# Delay Analysis of GTS Bridging between IEEE 802.15.4 and  IEEE 802.11 Networks for Healthcare Applications

Authors: Jelena Mišić; Xuemin (Sherman) Shen
Journal: International Journal of Telemedicine and Applications
 (2009)

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## Abstract

We consider interconnection of IEEE 802.15.4 beacon-enabled network cluster with IEEE 802.11b
network. This scenario is important in healthcare applications where IEEE 802.15.4 nodes comprise
patient's body area network (BAN) and are involved in sensing some health-related data. BAN nodes
have very short communication range in order to avoid harming patient's health and save energy.
Sensed data needs to be transmitted to an access point in the ward room using wireless technology
with higher transmission range and rate such as IEEE 802.11b. We model the interconnected network
where IEEE 802.15.4-based BAN operates in guaranteed time slot (GTS) mode, and IEEE 802.11b
part of the bridge conveys GTS superframe to the 802.11b access point. We then analyze the
network delays. Performance analysis is performed using EKG traffic from continuous telemetry, and
we discuss the delays of communication due the increasing number of patients.


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## Body

## 1. Introduction

Wireless sensor networks in healthcare applications
require small lightweight devices with sensing, computational, and communication
features to be unobtrusively placed on patient's body. They need to communicate
results of sensing of healthcare data periodically over very short range to the
devices which can be carried by the patient or mounted on patient's bed. We
refer to the wireless sensor network on patient's body as body area network
(BAN). Low power, that is, short communication range of wireless sensors is
needed for health, interference, and security reasons. Devices which collect
the results of measurements need to provide some limited data processing and
aggregation, add security/privacy functions, and communicate aggregated data to
the LAN access point in patient's ward room as shown in Figure1. We refer to
this device as bridge.Figure 1
Networking structure of the ward room with BANs, bridges, and ward LAN.In this paper, we consider interconnection of IEEE
802.15.4 beacon-enabled network cluster with IEEE 802.11b network. The IEEE
802.15.4 nodes comprise patient's body area network (BAN) and are involved in
sensing some health-related data which will be transmitted to the access point
in the ward room using wireless technology such as IEEE 802.11b. It is clear
that the network performance depends on the characteristics of the interconnection
device. Therefore, we model the interconnected network where IEEE
802.15.4-based BAN operates in guaranteed time slot (GTS) mode, and IEEE
802.11b part of the bridge conveys GTS superframe to the 802.11b access point.
We then analyze the impact of important parameters such as acceptable load
ranges and the delays of communication due the increasing number of patients.
Since real-time operation of the bridges is necessary for many measurements in
hospitals besides intensive care units (ICUs), we will study communications
through the bridge for simple case of EKG continuous telemetry.The remainder of the paper is organized as follows. We
review the networking aspect of healthcare wireless sensor networks with the
emphasis on continuous electrocardiogram telemetry in Section2. In Section 3,
we review the properties of 802.15.4 beacon-enabled MAC and IEEE 802.11b MAC
related to the operation of bridge. In Section 4, we present the concepts of
bridge design between IEEE 802.15.4 BAN and IEEE 802.11b ward LAN. Analytical
model of bridge where BAN operates in GTS mode is presented in Section 5. In
Section 6, we present performance results for interconnected clusters under
various modes of bridge access. Finally, Section 7 concludes the paper.


## 2. Wireless Sensor Networks for Healthcare

In today's hospitals, there is an urgent need for
timely monitoring the health status of many patients, especially those with
respiratory and cardiac problems. The need for continuous fetal heart rate
monitoring as well as monitoring for movements of patients suffered from stroke
or Parkinson's disease is also high. Although these applications require
different kinds of sensors to measure levels of oxygen in blood, heart rate, or
motion of body parts, there is unified need for sensors to be unobtrusively
attached to the patient's body and for measured data to be transmitted in a
reliable and secure way in order to be recorded on monitoring devices in real
time. Most of the health variables are periodic and have to be periodically sampled
and digitized. The sampling period has to be at least twice as large as the
highest frequency of the healthcare variables.Recently, several medical telemetry applications have
been prototyped so far and moved to production phase such as pulse oximeters,
EKG devices, and motion analysis systems [1]. Wireless transmission is currently implemented using
Bluetooth IEEE 802.15.1 and IEEE 802.11b technologies although IEEE 802.15.4
emerges as most suitable for medical applications due to its low-power and
low-bandwidth requirements. Some initial work in this area has been reported in
[1–4]. However, current reports on wireless healthcare
products are focused on reliable hardware and software designs of sensor
modules while the wireless transmission has been considered in testing phase
and for single device only. There is an area of research involving coordination
and real-time transmission of large number of healthcare measurements, which
has not attracted sufficient attention. In this paper, we will address the
following problems.(1)
Interconnection of low-power IEEE 802.15.4 motes
(which are convenient for attachment on patient's body) with IEEE 802.11b
network which has larger bandwidth and larger transmission range. We will
design bridge between IEEE 802.15.4 wireless communication interface(s)
residing at patient's body and IEEE 802.11b residing at bedside or carried in
patient's pocket. More specifically, we will use TDMA feature of IEEE 802.15.4
called guaranteed time slots to fill it with digitized samples and pass it to
the interface of IEEE 802.11b for further transmission to the hospital room's
access point.(2)
Analysis of delay of real-time health measurement
data incurred by transmission technologies. We will use measurement data for
electrocardiogram and analyze traffic when the number of patients increases.Security is another important issue in wireless
healthcare sensor networks. In this paper, we will also address data integrity
issue by assuming that there is a shared secret key between 802.15.4 sensor
mote and bridge device. Secret key will be used to provide message
authentication code in each 802.15.4 superframe (packet) using HMAC function
[5, 6].


### 2.1. EKG Measurement

Electrocardiogram (ECG or EKG) is a surface
measurement of the electrical potential generated by the electrical activity,
which controls pumping action of cardiac muscle fibers. These electrical
impulses generate voltage, which further generates current flow in the torso
and potential differences on the skin. Standard EKG monitoring involves
short-term (≤30 seconds) monitoring of heart pulses using
12 skin electrodes (called leads) placed at designated locations on the
patient's body including chest, arms, and legs. Each pair of leads measures
voltage which gives one aspect of the heart's activity. An EKG picture produced
by 12 leads allows diagnosis of wide range of heart problems. However, this
measurement is short-term and requires wired connection between the patient and
electrocardiograph.In many cases, however, it is necessary to have
continuous and tetherless measurements of heart rate. For such application,
only three leads placed at patient's upper and lower chest can trace a wide
range of cardiac arrhythmias. One node of these three collects signals,
amplifies the signal difference, samples the amplified analog signal, and
digitizes it. Standard clinical EKG application has the bandwidth of 0.05 Hz to
100 Hz. For pacemaker detection, upper frequency can be up to 1 kHz. There are
many design issues out of scope of this work related to noise suppression and
filtering frequencies from power line and respiration. In this paper, we assume
that upper frequency of the EKG signal is 100 Hz. EKG signal is sampled with
200 Hz, and each sample is digitized with 12 bits [3]. Therefore, basic bandwidth of EKG signal in standard
continuous telemetry is only 2400 bps.


## 2.1. EKG Measurement

Electrocardiogram (ECG or EKG) is a surface
measurement of the electrical potential generated by the electrical activity,
which controls pumping action of cardiac muscle fibers. These electrical
impulses generate voltage, which further generates current flow in the torso
and potential differences on the skin. Standard EKG monitoring involves
short-term (≤30 seconds) monitoring of heart pulses using
12 skin electrodes (called leads) placed at designated locations on the
patient's body including chest, arms, and legs. Each pair of leads measures
voltage which gives one aspect of the heart's activity. An EKG picture produced
by 12 leads allows diagnosis of wide range of heart problems. However, this
measurement is short-term and requires wired connection between the patient and
electrocardiograph.In many cases, however, it is necessary to have
continuous and tetherless measurements of heart rate. For such application,
only three leads placed at patient's upper and lower chest can trace a wide
range of cardiac arrhythmias. One node of these three collects signals,
amplifies the signal difference, samples the amplified analog signal, and
digitizes it. Standard clinical EKG application has the bandwidth of 0.05 Hz to
100 Hz. For pacemaker detection, upper frequency can be up to 1 kHz. There are
many design issues out of scope of this work related to noise suppression and
filtering frequencies from power line and respiration. In this paper, we assume
that upper frequency of the EKG signal is 100 Hz. EKG signal is sampled with
200 Hz, and each sample is digitized with 12 bits [3]. Therefore, basic bandwidth of EKG signal in standard
continuous telemetry is only 2400 bps.


## 3. Basic Properties of IEEE Std 802.15.4  and IEEE 802.11b MACs

### 3.1. Basic Properties of IEEE Std 802.15.4 MAC

In beacon-enabled networks, the personal area network
(PAN) coordinator divides its channel time into superframes [7]. Each superframe begins with
the transmission of a network beacon, followed by an active portion and an
optional inactive portion, as shown in Figure 2. The coordinator interacts with
its PAN during the active portion of the superframe, and may enter a low-power
mode during the inactive portion. Raw data rate in industrial, scientific, and
m edical (ISM) band is 250 Kbps. Basic time unit in the standard is backoff
period which contains 10 bytes. Duration of active and inactive parts of the
superframe is regulated with MAC parameters SO=0,…,14 which is known as macSuperframeOrder and BO=0,…,14, also called macBeaconOrder. Active superframe
part is divided into 16 slots. Each slot consists of 3⋅2SO backoff periods, which gives the shortest
active superframe duration aBaseSuperframeDuration of 48 backoff periods
when SO=0. Duration of an active superframe part is denoted as SD = aBaseSuperframeDuration⋅2SO (superframe duration). The time interval
between successive beacons is equal to BI = aBaseSuperframeDuration*2BO. The duration of the inactive period of the superframe can be determined as I = aBaseSuperframeDuration*(2BO−2SO). Period between the beacons is equal to the active superframe duration only if
there is no inactive period in the cluster time, and, otherwise, it is larger
than active superframe part, that is, BO≥SO.Figure 2
The composition of the superframe under IEEE Std 802.15.4 (adopted
from [7]).An active superframe part consists of contention part
and TDMA, that is, guaranteed time slot (GTS) part. GTS bandwidth must be
requested by the node using the MAC command frame. Coordinator allocates the
GTS bandwidth in multiples of slots. One slot contains3*2SO backoff periods. Data transfer from a node to
PAN coordinator can be done in GTS slots or using slotted CSMA-CA access
described below. Slotted CSMA-CA algorithm consists of backoff activity, two
clear channel assessments (CCAs), packet transmission, and optionally receipt
of the acknowledgment. Backoff value is uniformly chosen in the range (0,w15−1) which is called contention window. During
backoff countdown node does not listen to the medium, and checks the activity
on the medium only twice when backoff count is finished. By default, the node
can have m15+1=5 transmission attempts with backoff window
sizes W15,0=8W15,1=16, W15,2=32, W15,3=32, and W15,4=32. To avoid confusion, we will use subscript 15 to label MAC parameters which have
their counterparts in the IEEE 802.11b standard.


### 3.2. Basic Properties of IEEE 802.11b Needed for Bridging

IEEE 802.11 has much more sophisticated CSMA-CA scheme
at the MAC layer. In this protocol (opposite to IEEE 802.15.4), a station
having a packet to transmit must initially listen to the channel to check if
another station is transmitting. If there is no transmission in distributed
interframe space (DIFS) time interval, the transmission can proceed. If medium
is busy, the station has to wait until current transmission has finished. Then,
station will wait for DIFS time period and then generate a random backoff time
before transmitting its frame. This backoff time is uniformly chosen in the
range (0,w11−1). Backoff counter will be decremented after
each slot time given that
transmission medium is free, otherwise, its value will be frozen until medium
becomes free again for DIFS time units (slot time is derived from the
propagation delay time to switch from receiving to transmitting mode and time
to pass the information about the physical channel state to MAC layer. It
actually corresponds to backoff period from IEEE 802.15.4). Station will
transmit when its backoff counter reaches zero value. When the packet is
received, receiver replies with acknowledgment (ACK) packet after short
interframe space (SIFS) time interval. Whenever packet collision occurs,
acknowledgment will not be received within SIFS + ACK time, and transmission
has to be reattempted with doubled contention window. If starting window size
is w11=W11,min after m11 retransmissions, its maximal value will become W11,max=2m11W11,min (in order to distinguish between similar
variables in two standards, we use subscript 11). In our model, we assume that
if packet experiences more than m11 collisions, last backoff stage will be entered
for every subsequent retransmission until frame is successfully transmitted. In
order to limit packet collision time, and guard against hidden terminal
problem, the standard allows small reservation packets request to send (RTS)
and clear to send (CTS) sent using CSMA-CA. After transmission of RTS packet,
receiver replies with CTS after short interframe space(SIFS) time. Due to
sensitivity of healthcare applications, we will assume that RTS/CTS scheme is
used to protect packets with measurement data of health variables.The IEEE 802.11b standard is mostly deployed in
current implementations of healthcare wireless sensor networks [1]. The IEEE 802.11b has
higher-speed physical layer than original IEEE 802.11 and allows transmissions
at 1, 2, 5.5, and 11 Mbps, while IEEE 802.11 supports transmission at 2 Mbps.
However, physical layer header is transmitted at 1 Mbps, MAC layer header and
payload can be transmitted at 1, 2, 5.5, or 11 Mbps while control frames RTS,
CTS, and ACK are transmitted at 1 or 2 Mbps. It is also worth noting that since
IEEE 802.11b adapters transmit at a constant power, distances covered with
transmission speeds of 1, 2, 5.5, and 11 Mbps are 120, 90, 70, and 30 m,
respectively [8].Starting with seminal work in [9], performance of IEEE 802.11
has been extensively studied first for saturated case and later for unsaturated
case [10–13]. Standard extension IEEE
802.11e enhances CSMA-CA access by introducing different interframe spaces and
different backoff window ranges for different traffic classes. This scheme has
been modeled using similar approach (although more complex) as basic 802.11
scheme in [14–16]. However, given the fact
that all BANs have the same priority and short packet sizes with sensing
information, we believe that IEEE 802.11b can serve the purpose and that
deployment of IEEE 802.11e at this point may not be necessary.


## 3.1. Basic Properties of IEEE Std 802.15.4 MAC

In beacon-enabled networks, the personal area network
(PAN) coordinator divides its channel time into superframes [7]. Each superframe begins with
the transmission of a network beacon, followed by an active portion and an
optional inactive portion, as shown in Figure 2. The coordinator interacts with
its PAN during the active portion of the superframe, and may enter a low-power
mode during the inactive portion. Raw data rate in industrial, scientific, and
m edical (ISM) band is 250 Kbps. Basic time unit in the standard is backoff
period which contains 10 bytes. Duration of active and inactive parts of the
superframe is regulated with MAC parameters SO=0,…,14 which is known as macSuperframeOrder and BO=0,…,14, also called macBeaconOrder. Active superframe
part is divided into 16 slots. Each slot consists of 3⋅2SO backoff periods, which gives the shortest
active superframe duration aBaseSuperframeDuration of 48 backoff periods
when SO=0. Duration of an active superframe part is denoted as SD = aBaseSuperframeDuration⋅2SO (superframe duration). The time interval
between successive beacons is equal to BI = aBaseSuperframeDuration*2BO. The duration of the inactive period of the superframe can be determined as I = aBaseSuperframeDuration*(2BO−2SO). Period between the beacons is equal to the active superframe duration only if
there is no inactive period in the cluster time, and, otherwise, it is larger
than active superframe part, that is, BO≥SO.Figure 2
The composition of the superframe under IEEE Std 802.15.4 (adopted
from [7]).An active superframe part consists of contention part
and TDMA, that is, guaranteed time slot (GTS) part. GTS bandwidth must be
requested by the node using the MAC command frame. Coordinator allocates the
GTS bandwidth in multiples of slots. One slot contains3*2SO backoff periods. Data transfer from a node to
PAN coordinator can be done in GTS slots or using slotted CSMA-CA access
described below. Slotted CSMA-CA algorithm consists of backoff activity, two
clear channel assessments (CCAs), packet transmission, and optionally receipt
of the acknowledgment. Backoff value is uniformly chosen in the range (0,w15−1) which is called contention window. During
backoff countdown node does not listen to the medium, and checks the activity
on the medium only twice when backoff count is finished. By default, the node
can have m15+1=5 transmission attempts with backoff window
sizes W15,0=8W15,1=16, W15,2=32, W15,3=32, and W15,4=32. To avoid confusion, we will use subscript 15 to label MAC parameters which have
their counterparts in the IEEE 802.11b standard.


## 3.2. Basic Properties of IEEE 802.11b Needed for Bridging

IEEE 802.11 has much more sophisticated CSMA-CA scheme
at the MAC layer. In this protocol (opposite to IEEE 802.15.4), a station
having a packet to transmit must initially listen to the channel to check if
another station is transmitting. If there is no transmission in distributed
interframe space (DIFS) time interval, the transmission can proceed. If medium
is busy, the station has to wait until current transmission has finished. Then,
station will wait for DIFS time period and then generate a random backoff time
before transmitting its frame. This backoff time is uniformly chosen in the
range (0,w11−1). Backoff counter will be decremented after
each slot time given that
transmission medium is free, otherwise, its value will be frozen until medium
becomes free again for DIFS time units (slot time is derived from the
propagation delay time to switch from receiving to transmitting mode and time
to pass the information about the physical channel state to MAC layer. It
actually corresponds to backoff period from IEEE 802.15.4). Station will
transmit when its backoff counter reaches zero value. When the packet is
received, receiver replies with acknowledgment (ACK) packet after short
interframe space (SIFS) time interval. Whenever packet collision occurs,
acknowledgment will not be received within SIFS + ACK time, and transmission
has to be reattempted with doubled contention window. If starting window size
is w11=W11,min after m11 retransmissions, its maximal value will become W11,max=2m11W11,min (in order to distinguish between similar
variables in two standards, we use subscript 11). In our model, we assume that
if packet experiences more than m11 collisions, last backoff stage will be entered
for every subsequent retransmission until frame is successfully transmitted. In
order to limit packet collision time, and guard against hidden terminal
problem, the standard allows small reservation packets request to send (RTS)
and clear to send (CTS) sent using CSMA-CA. After transmission of RTS packet,
receiver replies with CTS after short interframe space(SIFS) time. Due to
sensitivity of healthcare applications, we will assume that RTS/CTS scheme is
used to protect packets with measurement data of health variables.The IEEE 802.11b standard is mostly deployed in
current implementations of healthcare wireless sensor networks [1]. The IEEE 802.11b has
higher-speed physical layer than original IEEE 802.11 and allows transmissions
at 1, 2, 5.5, and 11 Mbps, while IEEE 802.11 supports transmission at 2 Mbps.
However, physical layer header is transmitted at 1 Mbps, MAC layer header and
payload can be transmitted at 1, 2, 5.5, or 11 Mbps while control frames RTS,
CTS, and ACK are transmitted at 1 or 2 Mbps. It is also worth noting that since
IEEE 802.11b adapters transmit at a constant power, distances covered with
transmission speeds of 1, 2, 5.5, and 11 Mbps are 120, 90, 70, and 30 m,
respectively [8].Starting with seminal work in [9], performance of IEEE 802.11
has been extensively studied first for saturated case and later for unsaturated
case [10–13]. Standard extension IEEE
802.11e enhances CSMA-CA access by introducing different interframe spaces and
different backoff window ranges for different traffic classes. This scheme has
been modeled using similar approach (although more complex) as basic 802.11
scheme in [14–16]. However, given the fact
that all BANs have the same priority and short packet sizes with sensing
information, we believe that IEEE 802.11b can serve the purpose and that
deployment of IEEE 802.11e at this point may not be necessary.


## 4. GTS Bridge Design

Bridge consists of IEEE 802.15.4 PAN coordinator and
ordinary IEEE 802.11b interface. These two components are interconnected
through a buffer which is filled by the PAN coordinator and emptied by IEEE
802.11b packet transmission facility. IEEE 802.15.4 PAN coordinator interface
and IEEE 802.11b interface have their wireless transmit/receive antennas. Both
networks operate in ISM band as shown in Figure3, and there is a need to
coordinate operation of bridge's interfaces either in TDMA or FDMA manner. From
Figure 2 and discussion in Section 3.1, we observe that it is possible to
achieve TDMA coordination between the interfaces using the fact that WLAN
bridge interface can operate during silent BAN periods. However, in the presence
of multiple BANs within WLAN coverage, this approach requires synchronization
of BAN beacons (we assume that interference among BANs is avoided by separation
in space or by allocating separate channels as shown in Figure 3). Also
bandwidth allocation through SO and BO parameters must be achieved such that bridged
traffic from all BANs can be delivered during (common) inactive superframe
part.Figure 3
Used spectra of wireless LAN and PAN technologies in ISM band.It is much more convenient if operation of BAN and
WLAN is separated in frequency domain because BAN beacons do not need to be
synchronized and more bandwidth is allocated to the bridge. BAN channels should
be chosen in such way that they do not overlap with ward WLAN channel. From
Figure3, we see that each WLAN channel overlaps with four BAN channels.
Therefore, for each ward WLAN channel, 12 out of 16 BAN channels should be used
in order to avoid interference.Duration of beacon intervalBI is tuned according to period of sensed health
variable. Duration of active period SD is chosen in order to(1)
achieve data transmission with high success
probability in the case of CSMA-CA MAC,(2)
in case of GTS transmission of sensed data,
GTS bandwidth has to match necessary size of a group of GTS packets and
acknowledgment lanes where group size corresponds to the number of IEEE
802.15.4 nodes in BAN. However, some small contention periods must be reserved
in the superframe in order to communicate command frames between sensing nodes
and PAN coordinator.Since bandwidth of IEEE 802.11b is much larger than
the bandwidth of IEEE 802.15.4 BAN, transmission of one IEEE 802.11b packet will
take short time, and rest of active period can be used to exchange some command
data between the bridge and access point of the ward room. Between two
transmission phases, sensing nodes and bridge are idle and can turnoff their
transmitters and receivers. Duration of this sleep time isBI−SD. We make an important remark about time scales in IEEE 802.15.4 and IEEE
802.11b. Duration of backoff period in 802.15.4 is 320 microseconds, and with
raw data rate of 250 Kbps, one backoff period carries 10 bytes of data. IEEE
802.15.4 slot duration is 3*2SO backoff periods. On the other hand, IEEE
802.11b backoff counter is decremented after slot time which is equal to 20
microseconds. Therefore, time-scale translation is needed between two networks.We assume that traffic intensity due to sensing of
health variables in BAN will be light given that the number of nodes is lower
than 16, and that offered load per node is lower than few Kbps. This is well
below the rate of 250 Kbps supported by IEEE 802.15.4.Bridge’s buffer will be served by IEEE 802.11b CSMA-CA MAC for which the Markov chain model is presented in Figure4. In our modeling, we will assume that data buffers at BAN nodes and at the
bridge are infinite. Although, this assumption may appear unrealistic for
sensor nodes (and we have always modeled small finite buffers in our work
[17]); offered load to
the node is low so that node's buffer is empty most of the time. Therefore,
both the queuing model with finite and infinite buffers will give similar
results. Given the lower computational complexity of the model with infinite
buffer, we use it in our analysis although use of finite buffer model is
straightforward. Assumption of infinite buffer at the bridge is reasonable
since it may contain more complex hardware and software, and offered load per
bridge is low-to-moderate, depending on the number of patients in vicinity of
access point.Figure 4
Markov chain for IEEE 802.11b coupled with device's queue.


## 5. Analytical Model of GTS Bridging

In general case of GTS, bridge sensors may report
different medical variables, such as heart rate, level of oxygen in blood, and
temperature. Each sensor is allocated a number of slots in uplink direction to
carry uplink sensing data and a slot in downlink direction to carry
acknowledgment. We will refer to the number of slots in uplink direction
aspacket lane.PAN coordinator receives data from stations in
separate GTS packet lanes, generates acknowledgments, and passes aggregated
packets to IEEE 802.11b buffer.Assume that each sensor needs to be served with data
rateDs bps. This results in allocation of ds packet lanes such that
(1)Ds=ds*3*2SO*8048*2BO*0.00032,
and that period between the
beacons BI=48*2BO*0.00032 matches the sampling period of health
variable. Assuming that there are n15<16 sensors in the BAN, each sensor will have one
GTS slot, and the last slot will contain aggregated acknowledgments for all
sensors. For larger number of sensors where 15(k−1)<n15≤15k period between the beacons has to be decreased k times, such that each superframe carries
readings from at most 15 sensors (and acknowledgments in the last GTS slot).For simplicity, letn15<16 and the payload of the IEEE 802.15.4
superframe becomes payload of IEEE 802.11b frame consisting of n15⋅ds⋅3⋅2SO⋅10 bytes. IEEE 802.11b frame length in bytes has
to be augmented with headers from physical and MAC 802.11b layer which is 50
bytes. Finally, we have to find frame size in 802.11b slots (backoff periods),
since each slot carries number of bits s11 equal to the product of raw data rate and slot
duration, and its value is equal to l11=(50+n15⋅ds⋅3⋅2SO⋅10)/s11.Duration of RTS, CTS, and ACK frames expressed in
slots will be denoted asrts, cts, and ack11, respectively (we will use subscript 11 to denote IEEE 802.11b whenever
potential ambiguity may arise between two standards). Duration of DIFS and SIFS
periods in slots will be denoted as difs and sifs.Probability generating function (PGF) for the
successful packet transmission time is equal to [12]
(2)St(z)=zrts+cts+l11+3sifs+difs+ack11,
with average value St¯=St′(1)=rts+cts+l11+3sifs+difs+ack11. In the case of collision of RTS packets activity on medium has PGF:
(3)Ct(z)=zrts+cts+sifs+difs,
with average value Ct¯=Ct′(1)=rts+cts+sifs+difs.Assume that there aren11 bridges attached to the IEEE 802.11b access
point. Each bridge communicates the same kind of sensing traffic towards the
access point. Using the assumption from previous work [2–5, 9, 14, 15] that probability of
successful transmission is independent of the backoff stage, we will denote it as γ11 while collision probability is 1−γ11. Access probability is also independent of the backoff stage and is denoted as τ11. Relationship between these two probabilities is
(4)γ11=(1−τ11)(n11−1).Probability that medium will be active during the
backoff countdown of one station has two components. First one is the
probability that station sensed the medium busy due to successful transmission
of one amongn11−1 stations, and it has the value pbs=(n11−1)τ11(1−τ11)(n11−2). The other component is the probability that station senses the medium busy due
to collision among some of n11−2 other stations and has the value pbc=1−(1−τ11)(n11−1)−pbs. Their sum is the probability that medium is busy during the backoff countdown,
and that backoff counter is frozen pb=pbs+pbc=1−γ11. The PGF for the duration of time between two successive backoff countdowns is
represented with the following equation [12]:
(5)Hd(z)=zγ11+(pbcCt(z)+pbsSt(z))Hd(z).At this point, we note that duration of period between
two successive decrements of backoff counter is limited to the maximum packet
size. After transmission is finished and DIFS period passes any station doing
the backoff, countdown has to decrement its backoff counter at least once
before packet transmission:(6)B11,i(z)=∑k=0W11,i−11W11,iHdk(z)=HdW11,i(z)−1W11,i(Hd(z)−1),
where W11,i=2iW11,0 for i≤m11, and W11,i=2m11W11,0 for i>m11.Assuming that packet will be retransmitted until valid
acknowledgement is received, the PGF for the packet service time
becomes(7)T11(z)=∑i=1m11+1(∏j=0i−1B11,j(z))(1−γ11)(i−1)Ct(z)(i−1)γ11St(z)+(∏j=0m11B11,j(z))∑i=m11+1∞(B11,m11(z))(i−m11)×(1−γ11)(i−1)Ct(z)(i−1)γ11St(z),
and its average value is obtained as T11¯=T11′(1).


### 5.1. Markov Chain Model and Queuing Model for the GTS Bridge's Output

In the derivations above, we have derived probability
of successful transmission and probability of freezing the backoff period using
the variable which represented access probability per 802.11b slotτ11. Access probability, on the other hand, has to be derived using two modeling
components. First one is the Markov chain which represents conditional
activities within the CSMA-CA process. Second component indicates the
probability that bridge will be idle and that it will not perform backoff count
and attempt transmission. This happens only when the bridge's packet buffer is
empty. In order to find this probability, we must deploy queuing theory and we
have to know the arrival process to the bridge's queue, the size of the
bridge's queue, and the probability distribution packet service time by which
packets depart from the queue. Therefore, Markov chain model and queuing model
of the bridge are coupled and have to be modeled and solved simultaneously. We
will first solve the Markov chain for CSMA-CA MAC using the variable π11,0 which represents the probability that bridge's
buffer is empty after the packet departure.Since similar Markov chain models have been solved
with detailed steps of setting transition probabilities in the past in
[9–12], we will just state the
most important steps in derivation of access probability. Markov chain {s(t),b(t)} is discrete as transitions are observed at ends of slot times. It is bidimensional (given that γ11 and pb are independent of backoff stage) where s(t) represents backoff stage and b(t) represents value of backoff counter. Corresponding states of the Markov chain will have the state probabilities yi,j, i=0,…,m11, j=0,…,W11,i−1. Since packet sizes in this application are relatively small,
we have included the states when transmission of RTS/CTS and data packets is going on. Access probability is equal to τ11=∑i=0m11yi,0.Probability of idle state when bridge's buffer is
empty is equal to(8)Pidle=τ11γ11π11,0ϕ11,
where ϕ11 denotes average packet arrival rate of the
arrival process to the bridge (note that packet arrival process is not Poisson
when packets arrive from IEEE 802.15.4 BAN to the bridge).By inserting all necessary transition probabilities,
we obtain(9)τ11=(γ11π11,0ϕ11+∑j=0m11γ11(1−γ11)j+∑j=0m11(W11,j−1)γ11(1−γ11)j2(1−pb)(pbcCt¯+pbsSt¯)+(W11,m11−1)(1−γ11)(m11+1)2(1−pb)(pbcCt¯+pbsSt¯)+γ11St¯+(1−γ11)Ct¯)−1.


### 5.2. Derivation of Probability Distribution of Occupancy of Bridge's Buffer

As we mentioned, we will assume that bridge's buffer
has an infinite capacity. Rationale behind that is that bridge device indeed
can have much larger memory than sensing device and that utilization of the
bridge is expected to be light-to-moderate. Therefore, bridge is not expected
to work in the regime close to its stability limit where it can reject packets
due to finite buffer.In GTS-based bridge period between arrivals of IEEE
802.15.4 superframes to the bridge is constant, and bridge can be modeled as
D/G/1 queuing system modeled at Markov points of packet departures from the
bridge. Let us denote period of arrival of sensing information from all the
sensors to bridge asΦ11=1/ϕ11. As mentioned earlier, if the number of sensors n15<16, then Φ11=BI, and if 15(k−1)<n15≤15k, then Φ15=kBI. Assume that PGF for the bridge's packet service time can be expressed as the
series as T11(z)=∑k=0∞t11,kzk. Probability of l, l=0,1,… arrivals of GTS superframes during packet
service time of the bridge has the value
(10)a11,l=Prob[lΦ11≤T11<(l+1)Φ11]=∑j=lΦ11(l+1)Φ11−1t11,j.PGF for the probability distribution of the number of
802.15.4 superframe arrivals during packet service time by the 802.11b
interface isA11(z)=∑l=0∞a11,lzl. An equation which shows number of packets in bridge's buffer left after the
departure of the packet has the form
(11)π11,l=π11,0a11,l+∑j=1l+1π11,ja11,l−j+1.
By multiplying both left-hand
and right-hand side of (11) with zl and summing over l=0,…,∞, we obtain PGF for the number of packets left in the bridge's queue
after the departing packet Π11(z)=∑l=0∞π11,lzl as
(12)Π11(z)=A11(z)(1−ρ11)(1−z)A11(z)−z,
where ρ11=ϕ11T11¯ presents offered load to the bridge.


### 5.3. Output Process and Throughput

Output process
from bridge has the PGF for packet interdeparture times as(13)Δ11(z)=(1−π11,0)T11(z)+π11,0zΦ11T11(z).Assuming that there aren11 bridges communicating with access point
throughput in 802.11b LAN can be then presented with expression
(14)Θ11=n11l11−2Δ11¯,
where 2 slots correspond to header information.


### 5.4. Distribution of Packet Waiting Time in Bridge's Buffer

Assuming FIFO service discipline, packet arriving at the bridge has to wait for the currently
transmitted packet to depart and for complete service time of all packets
already queued. According to renewal theory, remaining service
time of the packet has PGF [18]
(15)T11+(z)=(1−T11(z))T11¯(1−z).Then, PGF for the waiting time of the packet has the form(16)W11(z)=π11,0+π11,1T11+(z)+π11,2T11+(z)T11(z)+π11,3T11+(z)(T11(z))2⋯=π11,0+T11+(z)(π11,1+π11,2T11(z)+π11,3(T11(z))2+⋯)=π11,0+T11+(z)Π11(T11(z))−π11,0T11(z)=π11,0(1+T11+(z)1−A11(T11(z))A11(T11(z))−T11(z)).Average delay can be obtained by differentiating (16)
and applying L'Hospital's rule:
(17)W11¯=ϕ11T11(2)2(1−ρ11),
where T11(2) denotes second moment of packet service time.
This result matches Pollaczek-Khinchin mean value formula [19].The complete access time which includes waiting time
and service time of the target packet is then equal toS11¯=W11¯+T11¯.


## 5.1. Markov Chain Model and Queuing Model for the GTS Bridge's Output

In the derivations above, we have derived probability
of successful transmission and probability of freezing the backoff period using
the variable which represented access probability per 802.11b slotτ11. Access probability, on the other hand, has to be derived using two modeling
components. First one is the Markov chain which represents conditional
activities within the CSMA-CA process. Second component indicates the
probability that bridge will be idle and that it will not perform backoff count
and attempt transmission. This happens only when the bridge's packet buffer is
empty. In order to find this probability, we must deploy queuing theory and we
have to know the arrival process to the bridge's queue, the size of the
bridge's queue, and the probability distribution packet service time by which
packets depart from the queue. Therefore, Markov chain model and queuing model
of the bridge are coupled and have to be modeled and solved simultaneously. We
will first solve the Markov chain for CSMA-CA MAC using the variable π11,0 which represents the probability that bridge's
buffer is empty after the packet departure.Since similar Markov chain models have been solved
with detailed steps of setting transition probabilities in the past in
[9–12], we will just state the
most important steps in derivation of access probability. Markov chain {s(t),b(t)} is discrete as transitions are observed at ends of slot times. It is bidimensional (given that γ11 and pb are independent of backoff stage) where s(t) represents backoff stage and b(t) represents value of backoff counter. Corresponding states of the Markov chain will have the state probabilities yi,j, i=0,…,m11, j=0,…,W11,i−1. Since packet sizes in this application are relatively small,
we have included the states when transmission of RTS/CTS and data packets is going on. Access probability is equal to τ11=∑i=0m11yi,0.Probability of idle state when bridge's buffer is
empty is equal to(8)Pidle=τ11γ11π11,0ϕ11,
where ϕ11 denotes average packet arrival rate of the
arrival process to the bridge (note that packet arrival process is not Poisson
when packets arrive from IEEE 802.15.4 BAN to the bridge).By inserting all necessary transition probabilities,
we obtain(9)τ11=(γ11π11,0ϕ11+∑j=0m11γ11(1−γ11)j+∑j=0m11(W11,j−1)γ11(1−γ11)j2(1−pb)(pbcCt¯+pbsSt¯)+(W11,m11−1)(1−γ11)(m11+1)2(1−pb)(pbcCt¯+pbsSt¯)+γ11St¯+(1−γ11)Ct¯)−1.


## 5.2. Derivation of Probability Distribution of Occupancy of Bridge's Buffer

As we mentioned, we will assume that bridge's buffer
has an infinite capacity. Rationale behind that is that bridge device indeed
can have much larger memory than sensing device and that utilization of the
bridge is expected to be light-to-moderate. Therefore, bridge is not expected
to work in the regime close to its stability limit where it can reject packets
due to finite buffer.In GTS-based bridge period between arrivals of IEEE
802.15.4 superframes to the bridge is constant, and bridge can be modeled as
D/G/1 queuing system modeled at Markov points of packet departures from the
bridge. Let us denote period of arrival of sensing information from all the
sensors to bridge asΦ11=1/ϕ11. As mentioned earlier, if the number of sensors n15<16, then Φ11=BI, and if 15(k−1)<n15≤15k, then Φ15=kBI. Assume that PGF for the bridge's packet service time can be expressed as the
series as T11(z)=∑k=0∞t11,kzk. Probability of l, l=0,1,… arrivals of GTS superframes during packet
service time of the bridge has the value
(10)a11,l=Prob[lΦ11≤T11<(l+1)Φ11]=∑j=lΦ11(l+1)Φ11−1t11,j.PGF for the probability distribution of the number of
802.15.4 superframe arrivals during packet service time by the 802.11b
interface isA11(z)=∑l=0∞a11,lzl. An equation which shows number of packets in bridge's buffer left after the
departure of the packet has the form
(11)π11,l=π11,0a11,l+∑j=1l+1π11,ja11,l−j+1.
By multiplying both left-hand
and right-hand side of (11) with zl and summing over l=0,…,∞, we obtain PGF for the number of packets left in the bridge's queue
after the departing packet Π11(z)=∑l=0∞π11,lzl as
(12)Π11(z)=A11(z)(1−ρ11)(1−z)A11(z)−z,
where ρ11=ϕ11T11¯ presents offered load to the bridge.


## 5.3. Output Process and Throughput

Output process
from bridge has the PGF for packet interdeparture times as(13)Δ11(z)=(1−π11,0)T11(z)+π11,0zΦ11T11(z).Assuming that there aren11 bridges communicating with access point
throughput in 802.11b LAN can be then presented with expression
(14)Θ11=n11l11−2Δ11¯,
where 2 slots correspond to header information.


## 5.4. Distribution of Packet Waiting Time in Bridge's Buffer

Assuming FIFO service discipline, packet arriving at the bridge has to wait for the currently
transmitted packet to depart and for complete service time of all packets
already queued. According to renewal theory, remaining service
time of the packet has PGF [18]
(15)T11+(z)=(1−T11(z))T11¯(1−z).Then, PGF for the waiting time of the packet has the form(16)W11(z)=π11,0+π11,1T11+(z)+π11,2T11+(z)T11(z)+π11,3T11+(z)(T11(z))2⋯=π11,0+T11+(z)(π11,1+π11,2T11(z)+π11,3(T11(z))2+⋯)=π11,0+T11+(z)Π11(T11(z))−π11,0T11(z)=π11,0(1+T11+(z)1−A11(T11(z))A11(T11(z))−T11(z)).Average delay can be obtained by differentiating (16)
and applying L'Hospital's rule:
(17)W11¯=ϕ11T11(2)2(1−ρ11),
where T11(2) denotes second moment of packet service time.
This result matches Pollaczek-Khinchin mean value formula [19].The complete access time which includes waiting time
and service time of the target packet is then equal toS11¯=W11¯+T11¯.


## 6. Performance Evaluation of GTS Bridge  in Continuous EKG Telemetry

In this section, we present performance results for
GTS bridge between IEEE 802.15.4 and IEEE 802.11b deployed in continuous EKG
telemetry. In design of GTS bridge for EKG telemetry, we assume that superframe
will contain only three GTS parts. First one is management slot used for
control communication between IEEE 802.15.4 mote and the bridge. Second part is
used to carry digitized EKG samples, and the third part should contain
acknowledgment from bridge to mote. Duration of these parts depends on the
duration of superframe and time distance between the beacons. For example, ifSO=0,
then superframe including the beacon frame contains 16 slots with three backoff
periods each. Duration of beacon frame is 30 bytes (3 backoff periods) since
beacon can carry acknowledgment information for previous superframe. Minimal
duration of management slot is three backoff periods (30 bytes). However, 14
slots are then left to carry samples and packet authentication code. We assume
that HMAC function adopted is constructed from secure hash algorithm (SHA-1
hash [6, 20]) which is a widely used
cryptographic hash function with a message digest output of 160 bits.
Therefore, 400 bytes are left in the superframe which covers at least 200
digitized samples, that is, measurement period of 1 second. This confirms that SO=0 is a correct
choice as long as the superframes are sent with the period less than a second.
Choice of the BO parameter, that is, the period between the
beacons is result of contradicting requirements (Table 2 outlines our design
options). First requirement is related to low power consumption and asks that BO is chosen to be as large as possible, but
still able to carry all the samples generated during beacon interval (preferably
close to 1 second). Second requirement is related to the packetization delay
and reliability. Low packetization delay requires small amount of data in the
packet. Second, both IEEE 802.15.4 and IEEE 802.11b (and even IEEE 802.15 1
Bluetooth if it happens to operate in vicinity) operate in ISM band and cause
interference to each other. Interference can corrupt the whole superframe, and,
therefore, shorter superframe sizes are preferable.Table 1
Comparison of MAC parameters between beacon-enabled IEEE 802.15.4 and
IEEE 802.11b.
CSMA-CA parameterIEEE 802.15.4IEEE 802.11bBackoff period size320μs20μsListen to the medium during backoff countnoyesFreeze the backoff ctr. when medium is busynoyesListen to the medium immediately before the
trans.yesnoAction when medium is sensed busyNew backoff phaseFreeze the backoff ctr.Typical size of minimum backoff window832Typical number of backoff phasesm55Raw data rate250 Kbps1, 2, 5.5 or 11 MbpsTypical physical + MAC layer header size48 + 72 bits192 + 272 bitsRTS and CTSNo in beacon enabled versionYesTable 2
Tradeoff between packetization delay and number of samples carried in each superframe.
BO valuePeriod betweenNumber of EKG samplesbeaconsin the superframe60.983s19650.492s9840.245s4930.123s24We consider an ideal wireless channel (without noise
and fading). MAC and physical layer parameters are given in Table3 resulting
in a period between the superframes of 0.123
seconds.Table 3
Parameters used in the analytical modeling.
Number of bridges20–200SO (802.15.4)0BO (802.15.4)3Raw data rate (802.15.4)250 KbpsSuperframe size (802.15.4)480 bytesMAC and payload data rate for 802.11b2 MbpsPayload size of 802.11b packet10 slots at 2 MbpsIEEE 802.11 physical + MAC header size16.4 slotsWe have numerically solved the overall system of
equations under varying number of bridge devices. Analytical processing was
done using Maple 11 from Maplesoft. We have also implemented the simulation
model using Petri Net simulation engine Artifex [21]. Figures 5 and 6 show values of basic network
parameters when the number of bridges is varying between 10 and 190. Delays are
shown in numbers of IEEE 802.11b slots (20 microseconds). Although total
network load is light, we observe that an increase of the number of devices
under constant load per device causes linear increase of access probability,
freeze probability, and throughput; while at the same time, transmission
success probability, probability that buffer is empty after departure
experiences linear decrease. We also observe that analytical (shown as line)
and simulation results (shown as points) are close.Access
probability, probability that backoff count will be frozen, probability of
successful transmission, and probability that buffer is empty after departing
packet. Analytical results are shown as lines and simulation results are shown
as points.
(a)
Access probability(b)
Probability of freeze in backoff period(c)
Probability of successful transmission(d)
Probability that buffer is empty after
departureMean number of
packets left in the bridge's queue after departing packet, mean packet
interdeparture time, bridge offered load, and throughput. Analytical results
are shown as lines, and simulation results are shown as points.
(a)
Mean number of packets behind departing
packet(b)
Mean packet interdeparture time(c)
Offered load for one bridge(d)
ThroughputFigures7 and 8 show first three moments of the packet
service time and packet access time which includes waiting time in the queue
and packet service time. We observe that for an increase of the average packet
service time of 30%, standard deviation has increased three times. We present
coefficient of skewness which is derived as the ratio of the third moment of
the probability distribution and third power of standard deviation [22] which indicates symmetry of
the probability distribution around the mean value. This coefficient is close
to zero for distributions which are symmetric around their mean values.
However, calculated values of skewness parameter indicate high level of
asymmetry, and we have been motivated to calculate complete probability
distributions and discuss them.Moments of
packet service time. Analytical results are shown as lines and simulation
results are shown as points.
(a)
Mean packet service time(b)
Standard deviation of packet service
time(c)
Coefficient of skewness of packet service
timeMoments of
system (access) time. Analytical results are shown as lines, and simulation
results are shown as points.
(a)
Mean system time(b)
Standard deviation of system time(c)
Coefficient of skewness of system
timeFigures9 and 10 show probability distributions of
packet service time and packet waiting time obtained analytically for cases
when the number of bridges increases from 10 to 190 in steps of 20. For packet
service time, each peak on the graph corresponds to one backoff attempt. We
notice that for small number of bridges, almost all packets are served in first
backoff attempt. The beginning of the first peak is determined by the time to
complete single packet transmission without the backoff count St¯=69 slots. The width of the first peak corresponds
to the size of initial backoff window enlarged by freezing. After first
backoff, transmission is either successful or collided where collision lasts
for Ct¯=29 slots (which corresponds to the distance
between the peaks). As the number of bridges increases, the number and
intensity of higher-order backoff attempts increases and higher-order peaks
become more pronounced. Situation is similar with packet waiting time in the
sense that its distribution becomes wider as the number of bridges increases.
The first peak of this distribution comes from the residual packet service time
(of the packet currently being transmitted) without the collision, and it
further widens with increasing number of backoff phases. Flat parts after the
first one are due to packet retransmissions after collision.Probability distribution of packet service time.
(a)
Probability distribution of packet
service time, 10 bridges(b)
Probability distribution of packet
service time, 30 bridges(c)
Probability distribution of packet
service time, 50 bridges(d)
Probability distribution of packet
service time, 70 bridges(e)
Probability distribution of packet
service time, 90 bridges(f)
Probability distribution of packet
service time, 110 bridges(g)
Probability distribution of packet
service time, 130 bridges(h)
Probability distribution of packet
service time, 150 bridges(i)
Probability distribution of packet
service time, 170 bridges(j)
Probability distribution of packet
service time, 190 bridgesProbability distribution of packet waiting time in bridges' buffer.
(a)
Probability distribution of packet
waiting time, 10 bridges(b)
Probability distribution of packet
waiting time, 30 bridges(c)
Probability distribution of packet
waiting time, 50 bridges(d)
Probability distribution of packet
waiting time, 70 bridges(e)
Probability distribution of packet
waiting time, 90 bridges(f)
Probability distribution of packet
waiting time, 110 bridges(g)
Probability distribution of packet
waiting time, 130 bridges(h)
Probability distribution of packet
waiting time, 150 bridges(i)
Probability distribution of packet
waiting time, 170 bridges(j)
Probability distribution of packet
waiting time, 190 bridgesBoth distributions show that packet delay in ward
network is random with large variance as the number of bridges increases. This
is bad news for real-time payload transmitted in the IEEE 802.11 packets since
EKG samples have to be displayed in constant time periods. The results shown
are useful to determine the amount of playback buffering for EKG data in order
to ensure intelligible display of data.


## 7. Conclusion

In this paper, we have presented the design issues and
performance evaluation of the bridge between the BAN implemented using
beacon-enabled IEEE 802.15.4 network and IEEE 802.11b wireless LAN. Bridge has
been implemented using GTS feature of IEEE 802.15.4. Performance results show
that for small offered load and very small packet sizes which carry EKG data
(with basic bandwidth of 2400 bps), large number of devices generates very wide
probability distribution of the packet access time. Given that EKG data has to
be displayed in real time, accurate estimation of access delay is necessary in
order to dimension buffering at the receiver. We have shown that probability
distributions of packet service time and packet waiting time cannot be
characterized using first two moments, instead the whole probability
distributions are needed in order to accurately estimate buffering delays at
the receiver.



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*Source: 987046-2008-12-02.xml*