Huai-Kuei Wu
Department of Information Networking and System Administration, Ling Tung University,
Taichung, Taiwan
Bih-Hwang Lee and M. Udin Harun Al Rasyid Department of Electrical Engineering, National Taiwan University of Science and Technology,
Taipei, Taiwan
Abstract—The personal area network (PAN) coordinator periodically transmits beacon frames to coordinator nodes as well as the coordinator nodes periodically transmit beacon frames to device nodes in the cluster tree topology of IEEE 802.15.4. The challenge in cluster tree network is the collisions between beacons or even between beacon and data frames, which degrades the network performance. In order to improve the collisions, this paper proposes the superframe adjustment and beacon transmission scheme (SABTS) by assigning the accurate values of beacon order and superframe order for PAN coordinator, cluster coordinators and device nodes, and deciding the precise time for beacon transmission of PAN and coordinator nodes. A Markov chain model for cluster tree network is developed with taking into account packet retransmission, acknowledgement, and defer transmission. Both analytical and simulation results present that SABTS performs better than IEEE 802.15.4 standard in terms of the probability of successful transmission, network goodput, and energy consumption.
Keywords: Markov chain, cluster tree network, IEEE 802.15.4, wireless sensor networks.
I. INTRODUCTION
The IEEE 802.15.4 standard has 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 standard has three kinds of topology: star topology, peer-to-peer topology, and cluster tree topology, which can operate on beacon and non-beacon enabled modes. In cluster tree topology, the PAN coordinator periodically transmits beacon frames to coordinator nodes as well as the coordinator nodes periodically transmit beacon frames to device nodes. The 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 [2-3]. In other words, it is a crucial challenge on the cluster scheduling and collision avoidance in cluster tree network.
In beacon enabled mode, each node employs two system parameters: beacon order (BO) and superframe order (SO), which define the beacon interval (BI) and superframe duration (SD), respectively. To solve the aforementioned challenge, a
time division beacon scheduling (TDBS) and superframe duration scheduling (SDS) 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 SDS 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 PAN coordinator of MDS 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 paper proposes the superframe adjustment and beacon transmission scheme (SABTS) which is based on the IEEE 802.15.4 slotted carrier sense multiple access with collision avoidance (CSMA/CA), to assign the accurate values of BO and SO for 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 [4-8]. Several modified Markov chain model including packet retransmissions have been investigated but not consider the defer transmission [9-11]. The improved Markov chain models with considering the defer transmission are proposed [12], [13]. An analytical model based on Markov chain for multi-hop cluster network has been studied without taking into account the acknowledgement (ACK) to confirm successful of data packet transmission, the defer transmission, and packet retransmission [14]. 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 [13].
II. THE DESCRIPTION OF SABTS
The cluster tree network is formed by several coordinators that send beacon frames regularly to the device nodes of their cluster. However, if the coordinator nodes send beacon frames
in the same time, the collisions will happen among these beacon frames. Consequently, the children nodes in the cluster cannot synchronize and communicate with their coordinator.
SABTS aims to assign the accurate values of BO and SO for PAN coordinator, cluster coordinators and device nodes, and to decide the precise time for beacon transmission of PAN and coordinator nodes.
In order to reduce the collisions of beacon transmission among coordinator nodes, SABTS adjusts the beacon starting time of PAN and coordinator nodes. Let denote TxOffsetPAN
and TxOffseti as the beacon starting time of PAN and the beacon starting time of the ith coordinator node, respectively.
TxOffsetPAN starts at the beginning of superframe, and then TxOffseti is adjusted by Eq. (9), where SDcoordi-1 denotes superframe duration of the (i-1)th coordinator node.
In order to guarantee the data traffic transmission, the beacon interval should be the round function to the interarrival time of data packets (INTV). Let denote BOPAN be the beacon order for PAN coordinator, which can be obtained by Eq. (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 62500 symbol/sec, 60 symbols and 16 slots, respectively. To reduce beacon collision between parent coordinator and children coordinator, the different BO between coordinators at different depth can be obtained by Eq.
(2), where BOcoord is the beacon order for coordinator. PAN coordinator might often be powered; therefore the superframe order for PAN coordinator (SOPAN) can be set to be its BOPAN
as shown in Eq. (3). In the superframe duration (SD), i.e., active period, we assume there is no contention free period (CFP), hence the superframe duration of coordinator (SDcoord) consists of contention access period (CAP) and beacon as defined in Eq. (4), where EstimatedCAPcoord denotes the estimated contention access period for coordinator and Lbeacon
denotes the length of beacon and is equal to 190 symbols.
.
=1
+ , i
Rs TxOffsetPAN LBeacon
i =
Based on the aforementioned description, SABTS can be resumed by flowchart as shown in Fig. 1. In this paper, we consider a cluster tree topology with 1 PAN, 3 coordinator nodes, and 9 device nodes as shown in Fig. 2. Fig. 3 shows an example of the superframe adjustment and precise time for beacon transmission for the cluster tree topology of Fig. 2, while INTV of each device node is equal to 0.1. 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. Moreover, we get the different starting time of beacon transmission among coordinator nodes to avoid beacon collisions.
Calculate BOPAN and SOPAN
by Eq. (1) and Eq. (3)
Calculate BOcoord and SOcoord
by Eq. (2) and Eq. (7)
Calculate BOdev and SOdev
by Eq. (8) coord EstimatedCAP L
SD = + (4)
EstimatedCAPcoord is equal to the beacon interval of coordinator (BIcoord) divided by the number of coordinator nodes (Ncoord), as shown in Eq. (5). Using Eqs. (4) and (5), SDcoord can be obtained as shown in Eq. (6). Therefore, the value of superframe order for coordinator (SOcoord) can be obtained by Eq. (7). BO and SO for device nodes (i.e., BOdev
and SOdev) are decided by its coordinator node, which are equal to BO and SO of its coordinator node as shown in Eq.
(8).
Dev2
Fig. 2 The cluster tree topology
Fig. 3 An example of SABTS for three coordinator nodes
III. 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. The Markov chain can be obtained by modifying the model in [13], whose state transition diagram is shown as Fig. 4. Let bi,j,k 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, as shown in Eq. (10), where bi,-1,k, bi,-2,k and bi,-3,k are the stationary probabilities for the first clear channel assessment (CCA1), the second clear channel assessment (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 Si,k
and Ci,k as shown in Eqs. (11) and (12), respectively, where m
and R are the maximum number of backoff stage and retransmissions, i.e., equal to 4 and 3, respectively.
bi,j,k = P{s(t)=i, c(t)=j, r(t)=k},
We will explain the parameters used in the Markov chain model as follows. The IDLE state is the state that a device node has no packet to transmit. Let wi =2BEibe the backoff window at the ith backoff stage of a device, where backoff exponent 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, where Ldata is the packet length (in bits) and Rb is the bit data rate (i.e., 250 kbps).
The MAC sublayer should transmit packet if the remaining CSMA-CA algorithm steps, i.e., two CCA analyses, frame transmission, and any acknowledgement, 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, where Ttxcca, Ttx, Tack and Ttxack are the CCA transmission time, packet transmission time, time to wait for acknowledgement (ACK), and time to transmit ACK from receiver to transmitter node, respectively.
Fig. 4 Markov chain model for CSMA-CA
Fig. 5 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 interarrival time of data packets by analytical model. The probabilities of X and Y of SABTS are lesser than those of IEEE 802.15.4 standard. Fig. 6 shows the probabilities of successful transmission arrives at PAN coordinator (PsucPAN) against the interarrival time of data packets by analytical and simulation. SABTS obtains higher probabilities of successful transmission arrives at PAN coordinator than those of IEEE 802.15.4 standard. Fig. 7 shows the network goodput against the interarrival time 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. Fig. 8 shows the network energy consumption against the interarrival time of data packets. SABTS obtains lesser network energy consumption than that 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.
Let α and β be the probabilities of CCA1 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 be the probability of collision of packet transmission, i.e., the tagged node at packet transmission state while at least one of other nodes at packet transmission state in the same time, as a result the collision will happen and the device (transmitter) node retransmits data packet as its consequence.
Let us also denote Pfail1 and Pfail2 are the probabilities of fail transmission due to the maximum number of retransmissions after collisions and due to no channel to be found after reaching the maximum backoff stage at the maximum retransmission stage, respectively.
After a series of derivations, the number of successful packets received by PAN (NrecvPAN) and the network goodput (G), can be expressed by Eqs. (13) and (14), respectively, where Ndev, Nbeacon, PsucPAN, and Time are the number of device nodes in network, the number of observed beacon interval period of PAN, the probability of successful transmission from coordinator node to PAN coordinator, and observed simulation time (in second),
respectively. V. Conclusions
INTV Time P
NrecvPAN= Ndev sucPAN
(13)
In this paper, 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 collisions of beacon and data packet transmissions. This paper 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 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.
PAN
IV. 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 Fig. 2, where the distance between nodes (dnode) is equal to 10 meters. The packet arrival rate follows the Poisson distribution with interarrival time of data packets (INTV) from 0.1 to 1, where packets have the same length of 70 bytes. 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 [15], where the transmitting power, the receiving power, the idle power, and the sleeping power per time unit are 31.32 mW, 35.28 mW, 712 µW, and 144 nW, respectively [12]. 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.
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 for network goodput, total network energy consumption, and the probability of successful packet transmission arrive at PAN.
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packets
Probabilities of collision, X and entering next backoff, Y
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
Interarrival time (seconds)
X, SABTS
Interarrival time (seconds)
Fig. 8 The network energy consumption against the interarrival time of data packets
Fig. 5 Probabilities of collision, X, and entering next backoff, Y, against the interarrival time of data packets