard; however, SABTS outperforms IEEE 802.15.4 standard as the traffic load increases.

Figure 9 shows the network energy consumption against the INTV of data packets. SABTS consumes lesser network energy than that of IEEE 802.15.4

^ >h 0.25

IS I 3

« ±3 o.i

«m s!

ai m «

.2 g o.osf S-S

□ X, SABTS

œ x, std bo=so=6

KS Y, SABTS

□ Y, Std BO=SO=6

0.8 0.7 0.6 0.S 0.4 0.3 0.2 0.1 Interarrival time (seconds) Figure 6 Probabilities of collision, x, and entering next backoff, y, against the INTV of data packets.

SABTS (ana) SABTS (sim) Std BO=SO=6 (ana) Std BO=SO=6 (sim)

1 0.9 0.8 0.7 0.6 0.S 0.4 0.3 0.2 0.1

Interarrival time (seconds)

Figure 7 The probability of successful transmission against the INTV of data packets.

standard. The energy consumption is obtained by summing the energy consumptions of the PAN coordinator, coordinator nodes, and children device nodes. By SABTS, the coordinator nodes and device nodes can save energy consumption during the inactive period as shown in Figure 4. Moreover, SABTS gains the greater probability of successful transmission than that of IEEE 802.15.4 standard especially in heavy traffic load, which means that SABTS minimizes the energy consumption when retransmitting data packets.

Conclusions

In this article, SABTS has been proposed to adjust two system parameters of superframe (i.e., BO and SO) and set the precise time for beacon transmission to achieve low energy consumption and to alleviate the collision of beacon and data packet transmissions. This article presented a comprehensive Markov chain analysis of IEEE 802.15.4, specifically for cluster tree network, to predict the network goodput as well as the network energy

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

Interarrival time (seconds)

Figure 8 The network goodput against the INTV of data packets.

Interarrival time (seconds)

Figure 9 The network goodput against the INTV of data packets.

consumption. The validity of the analytical model is shown by closely matching its predictions to the simulation results. The results obtained by analytical model and simulation experiments show that SABTS performs better than IEEE 802.15.4 standard especially in the network goodput and the network energy consumption. However, this article pays much attention to the slotted CSMA/CA channel access mechanism within the CAP of a superframe, but for certain applications with low latency or specific bandwidth requirements it needs dedicated guaranteed time slots (GTS) channel to transmit its data packets without contention. For further research, the SABTS algorithm will be expected to consider GTS within the CFP of a superframe to improve the network performance.

Abbreviations

ACK: Acknowledgement; BE: Backoff exponent; BI: Beacon interval; BO: Beacon order; CAP: Contention access period; CCA: Clear channel assessment; CFP: Contention free period; CSMA/CA: Carrier sense multiple access with collision avoidance; CW: Contention window; IFS: Interframe space; INTV: Interarrivaltime of data packets; LR-WPAN: Low-rate wireless personalarea network; MAC: Medium access controlsublayer; NB: Number of backoffs; PAN: Personalarea network; SD: Superframe duration (in symbols); SDT: Superframe duration time (in seconds); SO: Superframe order; UBP: Unit backoff period (80 bits).

Competing interests

The authors declare that they have no competing interests.

Acknowledgments

This study was supported in part by the NationalScience Council(NSC) of Taiwan under Grant No. NSC 96-2221-E-011-055.

Author details

1NationalTaiwan University of Science and Technology, 43, Keelung Rd., Section 4, Taipei 106, Taiwan. 2Ling Tung University, 1, Ling Tung Rd., Taichung 408, Taiwan.

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doi:10.1186/1687-1499-2012-219

Cite this article as: Lee et al.: Analysis of superframe adjustment and beacon transmission for IEEE 802.15.4 cluster tree networks. EURASIP Journal on Wireless Communications and Networking 2012 2012:219.

Received: 24 March 2012 Accepted: 4 June 2012 Published: 17 July 2012