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USC Computer Science Technical Reports, no. 778 (2002)

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USC Computer Science Technical Reports, no. 778 (2002)

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Content 1
PATHS: analysis of PATH duration Statistics and their impact on reactive
MANET routing protocols
Narayanan Sadagopan, Fan Bai, Bhaskar Krishnamachari, Ahmed Helmy
Abstract—We develop a detailed approach to study how
mobility impacts the performance of reactive MANET rout-
ing protocols. In particular we examine how the statistics
of path durations including PDFs vary with the parame-
ters such as the mobility model, relative speed, number of
hops, and radio range. We find that at low speeds, cer-
tain mobility models may induce multi-modal distributions
that reflect the characteristics of the spatial map, mobility
constraints and the communicating traffic pattern. How-
ever, our study suggests that at moderate and high veloci-
ties the exponential distribution with appropriate parame-
terizations is a good approximation of the path duration dis-
tribution for a range of mobility models. As an analytical
case study, we then show how the mathematical expression
obtained for the path duration distribution can be used to
prove that the non-propagating cache hit ratio in DSR is in-
dependent of velocity for the freeway mobility model. The
case study illustrates how various aspects of protocol perfor-
mance can be analyzed with respect to a number of signifi-
cant parameters, given a good model for the path duration
distribution. The reciprocal of the average path duration is
analytically shown to have a strong linear relationship with
the throughput and overhead that is confirmed by the sim-
ulation results for DSR.
I. INTRODUCTION
Availability of small, inexpensive wireless communi-
cating devices has played an important role in moving ad
hoc networks closer to reality. Consequently, Mobile Ad
hoc NETworks (MANETs) are attracting a lot of attention
from the research community. MANETs are advantageous
because of their readily deployable nature as they do not
need any centralized infrastructure. Since this field is still
in its developing stage, not many MANETs have been de-
ployed yet. Thus, most of the research in this area is sim-
ulation based. These simulations have several parameters
such as the mobility model, traffic pattern, propagation
Department of Computer Science, University of Southern California,
E-mail: narayans@cs.usc.edu
Department of Electrical Engineering, University of Southern Cali-
fornia, E-mail: fbai@usc.edu
Department of Electrical Engineering, University of Southern Cali-
fornia, Email: bkrishna@usc.edu
Department of Electrical Engineering, University of Southern Cali-
fornia, E-mail: helmy@ceng.usc.edu
model, etc to name a few. In this paper, we focus on de-
veloping a detailed approach to study the effect of mobil-
ity on the performance of reactive MANET routing proto-
cols like DSR [2] and AODV [5]. This paper proposes a
novel approach to understand the effect of mobility on pro-
tocol performance. It uses statistical analysis (of simula-
tion data) to obtain detailed statistics of link and path dura-
tion including their Probability Density Functions (PDFs).
Then, the approach uses a case study of DSR to demon-
strate how the path duration PDF can be used to analyti-
cally determine the non-propagating cache hit ratio in the
freeway mobility model. Further, through simple analyti-
cal models, using the case study of DSR, it shows a strong
correlation between the reciprocal of average path dura-
tion and the throughput and overhead of reactive proto-
cols.
Recently, there has been a greater focus on a system-
atic study of the effect of mobility on the performance
of routing protocols. [17] proposed the IMPORTANT
framework to systematically analyze the effect of mobility
on routing protocols. In this framework, the authors pro-
posed to evaluate the MANET routing protocols using a
“test-suite” of mobility models that span several mobility
characteristics like spatial dependence, geographic restric-
tions, etc. These models included the Random Waypoint
(RW), Reference Point Group Mobility (RPGM), Freeway
(FW) and Manhattan (MH). They found that mobility sig-
nificantly impacts the performance of the protocols, which
is in agreement with several other studies. Moreover, they
also proposed a reason for How mobility impacts perfor-
mance: Mobility impacts the connectivity graph (average
link duration in particular) which in turn impacts the pro-
tocol performance.
To explain Why mobility impacts the performance, [18]
introduced BRICS methodology. It proposed that a proto-
col could be considered to be made up of parameterized
“building blocks” or basic mechanisms. The effect of mo-
bility on the entire protocol can be explained in terms of its
effect on these “building blocks”. Some of the “building
blocks” proposed by BRICS for reactive protocols were
flooding, caching, error detection, error notification and
error recovery. Both DSR and AODV use these “building
blocks” in their operation. However, they still behave dif-
2
ferently for a given mobility model. BRICS suggested that
a possible reason for this difference might be the different
parameter settings for the “building blocks” in AODV and
DSR. This leads to different impacts of mobility on these
mechanisms. A brief overview of the work done in [17]
and [18] is given in the section III.
In this paper, we develop an approach that combines sta-
tistical analysis of simulation data and analytical modeling
to get a deeper understanding of the protocol performance
in the presence of mobility. [17] concluded that average
link duration is a useful metric for relating mobility with
protocol performance. At the same time, intuitively, the
protocol performance depends on the duration of a path be-
tween the source and the destination. Path duration is sig-
nificantly related to link duration. It is actually the min-
imum link duration along a path. In general, longer the
path duration, better the performance in terms of through-
put and overhead. However, the relationship between the
path duration and protocol performance (throughput and
overhead) has not been categorized yet. In this paper, we
examine the detailed statistics of link and path duration
including PDFs across the “test-suite” of mobility mod-
els proposed in [17]. We first attempt to relate the path
duration PDFs to the impact of mobility on the “building
blocks” of reactive protocols. We then attempt to cate-
gorize the relationship between path duration and proto-
col performance as either strongly (or weakly) linearly (or
non-linearly) related. The contributions of this study are
the following:
1) Characterizing the statistics of link and path dura-
tions including PDFs for the different mobility mod-
els used in our study using simple statistical analy-
sis. This also leads to a characterization of link and
path durations based on the communicating traffic
pattern.
2) Investigating possible distributions to approximate
the path duration PDF across the mobility models
used. At moderate to high mobility, we suggest
that an exponential distribution with an appropriate
parameterization is a reasonable approximation to
most of our studied models.
3) Illustrating the use of the path duration PDF to an-
alytically model protocol performance (using the
case study of the non-propagating cache hit ratio in
DSR for the FW model).
4) Establishing a linear relationship, through simple
first order analytical models (that are validated by
simulation results), between the reciprocal of path
duration and protocol performance, that helps ex-
plain several performance trends under various mo-
bility models.
The rest of the paper is organized as follows: Section
II gives an overview of the related work. Section III sets
our work in context with the recent work in this area. Link
and path duration are formally defined in section IV. Sec-
tion V discusses our simulation setup while the results of
these simulations are discussed in section VI. Section VII
gives first order analytical models relating the path dura-
tion statistics (PDFs and averages) and the protocol perfor-
mance of reactive protocols using the case study of DSR.
Our conclusions and future work are listed in section VIII.
II. RELATED WORK
In this paper, we study the detailed statistics of link and
path duration including their PDFs across a rich set of mo-
bility models. As mentioned in section I, we believe such
a study might help in formulating analytical models for
protocol performance across these mobility models. How-
ever, such a thought was inspired by other pioneering work
done in MANET research.
A. Mobility Models:
Mobility models for simulations have been one of the
early topics of research in this field. One of the early con-
tributions was made by Broch, Maltz, Johnson, et al where
they evaluated DSR, AODV , DSDV [3] and TORA [16]
using the RW model [1]. They concluded that mobil-
ity does impact the performance of routing protocols. To
evaluate these protocols over a wider range of scenarios,
Johansson, Larsson, Hedman, et al proposed the scenario
based performance analysis [10]. In this study they pro-
posed mobility models for disaster relief, event coverage
and conferences. Hong, Gerla, Pei, et al proposed the Ref-
erence Point Group Mobility (RPGM) model in [8]. One
of the main applications of this model is in battlefield com-
munications. The authors give several other applications
of RPGM in [8]. While defining their framework, [17]
proposed to evaluate the protocols under a richer set of mo-
bility models. Apart from using the RW and RPGM, they
used two other mobility models i.e. the FW and the MH
models. In this study, we use these four models for our
simulations.
B. Protocol Independent Metrics:
Apart from analyzing the effect of mobility on proto-
col performance, it is useful to characterize mobility inde-
pendent of the protocols. Hence, there have been several
attempts to propose mobility metrics. Johansson, Lars-
son, Hedman, et al proposed the relative motion between
mobile nodes to distinguish the different mobility models
used for their scenario based study in [10]. [17] used
3
the metrics of relative motion and average degree of spa-
tial dependence to characterize the different mobility mod-
els used in their study. They also proposed the connectiv-
ity graph metrics as a “bridge” relating the mobility met-
rics to the protocol performance. They found that average
link duration at the graph level could explain this relation-
ship. Hong, Gerla, Pei and Chiang proposed the rate of
link change as a metric to differentiate the various kinds of
RPGM and RW models in [8]. We agree with [17] and [8]
that the connectivity graph characteristics might help in re-
lating mobility with protocol performance. As mentioned
in section I, we believe that the path duration can also be
added to this set of connectivity graph metrics. Moreover,
unlike other studies, we not only examine the averages, but
also focus on the detailed statistics including the PDFs of
link and path duration across several mobility models.
C. Reactive Protocols:
In this paper, we focus on evaluating the reactive
MANET routing protocols like DSR and AODV . There
have been several studies to compare both proactive and
reactive routing protocols. [11], [13], [2], [12] and [4]
give a very good exposition of this subject. Here, we dis-
cuss the work that focus completely on reactive protocols.
Johnson, Maltz, Broch, et al proposed DSR in [2], while
AODV was proposed by Perkins in [5]. Maltz, Broch,
Jetcheva and Johnson gave a very comprehensive analy-
sis of DSR in terms of its basic mechanisms of route dis-
covery and caching [4]. They proposed several optimiza-
tions for reducing the route discovery overhead. Most of
these optimizations are now part of the DSR implementa-
tion in the network simulator (ns-2) [15]. Das, Perkins
and Royer compared the performance of AODV and DSR
in [12]. They observed that DSR outperformed AODV
in less demanding situations, while AODV outperformed
DSR at heavy traffic load and high mobility. To explain
these differences, the BRICS methodology was proposed
to decompose protocols into basic “mechanisms” [18]. It
illustrated an approach for this decomposition by suggest-
ing a common architecture that encompassed both AODV
and DSR. Though both AODV and DSR consist of simi-
lar mechanisms or “building blocks” (that are parameter-
ized), they behave differently in the presence of mobil-
ity. Some of these mechanisms are caching, flooding, etc.
BRICS claimed that this difference arises due to the dif-
fering impact of mobility on the mechanisms of the proto-
cols. The difference in impact on the mechanisms seems
to arise from the different parameters chosen by these pro-
tocols for these mechanisms. In this study, using the case
study of DSR in the FW model, we propose an analytical
model relating the path duration PDF to the performance
of one of the “building blocks” i.e. the non-propagating
cache hit ratio. Both [4] and [18] consider this mech-
anism to play an important role in determining the rout-
ing overhead of DSR (and reactive protocols in general).
Moreover, through first order analytical models, using the
case study of DSR, we also show the relationship (linear
or non-linear) between the average path duration and the
reactive protocol performance.
D. Analysis
Apart from simulation-based studies, the MANET re-
search literature also contains analytical work on mobil-
ity and protocol performance modeling. One of the earli-
est analysis of mobility was done by Mc Donald and Znati
in [6]. They used a RW like mobility model and derived
expressions for the probability of path availability and
link availability for different initial conditions. Stochas-
tic properties of the RW model were studied recently in
[20], [21] and [22]. Su, Lee and Gerla exploited the non-
random movement of mobile nodes during intervals to pre-
dict its location in [9]. They proposed a model for link du-
ration and evaluated it using the RW model. In this paper,
we examine the detailed statistics of link and path duration
including PDFs across several mobility models used in our
study. Gruber and Li presented a very detailed analysis of
link duration times for a two hop MANET in [23]. In this
study, the distribution of the link duration appeared to be
exponential. Their analysis assumed that the source and
destination are fixed while the intermediate hop is moving
using the RW model. The exponential distribution of link
duration also comes up in the analysis of single path and
multipath DSR by Nasipuri, Castaneda and Das in [19].
They assumed that the link durations are exponentiallydis-
tributed independent random variables (i.i.d) and analyt-
ically derived the distributions for path duration, which
turns out to be exponential as well. The underlying mo-
bility model was not very clearly specified. Moreover, the
exponential distribution assumption was not validated by
simulation or real data. Inspired by these works, in this pa-
per, we examine the detailed statistics of link and path du-
ration includingPDFs across the RW, RPGM, FW and MH
models. We observe that under certain conditions the path
duration PDFs can be approximated by exponential distri-
butions for the models used in our study. We demonstrate
the effect of the number of hops, the transmission range
and the relative speed of the mobilitymodel on the path du-
ration PDF. Using the case study of DSR in the FW model,
we show how the path duration PDF can be analytically re-
lated to the performance of the non-propagating cache hit
ratio “building block”. We also show how such an analysis
can be extended to AODV as well. Later, again using the
4
case study of DSR, we propose simple analytical models
that relate the average path duration to the performance of
reactive protocols.
III. BACKGROUND
Our approach of evaluating the protocols across mobil-
ity models was inspired by the IMPORTANT framework
proposed in [17]. This framework made an attempt to-
wards the systematic evaluation of the impact of mobility
on MANET routing protocols. It defined protocol inde-
pendent metrics like the average degree of spatial depen-
dence (
) and the average relative speed (
RS)to cap-
ture certain mobility characteristics. One of these charac-
teristics was the extent to which the motion of a node is in-
fluenced by nodes in its neighborhood (which is captured
by
). Another characteristic was the presence of
geographic restrictions on mobility. Once these metrics
were defined, mobility models that spanned these mobil-
ity characteristics were chosen. These models were:
1) Random Waypoint (RW): At every time instant, a
node randomly chooses a speed and destination, and
moves towards it. Each node moves independently
of other nodes.
2) Reference Point Group Mobility (RPGM): Nodes
move in either single or multiple groups. The move-
ment of a node in a group is strongly influenced by
the leader of the group.
3) Freeway (FW): Each node moves in its lane on
the freeway. Its movement is constrained by nodes
moving ahead of it in the same lane.
4) Manhattan (MH): Nodes move on a grid. As in the
FW model, each node is constrained by nodes mov-
ing ahead of it. However at the cross points of the
grid, a node is free to change its direction unlike the
FW model.
Different mobility patterns following the above mobility
models were generated by varying the maximum speed of
the mobile nodes. The mobility metrics of these mobility
patterns were evaluated. Using these patterns, simulations
were run in the network simulator (ns-2 [15]) environment
with the CMU Wireless Ad Hoc networking extension to
evaluate the performance of DSR, AODV and DSDV in
terms of throughput and routing overhead. To explain the
relationship between the mobility metrics and the proto-
col performance, certain connectivity graph metrics were
defined. Some of these metrics were the number of link
changes, the path availability and the average link dura-
tion. For their study, the most useful of these graph metrics
was the average link duration (
LD), which could help in
relating the mobility metrics to the protocol performance
metrics. The study observed that, given a communication
traffic pattern, the underlying mobility pattern does have
a significant impact on the performance of routing proto-
cols. Moreover, it concluded that there is no clear perfor-
mance based ranking of the protocols across these mobility
models.
To explain Why mobility affects the protocol perfor-
mance, [18] proposed the BRICS methodology to sys-
tematically decompose routing protocols into basic mech-
anisms or “building blocks”. This methodology claimed
that the difference in the protocol performance comes from
the fact that the basic mechanisms (or “building blocks”)
of these protocols are different. For example, DSR and
AODV are reactive while DSDV is proactive. However,
although DSR and AODV belong to the class of reac-
tive protocols, they behave differently for a given mobility
model. To understand this difference better, BRICS pro-
posed the following possibledecomposition of the reactive
routing protocols:
Reactive protocols consist of two major phases:
1) Route Setup Phase: In this phase, a route between
the source and destination is setup on demand. The
basic mechanisms (and their parameters) used in this
phase are:
a) Flooding: It is responsible for distributing the
source’s route request in the network. Its pa-
rameter is the range of flooding, which is spec-
ified by the Time To Live (TTL) field in the IP
header.
b) Caching: Caching is an optimization to re-
duce the overhead of flooding. If a node has
a cached route to the destination, it will re-
ply to the source’s route request. Its param-
eter is whether aggressive caching should be
used. i.e. should the nodes use all the over-
heard route replies and should they cache mul-
tiple routes to the destination.
2) Route Maintenance Phase: This phase is responsi-
ble for maintaining the path between the source and
the destination. The basic mechanisms used in this
phase are Error Detection, Error Notification and
Error Recovery.
Both DSR and AODV make different choices for the pa-
rameters of the “building blocks” mentioned above. For
example, in the caching “building block”, DSR performs
aggressive caching while AODV does not. In the flood-
ing “building block”, before flooding a route request in the
network, DSR issues a route request with a TTL of 1 (non-
propagating route request). On the other hand, AODV per-
forms an expanding ring search (with TTL = 1, 3, 5 and 7)
5
before initiating the flooding . As in [18], we define the
non-propagating cache hit ratio as the ratio of the route
requests which are answered by the one hop neighbors to
the total number of route requests. [18] observed that the
“building blocks” are impacted differently by a given mo-
bility model, depending on their choice for the parameters.
Moreover the performance of the entire protocol is deter-
mined by the performance of these building blocks. For
example, the overhead of the protocol is affected by the
non-propagating cache hit ratio. Higher the ratio, lower
will be the frequency of route request flooding. Since both
AODV and DSR use different caching strategies, this non-
propagating cache hit ratio for the two protocols might be
different, which leads to different routing overheads for
these protocols for a given mobility model.
In this paper, we attempt to develop a deeper under-
standing of the impact of mobility on the protocol perfor-
mance. We take a step further in the analysis of the impact
of mobility on the connectivity graph. We determine the
detailed statistics (including PDFs) of link and path dura-
tion at the connectivity graph level across the “test-suite”
of mobility models proposed by [17]. Our study suggests
that for moderately high speeds and paths with more than
two hops, the path duration PDF can be approximated as
an exponential distribution for the mobility models used.
We then show how the path duration PDF can be analyti-
cally related to the performance of reactive protocols. For
this purpose, we model the non-propagating cache hit ra-
tio of DSR in the FW model as a case study. Further, the
average path duration is related to the performance of reac-
tive protocols through simple first order analytical models
(that are validated by simulation results), using DSR as a
case study.
In the next section, we formally define the link and path
duration metrics.
IV. CONNECTIVITY GRAPH METRICS
One of the main challenges for routing in MANETs is
to deal with the topology (connectivity graph) changes re-
sulting from mobility. The performance of a protocol is
greatly determined by its ability to adapt to these changes.
Realizing this, researchers have proposed metrics to char-
acterize the effect of mobility on the connectivity graph
with an aim to explain the effects of mobility on protocol
performance. We define the link duration and path dura-
tion metrics in this section.
First, we mention some commonly used symbols in this
section. Let
Although, the initial design does not specify the expanding ring
search, the ns-2 implementation of AODV uses the expanding ring
search.
1)
be the total number of nodes.
2)
be the Euclidean distance between nodes and at time
.
3) be the transmission range of the mobile nodes.
The connectivity graph is the graph , such
that =
. At time t, a link
iff
.
Let be an indicator random variable which has
a value iff there is a link between nodes and at time
. Otherwise, .
1) Link Duration: For two nodes and , at time
,
duration of the link
is the length of the longest
time interval [
,
! ] during which the two nodes are
within the transmission range of each other. More-
over these two nodes are not within the transmission
range at time
"$#
and time
!&%
# for
#(’
. For-
mally,
LD
! " iff ) *+,!-
#’ /.0
1 and
2"0#
3 and !4%
# 3 . Other-
wise, LD
.
2) Path Duration: For a path 5687-9
9 !-;:<:<:
9>=@? ,
consisting of A nodes , at time
, path duration is
the length of the longest time interval [
! ], dur-
ing which each of the A " links between the nodes
exist. Moreover, at time
B"3#
and time
!% # ,
#C’
, at least one of the A links does not exist. Thus,
path duration is limited by the duration of the links
along its path. Specifically, at time
, path duration
is the minimum of the durations of the A " links
9 9 !@-
9 !@
9ED
@:<:<:
9>=@F
9>=
at time
. Formally,
PD
5 GHA = = @
’ . i.e.
none of the nodes having the cache in the same lane
as S are within the transmission range of S at time
.
13) be the probability that ) @
" i.e.
none of the nodes having the cache in the opposite
lane are in the range of S at time
.
14) Finally, be the probability that none of the nodes
having the cache are within the transmission range
of S at time
.
B!
(4)
We now evaluate and . Since the average relative
speed of nodes on the same lane w.r.t.S is different
from that in the opposite lane, both the lanes will have
different PDF (and CDF) for the path duration as shown
in equations 2 and 3. Hence we consider them separately
in this analysis.
Determining " :
If the farthest node (having the cache) in the opposite lane
moves out of range of S, all the nodes (having the cache)
would have moved out of range of S. Thus, " is now the
probability that the farthest node (having a cache) in the
opposite lane moves out of the range of S. Let this farthest
12
node be . Let >%
.
5 @ " (5)
5 4%
" " 5 "
" " 5 ’ % 5 ’ % " @
% (6)
where
is the average relative speed in the lane opposite
to S and D.
is the CDF of the path duration on the op-
posite lane. Thus, from equation 3,
F

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Description

Narayanan Sadagopan, Fan Bai, Bhaskar Krishnamachari, Ahmed Helmy. "PATHS: Analysis of PATH duration statistics and their impact on reactive MANET routing protocols." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 778 (2002).

Asset Metadata

Creator Bai, Fan (author), Helmy, Ahmed (author), Krishnamachari, Bhaskar (author), Sadagopan, Narayanan (author)

Core Title USC Computer Science Technical Reports, no. 778 (2002)

Alternative Title PATHS: Analysis of PATH duration statistics and their impact on reactive MANET routing protocols (title)

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)

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Repository Name USC Viterbi School of Engineering Department of Computer Science

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