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Analysis of the Bluetooth device discovery protocol

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Device discovery and connection establishment are fundamental to communication between two Bluetooth (BT) devices. In this paper, we give an analytical model of the time it takes for the master in a piconet to discover one slave. We show that, even in the absence of packet interference, the discovery time can be long in some instances. We have simulated the discovery protocol by actually implementing it to validate the analytical model. By means of simulations, we show how discovery time is affected by (i) the presence of multiple potential slaves, and (ii) changes in the maximum backoff limit. Using simulation studies we observed the effectiveness of two proposed improvements to device discovery, namely, (i) avoiding repetitions of the A and B trains before a train switch, and (ii) eliminating the idea of random backoff, or reducing the backoff limit. We show that discovery time can be reduced by avoiding repetitions of the A and B trains before a train switch. However, complete elimination of the random backoff is not a good idea, as discovery time will be too long when the number of BT devices is large. Instead, choosing a small backoff limit of 250–300 slots is highly effective in reducing discovery time even in the presence of a large number (say, 50) of potential slaves.
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Analysis of the Bluetooth device discovery protocol
Goutam Chakraborty ÆKshirasagar Naik Æ
Debasish Chakraborty ÆNorio Shiratori Æ
David Wei
Springer Science+Business Media, LLC 2008
Abstract Device discovery and connection establishment
are fundamental to communication between two Bluetooth
(BT) devices. In this paper, we give an analytical model of
the time it takes for the master in a piconet to discover one
slave. We show that, even in the absence of packet inter-
ference, the discovery time can be long in some instances.
We have simulated the discovery protocol by actually
implementing it to validate the analytical model. By means
of simulations, we show how discovery time is affected by
(i) the presence of multiple potential slaves, and (ii)
changes in the maximum backoff limit. Using simulation
studies we observed the effectiveness of two proposed
improvements to device discovery, namely, (i) avoiding
repetitions of the Aand Btrains before a train switch, and
(ii) eliminating the idea of random backoff, or reducing the
backoff limit. We show that discovery time can be reduced
by avoiding repetitions of the Aand Btrains before a train
switch. However, complete elimination of the random
backoff is not a good idea, as discovery time will be too
long when the number of BT devices is large. Instead,
choosing a small backoff limit of 250–300 slots is highly
effective in reducing discovery time even in the presence of
a large number (say, 50) of potential slaves.
Keywords Bluetooth Device discovery Inquiry
Inquiry scan
1 Introduction
The initial goal of Bluetooth technology [12] was to
replace cables between pairs of devices, such as a computer
and a printer, a cell phone and a head-set, a laptop and a
desktop, and so on. However, the Bluetooth specification
has gone far beyond simple cable replacement, by detailing
the concepts of piconets and scatternets. Consequently,
there have been numerous innovative efforts toward
applying the technology to form personal area networks
and multi-hop ad hoc networks [3,7,8].
In Bluetooth, a piconet is a basic networking unit con-
sisting of one master and 1–7 active slave devices. The
smallest piconet consists of two devices—one master and
one slave. The device which initiates the process of
forming a piconet is designated as the master. The process
A preliminary version of this paper was presented at the IEEE
Vehicular Technology Conference, Fall 2004 [2].
G. Chakraborty
Department of Software and Information Science, Iwate
Prefectural University, Iwate, Takizawamura 020-0193,
Japan
e-mail: goutam@soft.iwate-pu.ac.jp
K. Naik
Department of Electrical and Computer Engineering,
University of Waterloo, Waterloo, Canada N2L 3G1
e-mail: knaik@swen.uwateloo.ca
D. Chakraborty (&)
Research Institute of Electrical Communication, Tohoku
University, Sendai 980-8577, Japan
e-mail: deba@shiratori.riec.tohoku.ac.jp
N. Shiratori
Research Institute of Electrical Communication,
Graduate School of Information Science,
Tohoku University, Sendai 980-8577, Japan
e-mail: norio@shiratori.riec.tohoku.ac.jp
D. Wei
Department of Computer and Information Science,
Fordham University, Bronx, NY 10458, USA
e-mail: wei@cis.fordham.edu
123
Wireless Netw
DOI 10.1007/s11276-008-0142-1
followed by a master to form a two-device piconet consists
of two sequential steps as explained below.
(i) Inquiry: In the inquiry phase, the master invites other
devices to join itself to form a piconet. Essentially, the
master solicits responses from other devices. Devices
willing to join a piconet respond to the master’s
solicitation. In the inquiry phase, the master solicits
responses by transmitting a standard packet, called ID
(identifier) packets, on different hop channels (i.e., on
different frequencies), and listens for response pack-
ets, called FHS (frequency hopping sequence) packets,
from potential slave devices. The sender of an FHS
packet puts its own address and clock values in the
packet. When the master receives an FHS packet, it
knows what device is willing to join the master to
form a piconet. However, mere response of a device
with an FHS packet does not form a piconet. After
receiving an FHS packet, the master executes the
paging step as explained below.
(ii) Paging: Having received the address and clock values
of a (potential) slave device, the master communicates
with the device via the paging process. During the
paging process the master establishes a connection
with a slave. The paging process falls outside the
scope of this work.
The master can repeat the inquiry process to discover
more devices, and invoke the paging process to establish a
connection with a newly discovered slave device. Once a
connection is established between the master and a slave in
a piconet, upper (application) level data are exchanged
between the two devices. Thus, the inquiry and paging
processes are fundamental to form a piconet.
In this paper, we give an analytical model of the average
time it takes for a master to discover a potential slave. To
obtain a better insight into the discovery protocol, we have
simulated the protocol by actually implementing the rele-
vant frequency hopping sequences. We performed
extensive simulations to study the pattern of discovery
time. Specifically, we have made the following observa-
tions: (i) even when there are only two devices, namely one
master and one slave, the discovery time can vary from a
couple of time-slots to more than 9000 time-slots, and (ii)
if device discovery is not successful within a few hundreds
of time-slots, it will, more often than not, be delayed by
more than 4000 time-slots.
By means of simulations, we have shown how the dis-
covery time is affected by more number of slaves and by
varying the maximum backoff limit from a small value,
say, 32 slots, up to the recommended value of 1023 slots.
We have investigated the effectiveness of two proposal to
improve the discovery time: (i) avoiding train repetitions
for 256 times [15], and (ii) eliminate random backoff or
reduce the backoff limit [13].
The rest of the paper is organized as follows. The device
discovery protocol has been explained in detail in Sect. 2.
In Sect. 3, we review the related works. An analytical
model of discovery time is given in Sect. 4. In Sect. 5,we
present simulation results. Two suggested improvements to
the discovery protocol have been studied in Sect. 6.
Finally, some concluding remarks are given in Sect. 7.
2 Device discovery protocol
The state diagram of the Bluetooth link controller [12] has
been shown in Fig. 1. We have clearly identified the device
discovery (inquiry) phase and the connection establishment
(paging) phase by enclosing the relevant states in separate
dotted boxes. In this paper, we will focus on the device
discovery portion. The STANDBY state means that the
device is not a part of any piconet. The CONNECTION
(Inquiry)
STANDBY
CONNECTION
Page Page Scan
Master
Response
Slave
Response
Inquiry Scan Inquiry
Response
Inquiry
Connection Establishment
(Paging) Device Discovery
Fig. 1 State diagram of
Bluetooth link controller [12]
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state means that the device is a part of a piconet. A device
can move from its present STANDBY or CONNECTION
state to the Inquiry state, if it wants to discover a new
device. The device which wants to discover another device
to form a piconet is designated as the master in the piconet.
Similarly, a device can move from its present STANDBY
or CONNECTION state to the Inquiry Scan state, if it
wants to be discoverd by another device. While a device is
in the process of discovering a new device it can tempo-
rarily move to the Inquiry Response state. The device
which is willing to be discovered by another device
(master) is designated as a slave in a piconet.
The device discovery protocol consists of two parts,
namely Inquiry and Inquiry Scan. A discovering device (or,
master) runs the Inquiry protocol, and a device willing to
be discovered (or, slave) runs the Inquiry Scan protocol.
The protocol has been explained in textual form in the
specification [12]. However, for the purpose of clear
understanding and easy analysis, we have represented the
protocols in the form of an extended finite-state machine
(EFSM). A state transition in an EFSM can be represented
as a six-tuple of the following form:
{source state, enabling condition, input, output, action,
destination state}.
The enabling condition and the input determine whether
or not a state transition takes place from the source state to
the destination state. In a time slot, if the enabling condi-
tion evaluates to true and the baseband layer receives the
specified input, then it transmits a packet specified in the
output part; after transmitting the packet, the baseband
layer takes some local action before transiting to the des-
tination state.
2.1 The Inquiry protocol
The EFSM model of the Inquiry protocol is shown in
Fig. 2. The protocol consists of two states: STANDBY/
CONNECTION and Inquiry. Initially, a device can be in
the STANDBY or the CONNECTION state. It is the Link
Manager Protocol (LMP) layer that decides when the
baseband layer may initiate the Inquiry protocol. At this
point, the LMP layer asks the baseband layer to enter the
Inquiry state, which has been represented by transition
number #1. In the action part of transition #1, the baseband
layer starts a time-out (TO) timer called inquiryTO. The
baseband layer moves from the Inquiry state to the original
STANDBY/CONNECTION state in two ways. The first
way, represented by transition #4, occurs when it is asked
to do so by the LMP. The second way, represented by
transition #5, occurs when the inquiryTO timer expires.
When the device is in the Inquiry state, two kinds of state
transitions occur depending on whether it is in a Tx
(transmission) slot or a Rx (reception) slot, as shown in
transition #2 and transition #3, respectively. In transition
#2, the discovering device transmits ID packets. Transition
#3 fires when the device receives an FHS packet, signaling
the discovery of a device. In the action part of transition #3,
the baseband layer informs the LMP of the discovery of a
device, and the device continues to be in the Inquiry state.
It may be noted that the discovering device does not
acknowledge the reception of an FHS packet.
In transitions #2 and #3, the transmit and receive fre-
quencies of a discovering device are determined by the
inquiry hopping sequence. The inquiry hopping sequence is
generated by the discovering device’s native clock (CLKN)
and the General Inquiry Access Code (GIAC). The GIAC
has the standard value x9E8B33, in the hexa-decimal
notation. In the 79-hop system, the inquiry hopping
sequence contains 32 distinct hop frequencies. The inquiry
hopping sequence is constructed as follows. The set of 32
frequencies is partitioned into two subsets of 16 frequen-
cies each, and two trains, namely train Aand train B, are
constructed from those two subsets. The two trains are
permutations of the two distinct sets of 16 frequencies.
Assuming that an ID packet is transmitted twice in each Tx
slot, once at the beginning and a second time at the middle
of a transmission time-slot, it takes eight Tx slots to
transmit a whole train of 16 frequencies. Because the Tx
and Rx slots are interleaved, the total length of time to
cover each train is 16 slots, or 10 ms (=16 9625 ls),
625 ls being the duration of a time-slot. A single train is
repeated for at least N
inquiry
=256 times before the other
train is used. In order to collect all responses in an error-
free manner, at least four trains must be used; in other
words, three train switches must take place. Therefore, the
Inquiry state lasts for 10.24 s (= 256 94910 ms).
The Inquiry protocol can run concurrently with data
traffic. This can be achieved by having the master transmit
ID packets for a duration of Tw inquiry time units in a period
of T
inquiry
, as illustrated in Fig. 3(a). Thus, the master can
support data traffic for a duration of Tinquiry Tw inquiry in
each period of T
inquiry
time units. The length of Tw inquiry is
Inquiry
Input: (Nil)
Output: Transmit ID packet
Action: {}
Out
p
ut: (Nil)
Condition: in Rx slot
Input: FHS packet
Action: {device discovered}
STANDBY/
CONNECTION
1
Output: (Nil)
Input: (Command from LMP)
Condition: True
Condition: True
Input: (Command from LMP)
Action: Start inquiryTO timer
Output: (Nil)
23
Action: Stop inquiryTO timer
Output: (Nil)
Condition: True
Input: inquiryTO timeou
t
Action: (Nil)
4
5
Condition: in Tx slot
Fig. 2 The Inquiry protocol
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at least equal to the length of three train switches, as
explained above, with a duration of 10.24 s.
2.2 The Inquiry Scan protocol
The EFSM model of the Inquiry Scan protocol is shown in
Fig. 4. If a device wants to be discovered by others, then
the LMP layer of the device issues a command to the
baseband layer to move from its present STANDBY/
CONNECTION state to the Inquiry Scan state, which has
been modeled by transition #1. In the action part, the
device starts the inqrespTO timer and initializes a Back-
offDone flag to false. It may be noted that the Bluetooth
specification does not concern itself with the detailed
specification of the backoff mechanism or the relevant
parameter of back-off time. However, in this paper, we
explicitly specify the backoff mechanism for a clear
understanding of the protocol. If the device receives an ID
packet and the backoff has not been performed, then it
starts an inquiry response timer irRAND, as we name it,
with a duration randomly set between 0 and 1023 slots, and
moves to its original state; the above behavior is specified
in transition #2. The device is allowed to spend irRAND
time slots in its STANDBY/CONNECTION state; upon
expiry of the irRAND timer the device moves to the
Inquiry Scan state, which is shown as transition #3. After
the backoff period, but before the expiry of the inqrespTO
timer, if the device receives a second ID packet in the
Inquiry Scan state, it starts another one-slot timer we call
oneslotTO. After the expiry of the oneslotTO it moves to
the Inquiry Response state; this behavior has been modeled
in transition #4. After waiting for exactly one slot in the
Inquiry Response state, the device transmits an FHS
packet, reinitializes the BackoffDone flag to false, and
moves to the Inquiry Scan state; this behavior has been
modeled in transition #5. By repeatedly executing the
transitions #2, #3, #4 and #5, the device continues to dis-
cover and possibly rediscover other devices in the
neighborhood. After the inqrespTO timer expires, the
device moves from the Inquiry Scan state to its original
STANDBY/CONNECTION state, which has been shown
by the transition #6.
The idea behind having the responding devices wait for
a random period is to avoid collision of their FHS packets.
In the Inquiry Scan protocol shown in Fig. 4, a device
Time
inquiry Tinquiry
w_inquiry
Tw_inquiryT
inquiryscanT
w_inquiryscanT
inquiryscanT
w_inquiryscanT
(a)
(b)
Time
T
Fig. 3 (a) Inquiry peroid and Inquiry window. (b) Inquiry Scan
period and Inquiry Scan window
CONNECTION
or
STANDBY
Inquiry Scan
Inquiry Response
Input: ID packet (Inquiry)
inqrespTO timer running
Condition: BackoffDone == True &&
2
4
Condition: True
Input: (Command from LMP)
3Condition: True
Condition: True
Input: oneslotTO timeout
Input: ID packet (Inquiry)
Condition: BackoffDone == False
Action: BackoffDone = True
Action: Start inqrespTO timer
BackoffDone = False
Action: Start a timer irRAND with a random
length between 0 and 1023 slots.
Action: Start a one-slot timer oneslotTO
Output: {}
Output: {}
Output: {}
Output: {}
Output: FHS packet
Action: BackoffDone = False
Increment phase offset in the inquiry hop sequence
1
5
6
Output: {}
Action: {}
Condition: True
Input: irRAND timeout
Input: inqrespTO timeout
Fig. 4 The Inquiry Scan
protocol
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123
receives ID packets in transitions #4 and #5 using the
inquiry scan hopping sequence, and transmits FHS packets
in transition #6 using the inquiry response hopping
sequence.
It is important to note that in the Inquiry Scan protocol a
device uses the same 32 frequencies to scan the medium as
used in the Inquiry protocol by a master. The difference is
that the Inquiry Scan protocol scans the medium on the
same frequency for 2048 slots. After 2048 slots, a different
scan frequency is chosen for another 2048 slots, and so on.
The Inquiry Scan protocol can run concurrently with
data traffic. This can be achieved by having a slave scan for
ID packets for a duration of Tw inquiryscan time units in a
period of T
inquiryscan
time units as illustrated in Fig. 3(b).
Thus, the slave can support data traffic for a duration of
Tinquiryscan Tw inquiryscan time units in each period of
T
inquiryscan
time units. The length of Tw inquiryscan is at least
16 slots.
In this paper, we will analyze the discovery time by
considering that the master and the slave are fully dedi-
cated to device discovery. Therefore, we assume that
Tw inquiry ¼Tinquiry and Tw inquiryscan ¼Tinquiryscan. Trivi-
ally, the discovery time will be more in the absence of the
above assumption.
2.3 Combined behavior of Inquiry and Inquiry Scan
protocols
The combined behavior of the Inquiry and Inquiry Scan
protocols is shown in Fig. 5in the form of a message
sequence chart. The master’s behavior running the Inquiry
protocol has been shown on the left hand side, whereas a
potential slave runs the Inquiry Scan protocol on the right
hand side. For simplicity, we assume that, initially, both the
master and the potential slave are in their STANDBY states.
Next, the master moves into the Inquiry state, and the slave
moves into the Inquiry Scan state—these two moves are
independently performed.
It is also assumed that a slave enters its Inquiry Scan
state no later than the master entering the Inquiry state. In
the absence of this assumption, the difference in time
between the instant when a slave enters the Inquiry Scan
state and the instant when the master enters the Inquiry
state becomes a part of the discovery time. However,
incorporating this time gap into discovery time is not a fair
way to evaluate the protocol. The above assumption
ensures that we start measuring discovery time once the
master is in its Inquiry state and a slave is in its Inquiry
Scan state.
As soon as the master enters the Inquiry state, it starts
transmitting ID packets twice per slot. The master is said to
have discovered a device when it receives an FHS packet
from another device. Thus, as shown in Fig. 5, we define
discovery time as follows.
Definition 2.1 Discovery time is defined as the time
interval between the instant when the master enters the
Inquiry state and the instant when it receives an FHS
packet from another device.
First, we explain how the master transmits ID packets on
different hop frequencies, and how a slave hops on dif-
ferent frequencies to scan for ID packets. It is essential to
understand the two hopping schemes in order to give a
model to calculate discovery time.
For simplicity, we discuss the case in which there is one
master and one potential slave, as shown in Fig. 6(a). A
device willing to be discovered, called a scanning device,
scans the medium for ID packets with frequencies hopping
very slowly—a scanning frequency that changes once
every 2048 slots (1.28 s). In Fig. 6(b), we show how the
hopping frequencies of the master and a slave change. Let
us denote the set of 16 A-train frequencies as
A¼fa1;a2;a16g}, and the set of 16 B-train frequencies as
B¼fb1;b2;b16g. The slow-hopping Inquiry Scanner fre-
quencies are a permutation of the 32 frequencies of A[B:
In Fig. 6(b), frequencies f
0
,f
1
,,f
31
denote an arbitrary
permutation sequence of the elements of A[B.
An Inquirer repeatedly transmits ID packets on the
A-train and B-train frequencies as follows: the A-train
is repeated for 256 times, followed by a repetition of
the B-train for 256 times, followed by a repetition of the
A-train for 256 times, and so on. Let A
?
represent the
repetition of the A-train for 256 times. Similarly, B
?
rep-
resents the repetition of the B-train for 256 times. Thus, the
Time
Device discovered
(Start of discovery process)
STANDBY state
Random backoff in
the range [0, 1023] slots
Inquiry Scan state
Slow Hopping Inquiry Scan
Slow Hopping Inquiry Scan
Inquiry by sending ID packets at fast hop
state
Inquiry response state
stateStandby
MASTER SIDE SLAVE SIDE
Standby state
I
nquiry
Scan stateInquiry
Fig. 5 Combined behavior of Inquiry and Inquiry Scan protocols
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123
individual length of A
?
and B
?
is 2.56 s (= 625 ls916 9
256). In terms of behavior, there is no difference between
A
?
and B
?
, except in their frequency components. On the
other hand, an Inquiry Scanner scans the medium for an ID
packet on a single frequency f
i
(f
i
[A[B) for 2048 slots
(= 1.28 s). The scanning frequency changes every 2048
slots.
At this moment, it is important to introduce the concept
of phase difference between an Inquirer and an Inquiry
Scanner, and its impact on device discovery time. If an A
?
or a B
?
train of the Inquirer and a new frequency scanning
interval of an Inquiry Scanner begin at the same time
instant, we say that the processes of inquiry and inquiry
scan are synchronized.
Otherwise, there is a phase difference. We denote the
phase difference by Dt, as shown in Fig. 6(b). Here, the
scanning frequency f
0
started Dttime before A
?
train. For
convenience, we let Dt=k*s, where kis an integer and
sis the length of one slot (= 625 ls). The range of possible
values for kwill be discussed in Sect. 4. We identify the
notion of phase difference because the discovery time is a
function of phase difference. It will be clear from the fol-
lowing discussion that restricting kto only integer values
does not affect the computation of discovery time.
3 Related research
Delay analysis of the device discovery protocol and pro-
posals to modify the protocol to reduce the delay have
generated much interest [1,5,6,9,10,11,1315].
Zaruba and Gupta [15] simplify the analysis of the
discovery protocol by assuming that none of the trains—A
or B—is repeated before a train switch. In other words, an
A-train is immediately followed by a B-train, followed by
an A-train and so on. They do not repeat a train for 256
times before switching, as it has been specified.
Jiang, Lin and Tseng [5] model the elapsed time from
the instant a slave starts inquiry scan to the instant it suc-
cessfully receives an ID packet from the master. It is
assumed that there is a master device performing the
inquiry procedure. Thus, the focus of their work is on the
average time to receive an ID packet by a slave. They
propose three techniques to improve this delay, namely, (i)
halve the T
inquiry
and Tw inquiry intervals, (ii) use a dual
Inquiry Scan scheme, and (iii) use a combination of both.
In the dual Inquiry Scan scheme, for every T
inquiryscan
period, the slave performs inquiry scan on two frequencies
each for a duration of Tw inquiryscan . However, to be pre-
cise, device discovery time needs to be measured from the
viewpoint of a master. That is, it is more useful to find out
how much time it takes a master to discover a slave,
assuming that the slave is performing the inquiry scan
procedure no later than when the master initiates its inquiry
protocol.
Connection establishment between two mutually
unknown devices takes 5.76 s in a typical case and as long
as 23 s in the worst case [1,4]. Thus, for Bluetooth tech-
nology to be useful in a mobile environment, where two
devices may not stay within each other’s radio range for
long, there is a need to speed up the discovery time. Welsh,
Murphy and Frantz [13] proposed three possible changes to
the Bluetooth specification in order to reduce the discovery
time. Their proposals are: (i) eliminate or decrease the
random backoff delay in the Inquiry Scan protocol, (ii) use
a single frequency train instead of two—Aand B—in the
Inquiry protocol, and (iii) combine the first two approa-
ches. The reader may note that the second proposal above
is the same as the proposal made by Zaruba and Gupta [15]
in their analysis of the discovery protocol.
Inquiry
scanner
T
x
R
x
R
x
R
x
R
x
R
x
R
x
T
x
T
x
(a)
I
nquirer
time slot
one
packet
FHS
random
backoff
transmit
timeslot
receive
timeslot
Inquirer
Inquiry
scanner
Α
+
Β
+
Α
+
4096 slots 4096 slots 4096 slots
0fff f
1234
t
. . . . . . . .
f
. . . .
2048 slots 2048 slots
(b)
Fig. 6 State transition for
device discovery: timing
diagram
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123
Woodings, et al. [14] proposed to bypass the uncertainty
in device discovery by using a direct IrDA channel
between devices that could potentially establish a con-
nection between them. A master device obtains the details,
such as device address and native clock values, of a slave
via a connection over an IrDA channel. Once the master
obtains the details of the slave, it initiates the paging
protocol.
Salonidis, Bhagwat and Tassiulas [10] have shown that
device discovery time can be reduced by having devices
alternate between two roles, namely, a discoverer and one
willing to be discovered. In other words, a device alter-
natingly runs the Inquiry protocol and the Inquiry Scan
protocol. For better effectiveness of this scheme, a device
executes those protocols for random durations, rather than
follow a periodic scheme.
4 Analysis of discovery time
In this section, we will present an analytical model of
discovery time as depicted in Fig. 5. The different com-
ponents of this time can be found on the slave side in
Fig. 5. Discovery time has four components as explained
below.
T
ID1
: This is the average time taken by a slave to receive
the first ID. This time is measured from the instant the
master starts transmitting ID packets to the instant when
a slave receives an ID.
T
b
: This is the average of the random backoff time after
the slave receives the first ID packet.
T
ID2
: This is the average time taken by the slave to
receive a second ID. This time is measured from the
instant the slave comes out of its random backoff to the
instant when it receives an ID.
1-slot: This is the 1-slot wait by the slave between
receiving a second ID and transmitting an FHS packet.
We will ignore this 1-slot component from further
consideration.
Therefore, discovery time, denoted by T, is expressed
as follows:
TID1þTbþTID2:ð1Þ
The Bluetooth specification states that a random backoff
interval be uniformly chosen from the range [0, 1023] slots.
Thus, the average value of T
b
is 512 slots. There is a
similarity between T
ID1
and T
ID2
. Both these intervals are
associated with the same condition. For T
ID1
we have
assumed that a slave enters its Inquiry Scan state no later
than the master entering the Inquiry state. Essentially, this
assumption implies that by the time the master starts
transmitting ID packets, a slave has already begun, or just
begins, scanning the medium to receive an ID packet. The
reader may observe that the same condition holds when a
slave returns from its STANDBY state to the Inquiry Scan
state at the end of its random backoff as depicted in Fig. 4
and 5. This is because the master continues transmitting ID
packets in its transmit slots, without knowing a state
change in a slave. The slave starts scanning the medium for
an ID packet as soon as it returns to Inquiry Scan.We
measure T
ID2
from the instant a slave enters Inquiry Scan
for a second time to when it receives a second ID. Thus,
T
ID1
and T
ID2
can be computed in the same way.
Consequently, we can rewrite Eq. 1 as,
2TID þTb;ð2Þ
where T
ID
=T
ID1
=T
ID2
represents the average time
taken by a slave to receive an ID packet from the instant
the master is transmitting ID packets and the slave is
scanning the medium. Thus, to give an expression for T,
we need to compute T
ID
.
Next, we discuss how the value of k(phase difference,
as defined in Sect. 2) affects the discovery time, and how k
plays an important role in determining the delay. Let F¼
A[Bbe the set of 32 frequencies used in the discovery
protocol. The members of Fare denoted by f
i
, where 1 Bi
B31. A slave scans the medium on the same frequency,
say f
i
, for 2048 slots. Since a slave scans the medium on the
same frequency for 2048 slots and the length of each of A
?
and B
?
is 4096 slots, the possible range of phase difference
is [0, 2046] slots, i.e., 0 BkB2046. Moreover, we con-
sider only the even values of kin the range [0, 2046]. This
is because the master transmits ID packets in its Tx slots,
which are followed by the Rx slots to receive an FHS
packet.
To show the impact of the value of kon discovery time,
we first consider values of kbetween 0 and 16. If k=0, as
shown in Fig. 7(a), a slave scans the medium on two dif-
ferent frequencies during the period when the master
transmits ID packets using A
?
frequencies.
Then the slave would not be able to receive ID packets if
f
0
,f162 A:On the other hand, if k[0, a slave scans the
medium on three different frequencies during the period
when the master transmits ID packets using A
?
frequen-
cies. This is evident from Figs. 8and 9. Consequently, the
probability of a slave being able to receive an ID packet is
higher. We identify another important value of k, namely,
k=16, as follows. Suppose that there is no match during f
0
and f
1
, because both f
0
and f162 A. When the scan fre-
quency changes to f
2
, as shown in Fig. 9, and if f
2
[A,
there will be an immediate match within the 16 consecutive
time slots.
On the other hand, if f262 A, subsequently there will be
a definite match of f
2
with a Btrain frequency as f
2
[A[
B. When 0 BkB14, the probability of such a match
Wireless Netw
123
during the f
2
scanning frequency becomes less and less as k
takes smaller values in the range [2, 14]. A similar argu-
ment can be used to show that the two ranges of k, namely
[2, 14] and [2034, 2046], lead to similar discovery times.
Therefore, to compute T
ID
, we need to consider four dis-
tinct ranges of kas follows:
(i) k=0
(ii) 2 BkB14
(iii) 16 BkB2032
(iv) 2034 BkB2046
As noted above, cases (ii) and (iv) lead to similar delay
behavior. In the following, we give a model of T
ID
for each
of the three cases. It may be noted that this delay behavior
is for one master and one slave. When the number of
potential slave devices is increased, the delay would be
longer due to collision of FHS packets. Due to the condi-
tional dependence of the delay on k, and because the values
of kfor individual slaves are independent variables,
deriving an analytical model for multiple slaves becomes
difficult. However, we have obatined simulation results for
more than one slaves in Sect. 5.
4.1 Discovery time for k=0
Computation of T
ID
for k=0 has been explained using a
tree structure in Fig. 7. The scan frequencies f
0
,f
1
,,f
31
at
the Inquiry Scanner is a permutation of all the 32
(a)
(b)
Fig. 7 Detailed computation of
discovery time for k=0
Wireless Netw
123
frequencies in the set F. We give an estimation of T
ID
using
the tree structure showing possible delays and their corre-
sponding probabilities, as shown in Fig. 7(b). If f
0
[A, for
which the probability is 16/32, the delay lies between 0.5
and 15 slots with equal probabilities. Thus, the average
delay is about 7.5 slots. The probability of the event f
0
[A
and the corresponding delay have been shown on the left
branch from the root. If f062 A;no ID will be received for
at least 2048 time slots before the frequency changes to f
1
.
Estimation of the delay will depend on the next frequency
f
1
. Thus, on the right branch of the root we record the
probability of f
0
[B(same as f062 A) as 16/32, and the
delay is denoted as d
0
.Iff
1
[A, for which the probability is
16/31, an ID will be received due to a matching scanning
frequency, and the corresponding delay will be 1 92048
?7.5. This probability and the delay have been shown in
the second row, left box. A similar case may happen with
f
2
,f
3
,If a match occurs on f
i
, the corresponding delay
will be i92048 ?7.5, and these have been shown in the
left branch boxes.
On the other hand, if f
1
[B, the Inquiry Scanner will not
receive an ID packet until f
1
changes to f
2
. The probability
of f
1
[Bis 15/31, and the estimation of the delay will
depend upon the next frequency f
2
. Thus, in the second row
right-hand box we record the probability of f
1
[Bas 15/31,
and the delay as d
1
. All the possible situations of receiving
or not receiving an ID packet have been shown with their
probabilities and delays in the boxes in Fig. 7(b). On the
right-hand side box at level 31, the probability of f
31
[Ais
1.0 and the delay is denoted by g.
(a)
(b)
Fig. 8 Delay analysis when k
takes a value in the closed range
[2,14]
Wireless Netw
123
An expression for T
ID
for k=0, denoted by T
ID,k=0
, can
be obtained by combining the probabilities and delays
recorded in the boxes in Fig. 7. Thus, we have the fol-
lowing expressions.
TID;ðk¼0Þ¼16
32 7:5þ16
32 d0
d0¼16
31 ð2048 þ7:5Þþ15
31 d1
d1¼14
30 ð22048 þ7:5Þþ16
30 d2
d2¼......
where the general expression for d
i
is,
di¼16 bðiþ3Þ=4c2
ð32 iÞððiþ1Þ2048 þ7:5Þ
þð32 iÞð16 bðiþ3Þ=4c2Þ
ð32 iÞdiþ1;
where 0 i30 and d31 ¼g:
One may note that the estimated value of gis T
ID,k=0
,but
the probability of occurrence of the event is negligibly
small. T
ID,k=0
is computed by successive approximation.
Initially, we set g=0 and successively modify gwith the
value of T
ID,k=0
obtained from the previous iteration.
T
ID,k=0
stabilized after two iterations.
4.2 Average delay when 2 BkB14
The frequency matching scenario between a master
running the Inquiry protocol and a potential slave run-
ning the Inquiry Scan protocol when ktakes a value in
the closed range [2, 14] has been described in Fig. 8.
The scanning frequencies have been denoted by f
i
,0Bi
B31. The tree structure shown in Fig. 8(b) is obtained
using an argument similar to the one used to construct
the tree shown in Fig. 7(b). However, there is a differ-
ence in Fig. 7(b) and Fig. 8(b). For example, in the tree
shown in Fig. 7(b), each node has at most two child
(a)
(b)
Fig. 9 The delay for the case
when 16 BkB2032
Wireless Netw
123
nodes, whereas it is at most three in Fig. 8(b). This is
due to the fact that when iis even in f
i
, the span of f
i
covers both A-train and B-train of frequencies—A-train
partially and B-train completely.
Following the argument in Sect. 4.1, it is easy to see
how the boxes (i.e. nodes), shown in level 0 and level 1,
can be obtained.
Here, level imeans boxes terminated on a branch of f
i
[Aor f
i
[B. For example, the probability of f
0
[Ais 16/
32 and the delay is approximately 7.5 slots. We represent
this information in the left node of level 0. On the other
hand, the probability of f
0
[Bis 16/32, and the delay,
denoted by d
0
in Fig. 8, depends on the subsequent
scanning frequencies. The value of d
0
is computed using
the part of the tree rooted at the right node of level 0.
With a similar argument the probabilities of events at
level 1 are obtained.
However, the situation is different at level 2, where
there are three distinct possibilities. This time, the scan-
ner’s tuning frequency f
2
overlaps with the A
?
train for k
slots and with the B
?
train for 2048 -kslots. Thus, the
probability of f
2
[Bis 14/30, and the corresponding delay
is 2 92048 -k?k?7.5 =2 92048 ?7.5 slots. The
probability of f
2
[Ais 16/30. The probability of a fre-
quency match between the Inquirer and an Inquiry
Scanner with f
2
[Ais (16/30) 9(k/16) and the corre-
sponding delay is 2 92048 -k?k/2. On the other
hand, the probability of no frequency match between the
Inquirer and an Inquiry Scanner with f
2
[Ais (16/
30) 9((16-k)/16) and the corresponding delay d
2
depends on the subtree rooted at this node. These three
different situations have been represented by three nodes
at level 2 of Fig. 8(b).
Using a similar argument, we can complete the tree
shown in Fig. 8(b), and an expression for T
ID
for 2 BkB
14 is given below.
TID;ð2k14Þ¼16
327:5þ16
32d0
d0¼16
31ð2048kþ7:5Þþ15
31d1
d1¼14
30ð22048þ7:5Þ
þ16
30

k
16

22048k
2

þ16
30ð16 kÞ
16 d2
d2¼14
29

ð32048 kþ7:5Þþ 15
29

d3
d3¼......
where the general expression for d
i
is,
di¼16 i
31 i

ðiþ1Þ2048 kþ7:5ðÞ
þ116 i
31 i

diþ1;where i¼0oriis even:
di¼15 i
31 i

ðiþ1Þ2048 þ7:5ðÞ
þ115 i
31 i

k
16

ðiþ1Þ2048 k
2

þ115 i
31 i

16 k
16

diþ1;where iis odd:
The average delay depends on the value of k, and it
decreases as kincreases.
4.3 Average delay when 16 BkB2032
The frequency matching scenario in the case of 16 BkB
2032 has been shown in Fig. 9. The tree showing the
probabilities of frequency matching and delay computation
is obtained using an argument similar to the one in
Sect. 4.1.
In this case, there will be a definite match by the time
a potential slave scans on f
2
. This is because by the time
the slave completes scanning the medium on frequency f
2
for at most (k?16) slots, it will have covered all the A-
train and B-train of frequencies transmitted by the
Inquirer. Thus, the delay T
ID
is given by the following
expression.
TID;ð16 k2032Þ¼16
32 7:5þ16
32
16
31 ð2048 kþ7:5Þþ15
31
14
30 ð22048 þ7:5Þþ16
30
ð22048 kþ7:5Þ
The average value thus depends on k, and when
averaged over all kbetween 2032 to 16, it is 1142 time-
slots.
4.4 Average delay when 2034 BkB2046
The frequency matching scenario when 2034 BkB2046
is similar to the scenario for 2 BkB14 as shown in
Fig. 10. Here, k0= 2048 -ktakes values from 14 to 2. A0is
the set of first k0frequencies of the A-train. The branches
show the conditions, and the boxes give the probabilities
and corresponding delays. The expression for T
ID
for 2034
BkB2046 is given below.
Wireless Netw
123
TID;ð2034 k2046Þ¼k0
32 k0
2þ32 k0
32

d0
d0¼16
31 ðk0þ7:5Þþ15
31 d1
d1¼16
30 ð2048 þk0þ7:5Þ
þ14
30

k0
16

22048 þk0
2

þ14
30

16 k0
16

d2
d2¼13
29 ð22048 þk0þ7:5Þþ16
29 d3
d3¼......;
where the general expression for d
i
is,
di¼16i1:5
31iði2048þk0þ7:5Þ
þ116i1:5
31i

diþ1;where i¼0oriis even:
di¼17 i
31 i

ði2048 þk0þ7:5Þ
þ117 i
31 i

k0
17 i

ðiþ1Þ2048 þk0
2

þ117 i
31 i

1k0
17 i

diþ1;where iis odd:
4.5 An expression for T
ID
Now we obtain an expression for T
ID
by combining the
expressions for T
ID,(k=0)
,T
ID,(2BkB14)
,T
ID,(16BkB2032)
and T
ID, (2034 BkB2046)
. The expression for T
ID
is,
(a)
(b)
Fig. 10 Delay analysis when k
takes a value in the closed range
[2034, 2046]
Wireless Netw
123
TID ¼1
1024 TID;ðk¼0ÞþX
14
k¼2
TID;ð2k14Þ
þX
2032
k¼16
TID;ð16 k2032Þ
þX
2046
k¼2034
TID;ð2034 k2046Þ:!ð3Þ
To get an expression for the discovery time, as given in
Eq. 1, we need to substitute T
ID
obtained from Eq. 3. As
the constituent terms of the above Eq. 3 are in recursive
form, we calculated the value of T
ID
using numerical
method.
5 Simulation result
We have developed a Bluetooth simulator to study the
performance of the device discovery protocol. We imple-
mented the frequency hopping kernel box specified in
Chapter 11 of the Bluetooth specification [12]. In Sect. 4,
we obtained an analytical model of discovery time by
considering the phase difference in four distinct blocks,
namely, k=0, 2 BkB14, 16 BkB2032, and 2034 Bk
B2046.
To verify that discovery time can be studied in terms of
those four blocks of kvalues, we performed 31000 distinct
experiments. The idea behind performing 31000 experi-
ments is this: There are 1024 distinct values of k, and we
wanted each value of kto appear for an average of 30
times. In the discovery protocol, the phase value depends
upon the native clocks of the two devices taking part in the
discovery process. We observed that each kvalue appears
between 10 and 70 instances in the total number of
experiments. In the 31000 experiments, we had two devi-
ces—one master and one slave.
For each of the four blocks of kvalues, we compute their
average discovery time and the result has been shown in
Fig. 11. As analyzed in Sect. 4, the average delays in the
four blocks of kvalues, namely, k=0, 2 BkB14, 16 B
kB2032 and 2034 BkB2046, are very distinct. The
distribution of delay is uniform within each of the four
blocks, but it varies from block to block as predicted in
Sect. 4.
We wanted to compare the analytical model of discov-
ery time with data obtained from simulation studies. Using
the expression for T
ID
given in Eq. 3, we computed T
ID
to
be 1169 slots. When the random backoff range is [0, 1023],
the average value of random backoff is 512 slots. Thus, the
average discovery time, when there is just one inquiry
scanner, is computed to be 21169 þ512 ¼2850
slots. The average device discovery time obtained from
simulations is compared with the theoretical value in
Fig. 12. Their small difference is due to non-uniform dis-
tribution of experiments with different k-values. We also
show the distribution of discovery time in Fig. 12 by
sorting the experiments on the basis of their delays. Fig-
ure 12 shows that there is a probability of almost 0.5 that
device discovery can be much higher than the average
value.
We observed in Sect. 4that discovery delay is a func-
tion of k. Moreover, the delay distribution is in the form of
a recursive function, and not in close form. Using the same
line of approach, and aiming similar accuracy, it is not
possible to deal the case for multiple slaves.
Two different sets of experiments were performed with
one master and multiple slaves as explained below.
1. There is one master, the maximum backoff limit is
fixed, and the number of potential slaves is varied. In
this experiment we measure the average total time
taken to discover all the known potential slaves. This
allows us to observe the effect of collision of FHS
packets on discovery time. We show the result of the
experiments in Fig. 13. Each data point in Fig. 13 has
been obtained from 1000 independent experiments. By
independent experiments we mean an experiment
−500 0 500 1000 1500 2000 2500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
Regions of phase values
Average discovery delay in each
region (in slots)
Fig. 11 The impact of phase difference on discovery time
0 0.5 1 1.5 2 2.5 33.5
x 104
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Individual experiments (sorted according to delay)
Discovery delay in individual
experiments (in slots)
Theoretical average delay
Simulated average delay
Fig. 12 Distribution of discovery time
Wireless Netw
123
begins with a new set of values of the device addresses
and their native clocks. In real applications, a user may
have to discover all the devices before selecting one to
activate the desired service. Thus, knowing the distri-
bution of the average total time to discover multiple
devices is useful.
2. There is one master, the number of potential slaves is
fixed, and the maximum backoff limit is varied. This
experiment allows us to observe the effect of backoff
time on device discovery. The idea of backoff has been
introduced to reduce the probability of collision of
FHS packets from two or more devices. However,
backoff time adds to the discovery delay. Some
researchers [13] have proposed to keep it smaller, or
even eliminate the idea of backoff. Thus, it is
interesting to know to what extent backoff time can
be reduced. In Fig. 14 we show how discovery time
varies when the backoff limit is increased. If the
number of potential slave devices is very small, say 3–
4, it is possible to make the backoff limit very small,
say 100 slots. However, for a large number of potential
slaves, a small backoff limit cannot prevent collision
of FHS packets. There is a threshold backoff time
below which the average delay is very long. Thus, the
backoff limit needs to be more than the threshold as
shown in Fig. 14. Even for a large number of devices,
say 50, a backoff limit of 300 slots is a good choice.
6 Improvement of discovery time
In order to reduce discovery time, there has been a proposal
to avoid the 256-time repetitions of the individual trains
[13,15]. The proposal suggests to use the sequence
ABAB, instead of the sequence A
?
B
?
A
?
B
?
. How-
ever, the impact of the proposal on discovery time has not
been studied in detail. To observe how the proposal affects
discovery time, we further investigated the delay behavior
through simulations, and the results are shown in Figs. 15
and 16. In Fig. 15, we show how discovery time varies
with increasing number of potential slaves for the two
cases of inquiry sequence, namely, A
?
B
?
A
?
B
?
and
ABAB, for different fixed values of the backoff limit. In
Fig. 16 we show how discovery time varies with increasing
backoff limit for the two cases of inquiry sequences,
namely, A
?
B
?
A
?
B
?
and ABAB, for different num-
ber of potential slaves. Figures 15 and 16 clearly
demonstrate that it is more effective to apply the sequence
ABABinstead of A
?
B
?
A
?
B
?
.
2 4 6 8 10 12 14 16
2000
2500
3000
3500
4000
4500
5000
5500
Number of Bluetooth enabled devices in a cluster
Average total delay in device discovery (in slots)
−o−: Backoff limit = 1023 slots
−x−: Backoff limit = 767 slots
−+−: Backoff limit = 511 slots
__: Backoff limit = 255 slots
Fig. 13 Average total delay in device discovery as a function of total
number of devices (one device is a master and the rest are potential
slaves)
0 200 400 600 800 1000 1200
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
x 104
Backoff limit in slots
Average total delay in device discovery (in slots)
−o−: Number of devices = 5
−+−: Number of devices = 15
−x−: Number of devices = 25
−*−: Numer of devices = 50
Fig. 14 Average total delay in device discovery as a function of
backoff limit
2 4 6 8 10 12 14 16
0
1000
2000
3000
4000
5000
6000
Upper set of 4 curves: A and B trains are repeated for 256 times each.
−o−: Backoff limit = 1023 slots
−x−: Backoff limit = 767 slots
−+−: Backoff limit = 511 slots
−*−: Backoff limit = 255 slots
Lower set of 4 curves: A and B trains are repeated for 1 time each.
Number of Bluetooth enabled devices in a cluster
Average total delay in device discovery (in slots)
Fig. 15 Average total delay in device discovery as a function of total
number of devices (one device is a master and the rest are potential
slaves)
Wireless Netw
123
There is another proposal to improve discovery time by
eliminating or reducing the random backoff time. How-
ever, it is clear from Fig. 14 and Fig. 16 that it is not a good
idea to completely eliminate random backoff. Instead, a
small backoff limit of 250–300 slots can be used even for
an environment with a large number (say, 50) of potential
slaves.
7 Discussion and conclusion
In this paper, we analyzed Bluetooth device discovery time
and compared it with simulation results. We performed a
large number of experiments to obtain insights into the
distribution of discovery time. We observed that discovery
time suffers from high variance. It can be as low as few
slots to as high as thousands of slots. By performing
additional simulations we observed how the total discovery
time varies with the number of potential slaves when the
backoff limit is constant. We also observed how the total
discovery time varies with the backoff limit when the
number of potential slaves is constant. With a very small
value of backoff limit, discovery time can be too long, if
there are more than 10 potential slaves in the same area. By
performing additional simulations we observed the effec-
tiveness of two proposed improvements to device
discovery. Specifically, it is useful to avoid repetitions of A
and Btrains before a train switch. On the other hand,
complete elimination of the concept of random backoff is
not a good idea because discovery time will be too long. As
a recommendation, choosing a small backoff limit of 250–
300 slots is highly effective in reducing discovery time
even if there is a large number (say, 50) of potential slaves
in the same region.
Acknowledgements This work was partially supported by the
Ministry of Education, Culture, Sports, Science and Technology,
Grants-in-Aid for Scientific Research, 20500071 and 19200005 and
Ministry of Internal Affairs and Communications in Japan, SCOPE
project(071502003).
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Hawaii International Conference on System Sciences, 2004.
0 200 400 600 800 1000 1200
0
0.5
1
1.5
2
2.5
3x 104
Backoff limit in slots
Average total delay in device discovery (in slots)
−o−: Number of devices = 5
−+−: Number of devices = 15
−x−: Number of devices = 25
−*−: Numer of devices = 50
Upper set of 4 curves:
A and B trains are repeated for 256 times each.
Lower set of 4 curves:
A and B trains are repeated for 1 time each.
Fig. 16 Average total delay in device discovery as a function of
backoff limit
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Author Biographies
Goutam Chakraborty received
his Ph.D. in 1993 from Tohoku
University, Japan. Presently he is
Professor and head of the Intel-
ligent Informatics Laboratory,
Department of Software and
Information Science, Iwate Pre-
fectural University, Japan. His
main research interests are Soft
computing algorithms to solve
pattern recognition, prediction,
scheduling and optimization
problems, and problems in wired
and wireless networks.
Sagar Naik received the B.S.
and M.Tech. degrees from
Sambalpur University, Sambal-
pur, India and the Indian
Institute of Technology, Khar-
agpur, respectively, the M.Math.
degree in Computer Science
from the University of Waterloo,
Waterloo, Canada and the Ph.D.
degree in Electrical and Com-
puter Engineering from
Concordia University, Montreal,
QC, Canada. He was a faculty
member with the University of
Aizu, Aizu, Japan, and Carleton
University, Ottawa, ON, Canada. At present he is an Associate Pro-
fessor in the Department of Electrical and Computer Engineering,
University of Waterloo. His research interest are in the areas of testing
communication protocols, smart antenna-based MAC protocols for
wireless LAN and optical networks, mobile computing, data access in
wireless networks, power-conscious software systems for portable
devices and coexistence of 802.11 and Bluetooth technologies.
Debasish Chakraborty re-
ceived his doctoral degree from
the Graduate School of Infor-
mation Science, Tohoku
University, Japan in 1999. Pre-
viously he was a Telecommu-
nication Advancement (TAO)
research fellow and a National
Institute of Information and
Communication Technology
(NiCT) foreign researcher at
Tohoku Research Center. Now
he is working as a visiting
Associate Professor in Research
Institute of Electrical Commu-
nication, Tohoku University. His main research interests are multicast
routing algorithm, QoS, Internet traffic analysis, and wireless and ad
hoc networking.
Norio Shiratori received his
doctoral degree from Tohoku
University, Japan in 1977. Pres-
ently he is a professor and vice
director of Research Institute
of Electrical Communication,
Tohoku University. He has been
engaged in research related to
symbiotic computing paradigms
between human and Information
Technology. He was the reci-
pient of IPSJ Memorial Prize
Wining paper award in 1985,
Telecommunication Advance-
ment Foundation Incorporation award in 1991, best paper award of
ICOIN-9 in 1994, IPSJ best paper award in 1997, and many others. He
is a fellow of IEEE, IPSJ and IEICE.
David Wei received his Ph.D.
degree in Computer and Infor-
mation Science from the
University of Pennsylvania in
1991. He is currently Professor
of Computer and Information
Science at Fordham University,
Bronx, NY. From May 1993 to
August 1997, he was on the
Faculty of the School of Com-
puter Science and Engineering,
University of Aizu, Japan, as an
Associate Professor and the a
Professor. He has authored and
co-authored more than 60 technical papers in the areas of distributed
and parallel processing, wireless networks and mobile computing, and
optical networks in various archival journals and conference pro-
ceedings. He is a lead guest editor of IEEE Journal on Selected Areas
in Communications for the special issue on Mobile Computing and
Networking. Currently, Dr. Wei focuses his research effort on mobile
computing and wireless networks.
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