Opportunistic Resource Exchange in Inter-vehicle Ad-hoc
Networks
∗
∗∗
∗
Bo Xu and Aris Ouksel and Ouri Wolfson
University of Illinois at Chicago
{boxu,aris,wolfson}@uic.edu
∗
Research supported by NSF Grants ITR-0086144,
NSF-0209190, ITR 0326284, NSF-0330342,
NSF-0320956, CCR-0070738, and EIA-0000516.
Abstract
In this paper we examine resource discovery in
inter-vehicle ad-hoc networks in an urban area, where
moving vehicles communicate with each other via
short-range wireless transmission. Our focus is on
real-time location-specific information. We explore an
opportunistic approach to resource discovery, in which
a vehicle obtains information about resources from
encountered vehicles. The vehicle uses a spatio-
temporal relevance function to sort the resources, and
save only the most relevant ones. Our theoretical and
experimental analysis indicates that the opportunistic
exchange algorithm automatically limits the
distribution of a resource to a bounded spatial area
and to the duration for which the resource is of
interest.
1. Introduction
Consider an urban area with hundreds of thousands
of vehicles. Drivers and passengers in these vehicles
are interested in information relevant to their trip. For
example, a driver would like his/her vehicle to
continuously display on a map, at any time, the
available parking spaces around the current location of
the vehicle. Or, the driver may be interested in the
traffic conditions one mile ahead. Such information is
important for drivers to optimize their travel, to
alleviate traffic congestion, or to avoid wasteful
driving. The challenge is processing queries in this
highly mobile environment, with an acceptable delay,
overhead and accuracy. One approach to solving this
problem is maintaining a distributed database stored at
fixed sites that is updated and queried by the moving
vehicles via the infrastructure wireless networks.
Potential drawbacks of this approach are (i) the
responses to queries may be outdated, (ii) the response
time may not meet the real-time requirements, and (iii)
access to infrastructure communication service is
costly. In this paper we explore a new paradigm that is
based on inter-vehicle communications.
We assume that two vehicles can communicate with
each other when their distance is smaller than a
threshold. This communication can be enabled by a
local area wireless protocol such as IEEE 802.11 [13],
Ultra Wide Band (UWB) [16], Bluetooth [14], or
CALM [15]. These protocols provide broadband
(typically tens of Mbps) but short-range (typically 50-
100 meters) peer-to-peer communication. With inter-
vehicle communication, a mobile user discovers the
desired information from the vehicles it encounters, or
from distant vehicles by multi-hop transmission relayed
by intermediate moving vehicles. Thus, resource
discovery is performed in an inter-vehicle ad hoc
network. Compared to the traditional fixed-station
based information query, this paradigm has the
following advantages:
1. It provides better information authenticity,
accuracy, and reliability, especially for real-
time information. Consider for example parking
space availability. Information collected from a
vehicle that is leaving a parking lot tends to be
more reliable than that from the fixed site.
2. It is free of charge, assuming that vehicles are
willing to relay messages for free (in exchange
for their messages being relayed).
In this paper we propose an opportunistic approach
to resource discovery, in which a vehicle either senses
the resources or obtains new resources from its
exchanges with encountered vehicles. For example, a
vehicle V either senses the location of the parking
space V vacated, or it finds out about available parking
spaces from other vehicles. In turn, either these spaces
have been vacated by these encountered vehicles, or
these vehicles have obtained this information from
other, previously encountered, vehicles. Thus the
parking space information transitively spreads out
across vehicles. This simple flooding procedure raises
an important issue: what constraints on the resource
spreading behavior are caused by limited memory
space in each vehicle. With a limited memory space, a
vehicle can only keep the most “relevant” resources it
obtains. This in turn raises the question on what should
be an appropriate relevance function in this
environment? What parameters must be taken in
consideration in this function? In the parking example,
the duration since the parking slot became available
and the distance of this slot from the vehicle ought to
play a significant role in determining relevance. As
both duration and distance increase, the likelihood is
very low that the parking slot will remain available.
The relevance function must therefore reflect these
intuitive considerations. In this paper, we will introduce
a spatio-temporal relevance function to compute the
relevance of resources on the basis of both time and
distance.
Our theoretical and experimental analysis reveals
some interesting and useful properties of the
opportunistic exchange approach based on the
relevance function. First, a resource only spreads
within a limited geographic area beyond the home of
the resource (e.g., the location of a parking space).
Second, within this limited area, the replication of a
resource increases as a vehicle approaches the home of
the resource. Furthermore, the boundary of this limited
area varies with time. It initially expands until a time
threshold beyond which there is no copy of the
resource in the system. These properties show that our
opportunistic exchange algorithm automatically limits
the distribution of a resource to a bounded spatial area
and to the duration for which the resource is of interest.
Thus, for example, a vehicle in Chicago will never hear
about a free parking slot in New York.
The rest of the paper is organized as follows. In
section 2 we introduce the resource model. In section 3
we describe the opportunistic exchange algorithm and
analyze it theoretically. In section 4 we analyze it by
simulations. In section 5 we discuss relevant work.
Finally in section 6 we conclude the paper and discuss
future work.
2. Resource Model
In this section we introduce several notions
regarding resources and the relevance of resources.
2.1. Resources and Their Organization
Resources may be spatial, temporal, or spatio-
temporal. Information about the location of a gas
station is a spatial resource. Information about the
price of a stock on 11/12/03 at 2pm is temporal.
Information about a free parking space is a spatio-
temporal resource.
A spatio-temporal resource, or a resource for short,
is a piece of information about a spatio-temporal event
e.g., the availability of a parking space at a certain
location at a certain time, or the vehicle speed at a
particular time and location. The home of the resource
is the point location of the event. For example, the
home of an available parking space is the location of
the parking space. The age of a resource is the length
of time since the resource has been created. For
example, consider the resource indicating that a
parking slot has become available at 2pm. The age of
the resource at time 2:02pm is 2 minutes. Similarly,
consider the resource indicating that the speed of a
vehicle at time 2pm at location x is v. The age of the
resource at time 2:05 is 5 minutes.
We assume that a moving object has a fixed amount
of memory allocated to each application (e.g. the user
allocates 10 entries for relevant parking slots. In other
words, the user wants only 10 parking slots to be saved
and displayed
1
). In this paper, we will only investigate
the behavior of the resource propagation in the case of
one application. The number of entries allocated for the
application is referred to as the memory allocation.
2.2. Relevance of Resources
The relevance of spatial resources decreases as
distance increases, and similarly, the relevance of
temporal resources decreases with age. The relevance
of spatio-temporal resources decreases as distance or
time increase. For the parking slot example, as the
information about a parking slot grows stale, it
becomes less and less relevant as the likelihood of its
availability decreases. Its relevance should therefore be
less than that of a more recent one. This comparison
must however be tempered by the distance factor. A
1
This parking slot information is only relevant to the
driver when he is close to his destination. However, the
driver should not be bothered indicating this and the
default is always showing all the slots saved in the
memory.
parking slot that is closer to a vehicle is certainly more
relevant than one that is farther away. In general, the
relevance of a resource decays as its age increases, and
the distance from its home increases. In this paper we
use the following function to compute the relevance of
resource R:
dtRF ⋅−⋅−=
β
α
)( )0,( ≥
β
α
(1)
t is the age of R and d is the distance from the home
of R.
α
and
β
are non-negative constants that represent
the decay factors of time and distance respectively. The
bigger the ratio
βα
, the more the relevance is
sensitive to time than to distance; conversely, the
relevance is more sensitive to distance than to time.
The relevance function we use in this paper is one
example in which the relevance decays linearly with
time and distance. But there are other possible types of
relevance functions in which other behaviors may be
exhibited. Furthermore, other factors such as the travel
direction with respect to the home of the resource may
be considered in the relevance function. However, in
this paper we confine ourselves to time and distance
alone.
3. Opportunistic Exchange
In subsection 3.1 below we describe the
opportunistic exchange procedure and follow it up in
subsection 3.2 with a theoretical analysis.
3.1. Procedure Description
Denote by r the wireless transmission range. We say
that two vehicles encounter each other when their
distance is smaller than r. When two vehicles A and B
encounter each other, A and B first exchange their
resources. Upon receiving new resources, vehicle A
computes the relevance for each received resource and
re-evaluates the relevance of its own resources. If all
the resources do not fit in A’s memory space, the least
relevant ones are purged. If two moving objects travel
within the transmission range for a period of time, after
the initial exchange only newly arrived resources are
exchanged.
We assume that if A encounters two or more
vehicles simultaneously, the exchanges occur
sequentially. In other words, we assume that there is a
mechanism to resolve interference and conflicts.
3.2. Spatial and Temporal Boundaries of
Resource Distribution
In this subsection, we theoretically analyze the
opportunistic exchange procedure, and show that with
the above procedure, a resource is always propagated
within a bounded area, and there exists an age
threshold beyond which the resource disappears from
the system. In the following analysis we assume that
the wireless transmission range r is negligible and the
time consumed by each resource exchange is
negligible.
Denote by M the memory allocation, and by v the
maximum speed a vehicle can travel with. We say that
a resource is rejected by O at time t if O receives but
does not save the resource at t. A resource is new for a
time interval [t
1
,t
2
] if the resource is created during this
time interval.
Theorem 1: If
0=r and the time consumed by
each resource exchange is 0, and each object receives
or generates at least K new resources per time unit, then
for each resource R,
(1) If
0>
α
, then there is no copy of R in the system
after
)1( v
K
M
⋅+⋅
α
β
time units since the creation of
R.
(2) At any point in time, there is no copy of R at any
location that is more than
K
M
v ⋅
distance units away
from the home of R.
Theorem 1 indicates that if there are sufficient
interactions between vehicles in the system, and if new
resources are generated at a certain pace, then the
spread of each resource is limited to a neighborhood
around its home, and the resource disappears from the
system after a bounded amount of time.
Example: If the memory allocation is 10, the
maximum speed is 60 miles/hour,
01.0=
αβ
, and
each object receives or generates at least 100 new
resources per hour, then the age threshold is 9.6
minutes and the spatial boundary is 6 miles.
Before proving Theorem 1, let us introduce the
following three lemmas.
Lemma 1: Let R be a resource created at time t
0
. If
R is rejected or purged by an object O at time t (t≥t
0
),
then at any time point t’ after t, the relevance of the
least relevant resource in O’s memory is higher than or
equal to
)'()(
0
ttv −⋅⋅+−
βα
.
Proof: Consider the relevance of R to O at time t.
Since R is created at t
0
and the transmission range is 0,
the distance between the location of O at t and the
home of R cannot exceed
)(
0
ttv −⋅ . Thus the
relevance of R for O at t cannot be lower than
)()(
00
ttvtt −⋅⋅−−⋅−
βα
. Since R is rejected
or purged by O at t, the relevance of the least relevant
resource in O’s memory at t cannot be lower than
)()(
00
ttvtt −⋅⋅−−⋅−
βα
. From time t to t’,
the maximum distance O can move is
)'( ttv −⋅ . Thus
the decrease of the relevance of the least relevant
resource in O’s memory from t to t’ cannot exceed
)'()'( ttvtt −⋅⋅+−⋅
β
α
. Therefore, the relevance of
the least relevant resource in O’s memory at t cannot be
lower than
))'()'(()()(
00
ttvttttvtt −⋅⋅+−⋅−−⋅⋅−−⋅−
β
α
β
α
)'()(
0
ttv −⋅⋅+−=
βα
.
Lemma 2: Let R be a resource created at time t
0
. If
R is received by an object O at time t (t≥t
0
), then at any
time point t’ after t, the relevance of R for O at t’ is not
lower than
)'()(
0
ttv −⋅⋅+−
βα
.
Proof: Consider the relevance of R to O at time t.
Since R is created at t
0
and the transmission range is 0,
the distance between the location of O at t and the
home of R cannot exceed
)(
0
ttv −⋅ . Thus the
relevance of R for O at t cannot be lower than
)()(
00
ttvtt −⋅⋅−−⋅−
βα
. From time t to t’,
the maximum distance O can move is
)'( ttv −⋅ . Thus
the decrease of the relevance of R from t to t’ cannot
exceed
)'()'( ttvtt −⋅⋅+−⋅
β
α
. Therefore, the
relevance of R for O at t cannot be lower than
))'()'(()()(
00
ttvttttvtt −⋅⋅+−⋅−−⋅⋅−−⋅−
βαβα
)'()(
0
ttv −⋅⋅+−=
βα
.
Lemma 3: At any point in time, the relevance of any
resource in any object’s memory is higher than or equal
to
)( v
K
M
⋅+⋅−
βα
.
Proof: Let t be an arbitrary time point. Let P be the
set of the new resources that an object O has received
or generated during the time interval
],[ t
K
M
t −
(namely the last
K
M
time units before t). Since O
receives or generates at least K new resources per time
unit, the size of P is at least M. Let Q be the set of
resources in O’s memory at t. There are two cases.
1.
PQ ⊆ . Let R be a resource in Q. Suppose that
R was created at t
0
. According to Lemma 2, the
relevance of R for O at t is no less than
)()(
0
ttv −⋅⋅+−
β
α
which is no less than
)( v
K
M
⋅+⋅−
βα
.
2. There is at least one resource in Q that is not in
P. Consider any resource R that is in P but not in
Q. R must have been rejected or purged by O at
sometime t’ between
K
M
t −
and t. Suppose
that R was created at t
0
. According to Lemma 1,
the relevance of the least relevant resource in
O’s memory at t is higher than or equal to
)()()(
0
v
K
M
ttv ⋅+⋅−≥−⋅⋅+−
βαβα
.
In either of the above two cases, the relevance of the
least relevant resource in O’s memory at t is higher than
or equal to
)( v
K
M
⋅+⋅−
βα
. In other words, at any
point in time, the relevance of any resource in any
object’s memory cannot be lower than
)( v
K
M
⋅+⋅−
βα
.
Now we prove Theorem 1.
Proof of Theorem 1: First let us prove that there is
no copy of R in the system after
)1( v
K
M
⋅+⋅
α
β
time
units since the creation of R. When the age of a
resource is greater than
)1( v
K
M
⋅+⋅
α
β
, its relevance
is lower than
)( v
K
M
⋅+⋅−
βα
. According to Lemma
3, this resource cannot exist in any object’s memory.
Now we prove that at any point in time, there is no
copy of R at any location that is more than
K
M
v ⋅
distance units away from the home of R. Consider the
relevance of R for an object O that is more than
K
M
v ⋅
away from the home of R. If O has R, the age
of R is greater than
.
K
M
Thus the relevance of R is
lower than
)( v
K
M
K
M
v
K
M
⋅+⋅−=⋅⋅−⋅−
βαβα
. This
contradicts Lemma 3.
4. Simulation
In this section we first describe the simulation
method, and then present the simulation results.
4.1. Simulation Method
We synthetically generated and moved objects
within a 50mile×50mile square area. For each object i,
we randomly chose two points within the square area,
and assigned them as the start point and the destination
point of i respectively. The path of i is the straight-line
segment between the start point and the destination
point. i moves along its path from the start point to the
destination point at a constant speed. All the objects
use the same constant speed. A resource is generated
and carried by i at the time point when i starts to move,
representing that for example, a parking slot is
available because of the leaving of i. The home of the
resource is the start point of i. The memory allocation
is the same for all the objects.
There are three parameters for each simulation run,
namely the memory allocation M, the transmission
range r, the constant speed v, and the traffic density d
(i.e. the number of objects per square mile). Each
simulation run is executed as follows. At the beginning
of the simulation run, 50×50×d objects are generated
and they start to move at the same time (time 0). When
the distance between two objects is smaller than r, they
exchange their resources, re-evaluate the relevance, and
purge less relevant resources if needed. Each exchange
is finished instantaneously. When an object reaches its
destination point, it is removed from the system, and a
new object is generated and started (again with the start
and destination points randomly chosen within the
square area). A resource is also generated for the start
of the new object. The length of each simulation run is
10 simulated hours.
During a simulation run, we trace the distribution of
each resource R at each time unit during R’s lifetime
(R’s lifetime is the time period from the time when R is
generated up to the time when it disappears from the
system). For the purpose of this, we generate 30 rings
centered at the home of R and with the width of 0.1
mile, such that the outer radius of the i-th (1≤i≤30) ring
is i×0.1 miles. Let t be the time of the k-th time unit of
R’s lifetime. The distribution of R at t is described and
recorded as follows. We compute the density of R
within each ring i, by dividing the number of copies of
R within i at t by the size of i. Thus we obtain a vector
),...,,(
3021
RkRkRk
ddd , where
Rk
i
d is the density of R
within ring i at t. We call this vector the density
histogram of R for the k-th time unit.
At the end of the simulation run, we average the density
histograms of each R for the k-th time unit, and thus get
a vector
),...,,(
3021
kkk
ddd , where
N
d
d
R
Rk
i
k
i
å
= ,
and N is the total number of resources that have been
generated. This vector is the average density histogram
for the k-th time unit. From the average density
histogram other two measures are derived. One is the
number of copies at the k-th time unit, which equals to
)(
30
1
å
=
⋅
i
i
k
i
Ad
where A
i
is the size of ring i. The other
is the 95%-boundary, which gives the smallest distance
such that 95% of the copies are within this distance
from the home. The system parameters and their values
are listed in Table 1 below:
Table 1: Simulation parameters and their values
Parameter Symbol Unit Value
Decay factor of time
α
1
Decay factor of distance
β
1
Side length of the
geographic area
mile 50
Memory allocation (given
in the number of memory
entries allocated)
M
25, 50,
75, 100,
125
Transmission range r meter
50, 100,
150, 200,
250
Traffic speed v miles/ hour
20, 40,
60, 80
Traffic density d objects/mile
2
25, 50,
100
Ring width in density
histogram
mile 0.1
Duration of a simulation
run
hour 10
4.2. Simulation Results
4.2.1. Propagation of a resource.