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USC Computer Science Technical Reports, no. 862 (2005)

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USC Computer Science Technical Reports, no. 862 (2005)

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Content Zebroids: Carrier-based Replacement Policies to Minimize
Availability Latency in Vehicular Ad-hoc Networks
Shahram
Ghandeharizadeh
Dept of Computer Science
Univ of Southern California
Los Angeles, CA 90089, USA
shahram@usc.edu
Shyam Kapadia
Dept of Computer Science
Univ of Southern California
Los Angeles, CA 90089, USA
kapadia@usc.edu
Bhaskar Krishnamachari
Dept of Computer Science
Dept of Electrical Engineering
Univ of Southern California
Los Angeles, CA 90089, USA
bkrishna@usc.edu
ABSTRACT
Zebroids are mobile devices that carry a referenced data
itemfromaservercontainingthatdataitemtoaclientthat
requested it. An environment employs zebroids in order to
minimize the availability latency incurred by the client. A
device acts as a zebroid when it is in close vicinity of a
server and travels along a path that rendezvous with the
client. Over time, the storage capacity of the zebroid might
become occupied with data items. To carry the requested
data item, it must evict one or more of its existing data
items. The primary contribution of this study is to quantify
thelatency-overheadtradeo®associatedwithalternativere-
placementpoliciesthatmightbeemployedbyazebroid. We
employ a simulation study to quantify the tradeo®s associ-
atedwithpoliciessuchasLeastRecentlyUsed(LRU),Least
Frequently Used (LFU), and a simple random policy. Ob-
tained results highlight the parameter space where the use
of zebroids provides superior performance when compared
with a static data placement strategy that does not use ze-
broids. Weverifythisandtheotherobservedtrendsusinga
simple analytical approximation of latency for a 2D random
walk mobility model.
1. INTRODUCTION
Advances in technology, both in the area of storage and
wireless communications, have now made it feasible to envi-
sion on-demand delivery of continuous media among mobile
vehicles. Vehicles may be equipped with devices consisting
ofseveralgigabytesofstorage,afastprocessorandawireless
interfacewithbandwidthsofseveral10sor100sofMegabits
per second. The radio range of these so called `C2P2' de-
vices is in the order of a few hundred feet enabling them to
collaborate to form a mobile ad-hoc network to deliver the
requested data to a client.
Typical components of a C2P2 system provide the fol-
lowing functionalities. First, a discovery component deter-
minesthosedataitemsavailablein ± timeunitsandvehicles
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Display B
link
= B
link
= B
link
=
time 10 Mbps 20 Mbps 50 Mbps
1 min 1:76 secs 0:88 secs 0:35 secs
2 min 3:52 secs 1:76 secs 0:7 secs
5 min 8:8 secs 4:4 secs 1:76 secs
Table 1: Typical times to replicate a data-item, in
thiscaseanaudioclipwithdisplayrateof 300Kbps,
from a server to a zebroid.
containing these data items. We term ± as the availability
latency of a data item
1
. A data item is available immedi-
ately when it resides in the local storage of the C2P2 device
serving the request. Second, an interface shows this list of
data items and their availability latency to a user, facili-
tating data item selection. Once a user initiates display
of a data item, an admission control component [9] (third
component) ensures availability of both resources and the
referenced data, to support a display free from disruptions
and delays termed hiccups, at the client. Fourth, a data
delivery scheduling technique utilizes resources as a func-
tion of time to deliver the data item to a displaying C2P2
device. This component, may switch between several can-
didate servers containing the referenced data item based on
their proximity, current availability of resources, and net-
work conditions. Fifth, an ad-hoc network routing protocol
facilitates delivery of data between C2P2 devices. Example
protocols are DSR [14], ZRP [13], CEDAR [20] to name a
few. Another system component may monitor whether the
systemisprovidingatargetC2P2withthedesiredQoSand
make adjustments as necessary.
In a typical scenario, a client of this system is provided a
list of available data items. Let ± denote the earliest time
afterwhichtheclientencountersacopyofitsrequesteddata
item. Thislatencyisafunctionofthecurrentlocationofthe
client, its destination andtravelpath, themobility model of
the C2P2 equipped cars, the number of replicas constructed
for the di®erent data items, and the placement of data item
replicas across the C2P2 equipped car. (Without loss of
generalityandinordertosimplifythediscussion,weassume
the term car refers to a C2P2-equipped vehicle.)
Thesystemmayemployavarietyoftechniquestoimprove
±. First, it may construct a larger number of replicas for
1
Without loss of generality, we will use the term data item
in this paper with the understanding that a data item can
be an audio title, video title etc.
thosedataitemswithahigherfrequencyofaccess[10]. Sec-
ond, it might control the placement of these replicas across
the cars. This might be done in a static manner when the
mobility model of cars is pre-deterministic and the requests
are known in-advance, e.g., a broadcast delivery model in-
stead of on-demand. Third, one may employ a dynamic
placement strategy that requires a car without a data-item
that rendezvous with a client.
An implementation of dynamic placement may assume a
two-tiered architecture consisting of a low bandwidth con-
trol plane (similar to the cellular infrastructure) and a high
bandwidthdataplane. Thedataplanesupportsratesinthe
order of tens to hundreds of Megabits per second [2] and
represents the ad hoc peer to peer network between the ve-
hicles. The bandwidth of the control plane is in the order of
a few hundred Kilobits per second used for exchange of con-
trol information between a base station and those vehicles
in its radio range. Example control information include the
dataitemsrequestedbythevehicles,thelocationofvehicles
and their destination. A dispatcher located at every base-
station
2
uses this control information as follows. When a
client references a data-item missing from its local storage,
the dispatcher identi¯es all cars with a copy of the data-
item as servers. Next the dispatcher identi¯es those cars, in
the vicinity of a server, that rendezvous with a client sooner
than the server. Among these, the dispatcher chooses a
single car-server pair that minimizes latency. It then coor-
dinates the transfer of a replica for the requested data item
to the car which carries it to the client. This data carrier
is termed a `zebroid'. To simplify discussion, we consider
dispatchers that use a single zebroid. Extensions that use
multiple zebroids transitively to improve latency is a future
research direction.
More formally, a zebroid is a car, other than either the
client or a server, whose path intersects with the client in
both space and time. The term rendezvous refers to this
spatio-temporal intersection. Like the other cars, zebroids
have limited storage. When the local storage of the chosen
zebroid is completely occupied, it must replace one or more
data items to accommodate the new data item that it then
carries to the requesting client. This motivates replacement
policies to maximize utilization of system storage. The pri-
mary contribution of this paper is to quantify the tradeo®
associated with alternative policies.
Timetotransferadataitemfromaservertoazebroidde-
pends on its size and the available link bandwidth. Table 1
shows times for audio clips using typical wireless link band-
widths. Throughout this paper, we assume that the time to
spawnanewreplicaonthezebroidissmallcomparedtothe
granularity of the mobility of the cars.
Initially, the data item replicas are distributed across the
C2P2s using a static replication scheme. This scheme com-
putesthenumberofdataitemreplicasasafunctionoftheir
popularity. It is chosen as the baseline for comparison with
thereplacementpolicies. Itisstaticsincethenumberofdata
item replicas in the system do not change and no replace-
ments are performed. Henceforth, we refer to this scheme
as the `no-replacements' policy. The replacements incurred
by a replacement policy cause °uctuations in the number of
data item replicas in the system. However, the dispatchers
with the help of the control plane ensure that no data item
2
Dispatchersmaycommunicateviathewiredinfrastructure
between base-stations.
is lost from the system. In other words, at least one replica
ofeverydataitemismaintainedinthead-hocnetworkatall
times. Hence, even though a zebroid may meet a requesting
client earlier than other servers, if its local storage contains
data items with only a single copy, then such a zebroid is
not chosen to carry a new data item.
The replacement policies incur the following overheads.
First, the complexity associated with the implementation of
a policy. Second, the bandwidth used to transfer a copy of
a data item from a server to the zebroid. Third, the average
numberofreplacementsincurredbythezebroids. Notethat
the no-replacements policy incurs neither overhead.
The primary contribution of this work is a zebroid frame-
workinwhichcarrier-basedreplacementpoliciesareusedto
reduce availability latency. Using a random walk mobility
model, wequantifytheimprovementsinlatencythatcanbe
obtainedusingzebroidsascomparedtotheno-replacements
policy. We investigate a variety of environments that di®er
in the contents that the vehicles store as well as the in-
formation about predictability of the cars routes'. In each
environment, a variety of replacement policies are deployed.
The main lessons are summarized in Table 2.
The rest of this paper is organized as follows. Section
2 gives a brief overview of the related work in the area.
Section 3 introduces some terminology used in the paper.
Section 4 describes the various environments used in this
study and a classi¯cation of the di®erent carrier-based re-
placement policies that are deployed in these environments.
Section 5 describes the detailed simulation results obtained
with the various environments and policies. Section 6 gives
thedetailsofouranalyticalapproximationthatcapturesthe
behavior of a replacement policy. Finally, section 7 presents
brief conclusions and future research directions.
2. RELATED WORK
Manypriorstudies[6,17],including[8,11,10],haveinves-
tigated techniques to compute both the number of replicas
for a data item and their placement across both stationary
and mobile devices. These techniques are either centralized
or decentralized. They assume the existence of meta in-
formation such as frequency of access to the di®erent data
items. Noneinvestigatetechniquestomanageavailablestor-
age of a mobile zebroid as a carrier of data.
Use of mobile nodes as data carriers has been proposed
forbothintermittentandsensornetworks. Intermittentnet-
works [12, 21, 16, 5, 4, 23] consider those environments
where a path between a server a client does not exist at
all times. The mobiles nodes act as carriers of data to fa-
cilitate data delivery. With sensor networks, data MULEs
have been proposed to collect data from sensors in a sparse
networks, bu®er this data, and deliver it to wired access
points [19, 15, 3]. However, techniques to manage storage
of a data carrier is an open research topic that has not been
investigatedtodate. Thisconstitutesourfocus,makingthis
study complementary to prior ones.
Apolicyforcontentdistributioninmobileinfostationnet-
works is presented in [24]. This study assumes each node is
interestedinall¯lesstoredatastaticinfostation. Moreover,
a node may serve as a mobile infostation for another node.
An exchange occurs between two nodes if each has a ¯le of
interest for its companion. This study shows that as the
total ¯le repository increases, near optimum resource uti-
lization can be obtained in such an environment even with
Lessons
1. It is better to have more cars with lower storage than fewer ones with more storage. (Figure 1)
2. A simple random eviction policy shows competitive performance. (Figure 1)
3. For a given storage per car, there exists a critical car density which o®ers the maximum gains in availability
latency. Similarly for a given car density, there exists a critical value for the storage per car where the improvement
in latency peaks. (Figures 2, 3)
4. Even when mobility patterns are less predictable, zebroids continue to improve availability latency. (Figure 4)
5. The enhancements in availability latency are obtained at the expense of a higher replacement overhead. (Figure 5, 6)
Table 2: Summary of lessons for the replacement policies from the simulation study.
Database Parameters
T Number of data items.
S
i
Size of data item i
f
i
Frequency of access to data item i.
Replication Parameters
R
i
Normalized frequency of access to data item i
r
i
Number of replicas for data item i
n Characterizes a particular replication scheme.
±
i
Average availability latency of data item i
±
agg
Aggregate availability latency
C2P2 System Parameters
G Number of cells in the map (2D-torus).
N Number of C2P2 devices in the system.
® Storage capacity per C2P2.
° Trip duration of the client C2P2.
S
T
Total storage capacity of the C2P2 system
Table 3: Terms and their de¯nitions
this incentive based non-cooperative policy. In this study,
we focus on availability latency and show a swap-based pol-
icy is inferior to alternatives such as LRU and LFU.
3. TERMINOLOGY
Table 3 summarizes the notation of the parameters used
inthepaper. Below,wedescribebrie°ythemainquantities.
AssumeanetworkofN C2P2-equippedcars,eachwithstor-
age capacity of ® bytes. The total storage capacity of the
systemisST=N¢®. ThereareT dataitemsinthedatabase,
each with size S
i
. The frequency of access to data item i is
denoted as f
i
with
P
T
j=1
f
j
= 1. Let the trip duration of
the client C2P2 under consideration be °.
We now de¯ne the normalized frequency of access to the
data item i, denoted R
i
, is: R
i
=
(f
i
)
n
P
T
j=1
(f
j
)
n
; 0·n·1
Theexponentncharacterizesaparticularreplicationtech-
nique. n = 0:5 denotes a square-root replication technique.
Ri is normalized to a value between 0 and 1. The num-
ber of replicas for data item i, denoted as r
i
, is: r
i
=
min(N;max(1;b
R
i
¢N¢®
S
i
c))
The availability latency for a data item i, denoted as ±
i
,
is de¯ned as the time after which a client C2P2 will ¯nd
at least one replica of the data item accessible to it, either
directly or via multiple hops. If this condition is not sat-
is¯ed, then we set ±i to °. This indicates that data item i
was not available to the client during its journey. Note that
since there is at least one replica in the system for every
data item i, by setting ° to a large value we ensure that the
client's request for any data item i will be satis¯ed. How-
ever, in most practical circumstances ° may not be so large
as to ¯nd every data item.
Weareinterestedintheavailabilitylatencyobservedacross
alldataitems. Hence,weaugmentthe±i foreverydataitem
i with its f
i
to obtain the following weighted availability la-
tency (±
agg
) metric: ±
agg
=
P
T
i=1
±
i
¢f
i
4. ENVIRONMENTS AND CARRIER-BASED
REPLACEMENT POLICIES
4.1 Environments
In the following, we introduce various environments con-
sidered in this study. Our environments assume two types
of vehicles: cars and buses. Cars have a limited storage
carrying a fraction of the data item repository. Buses have
su±cient storage to carry the entire repository (see envi-
ronment 3). Each vehicle is equipped with a single C2P2
device. The dispatchers at the base stations, with the help
of the control plane, ensure that at least one copy of every
data item is maintained in the ad hoc network at all times.
In other words, none of the environments lose data. Table 4
summarizesthepropertiesexhibitedbythevariousenviron-
ments.
Environment1assumesvehiclesarecars. Thedispatch-
ers know complete routes of all cars at all times.
Environment2alsoassumesvehiclesarecars(nobuses).
It di®ers from environment1, in that, the routes of all cars
are not known at all times. Instead, the car routes are gov-
ernedbyacertainroutepredictionaccuracyparameter. The
prediction accuracy parameter inherently provides a certain
probabilistic guarantee on the con¯dence of the car route
predictions. For example, a 70% value for this parameter
indicatesthattheroutepredictedforthecarswillmatchthe
actual ones with probability 0:7. Note that this probability
is spread across the car routes for the entire trip duration.
Environment3assumespresenceofbothbusesandcars.
Carandbusmovementsaregovernedbythemobilitymodel.
Busescanbeconsideredas`universal'serverssincetheycan
directly serve any data item request at any time for any
client as long as the client is in their vicinity.
4.2 Carrier-based Replacement policies
Thereplacementpoliciesconsideredinthispaperarereac-
tivesinceareplacementonlyoccursinresponsetoarequest
issued for a certain data item. Recall that the latency for a
data item request is de¯ned as the time between when the
request was issued at a client to when the client encoun-
tersacarcontainingareplica oftherequested dataitemfor
the ¯rst time. With the help of the control plane, the dis-
patchers are able to determine if there is a zebroid that will
encounter the client earlier than any of the other potential
servers. If there are many such zebroids, the one that meets
the client earliest is chosen. When multiple zebroids meet
the client at the same time, one is chosen randomly. Next,
Characteristic Environment 1 Environment 2 Environment 3
Requestors/Clients Cars Cars Cars
Servers Cars Cars Cars and Buses
Zebroids Cars Cars Cars
Mobility Exact routes known for Routes of cars known with Exact routes known for
all cars a certain probability for all cars and buses
Who carries Cars carry a few data items Cars carry a few data items Buses carry the entire data item
what? as per their storage capacity as per their storage capacity repository while cars carry
only a few data items depending
on their storage
Table 4: Summary of characteristic properties exhibited by the various environments.
the dispatcher replicates the requested title on that zebroid.
However, the zebroid's local storage may be completely ex-
hausted. Hence, it might need to evict another data item`s
replica in order to accommodate this new one. This prob-
lem is analogous to that encountered in case of operating
system paging where the goal is to maximize the cache hit
ratiotopreventthediskaccessdelay[22]. Wepresentbelow
a list of carrier-based replacement policies adapted from the
di®erent page replacement ones.
1. Least recently used (LRU) LRU-K [18] maintains
a sliding window containing the time stamps of the
K
th
most recent references to pages within the bu®er.
During eviction, the page whose K
th
most recent ref-
erence is furthest in the past is evicted. Here we con-
sider the case with K = 1. (a) Local (lru-local):
Each C2P2 keeps track of which data item within its
localrepositorywasleastrecentlyaccessed. Duringre-
placement at the chosen zebroid, this is the data item
whose replica is evicted. (b) Global (lru-global):
The dispatcher maintains the identity of the least re-
cently requested data item computed across all client
requests. The dispatcher maintains the list of data
items resident on each C2P2. This metadata is in the
order of Kilobytes. A zebroid contacts the dispatcher
for a victim and the dispatcher chooses the data item
thatitshouldevict. Thisreplacementpolicyiscentral-
ized and requires (1) a client to transmit its data item
requests to the dispatcher, and (2) for the dispatcher
to maintain su±cient metadata to choose a victim for
each zebroid.
2. Leastfrequentlyused(LFU)(a)Local(lfu-local):
Each C2P2 keeps track of the least frequently used
data item within its local repository. During evic-
tion
3
,thisisthecandidatereplicathatisreplaced. (b)
Global (lfu-global): The dispatcher maintains the
frequency of access to the data items based on client
requests. Whenazebroidcontactsthedispatcherfora
victim data item, the dispacher chooses the data item
with the lowest frequency (global) of access.
3. Random policy (random) In this case, the chosen
zebroidevictsadataitemreplicafromitslocalstorage
chosen uniformly at random.
4. Swap (exchange) policies: With this class of re-
placement policies, every time a zebroid is chosen to
3
The terms eviction and replacement are used interchange-
ably.
transport the requested data item to the client two re-
placements are performed, one at the zebroid and the
other at the server. The server transfers the requested
data item's replica to the zebroid which in exchange
transfers the data item replica it evicted to the server.
Inthisway, thetotalnumberofreplicasforeverydata
item in the system is the same. Note that the evic-
tion policy used at the zebroid can be LRU, LFU or
random.
5. SIMULATION STUDY
5.1 Simulation Set-up
We ¯rst list the assumptions of the simulation study and
then describe the parameter settings used in our experi-
ments.
² The map used is an n£n 2D torus.
² A Markovian mobility model representing a 2D ran-
dom walk on the surface of the torus describes the
movement of the cars across this torus.
² Each grid/cell is a unique state of this Markov chain.
² Only C2P2 equipped cars within the same cell may
communicate with each other.
² A car can transition from a cell to any of its neighbor-
ing 8 cells.
² In each time slot, every car moves from one cell to an-
otherdependingonitscurrentpositionandprobability
transitionmatrix Q=[qij]whereqij istheprobability
of transition from state i to state j.
² A homogeneous repository of equi-sized data items is
used (Si =S).
² The parameters °, ± have been discretized and ex-
pressed in terms of the number of time slots.
² AC2P2devicedoesnotmaintainmorethanonereplica
of a data item. This is because additional replicas oc-
cupy storage without providing bene¯ts.
Here, we set S
i
for every data item to be 1. ® represents
the number of storage slots per C2P2. Each storage slot
storesonedataitem. °representsthedurationoftheclient's
journey in terms of the number of time slots. Hence the
possible values of availability latency are between 0 and °.
± is de¯ned as the number of time slots after which a client
C2P2 device will encounter a replica of the data item for
the ¯rst time. If a replica for the data item requested was
encountered by the client in the ¯rst cell then we set ± =0.
If ± > ° then we set ± = ° indicating that no copy of the
requested data item was encountered by the client during
its entire journey.
Throughout this section, we consider a 5x5 2D-torus with
° set to 10. Our experiments indicate that the trends in
the results scale to maps of larger size with corresponding
scalingintheotherexperimentalparameters. Wesimulated
0 20 40 60 80 100
0
0.5
1
1.5
2
2.5
3
3.5
4
Number of cars
no−replacements
rep_global
lfu_global
lru_global
random
lfu_local
lru_local
Aggregate availability latency (δ
agg
)
1.a
0 20 40 60 80 100
0
10
20
30
40
50
60
Number of cars
rep_global
lfu_global lru_global
lfu_local
random
lru_local
% improvement in δ
agg
wrt no−replacements (ω)
1.b
Figure 1: Figure 1.a and Figure 1.b show ±
agg
and
! for various replacement policies as a function of
(N,®) values when the total storage in the system is
kept ¯xed, ST = 200. Here T = 50 and the map is a
5x5 Torus.
a skewed distribution of access to the T data items using a
Zipf distribution with a mean of 0:27. This distribution is
shown to correspond to sale of movie theater tickets in the
United States [7]. Initially, all cars are distributed across
the map as per the steady-state distribution governed by Q.
Also, the replicas for data items are calculated as per the
square-root replication technique. The data item replicas
aredistributeduniformlyacrosstheC2P2devices. Atevery
time slot a new request is issued. The client that issues the
requests is chosen in a round-robin manner. After a maxi-
mum period of °, the latency encountered by this request is
recorded.
Theinitialplacementofcarsacrossthemapisdetermined
by a random number generator initialized with a seed. All
results presented in this section are averages over 10 such
seeds each invoking 20,000 requests. Hence, each point in
all the presented results is an average of 200,000 requests.
Themetricsconsideredcomprise±
agg
,percentageimprove-
ment in ±agg with a replacement policy as compared to the
no-replacements case and overhead of a replacement policy.
Thislatermetricisquanti¯edusingnumberofreplacements
performed by zebroids.
5.2 Results
The lessons we obtain through an extensive simulation
study have been summarized in table 2. In the following,
we describe the results to support each lesson.
Lesson 1: First, we present the scale-up experiments
with environment 1 to indicate how having more cars with
low storage as opposed to fewer ones with high storage is
morebene¯cialtothereplacementpoliciesinachievinglower
latency. In these experiments, we change ® and N propor-
tionally to keep the total system storage, ST, as well as the
database size constant (T is held constant). The results for
the scale-up experiment are shown in Figure 1. Here, we
set T = 50 and S
T
= 200. Then we choose the following
values of (N,®) = f(20,10), (25,8), (50,4), (100,2)g. As ®
decreases and N increases, all the policies show a rapid im-
provement in latency as compared to the no-replacements
case. This is because additional cars (N) increase the num-
ber of zebroids. With this increase in the zebroid density,
the dispatcher is almost always able to ¯nd a zebroid that
candelivertherequesteddataitemtotheclientearlierthan
any of the potential servers.
Somewhat surprisingly, ±
agg
for the no-replacements pol-
icy goes up as N is increased, while the ±
agg
curves for the
replacementpoliciesshowadownwardtrend. Therearetwo
reasons for this. First, both the total storage capacity and
the database size are ¯xed. Second, as N increases, the
sample space of the potential clients that issue requests in-
creases. Forexample,if10000requestsweregenerated,with
N = 20, each C2P2 initiated 500 data item requests. With
N =100, each C2P2 initiated only 100 requests. Moreover,
® per C2P2 device reduces from 10 when N =20 to 2 when
N = 100. Note that the no-replacements policy assigns the
same number of data item replicas for all (N,®) valuessince
ST remains ¯xed.
Lesson 2: The results in ¯gure 1 indicate that the local
policies lru-local, lfu-local and random show similar perfor-
mance. They do better than the global policies in terms of
latency. A replacement policy in which the zebroids evict
data items randomly performs very well. This policy is sim-
ple, decentralized and easy to implement. It makes an evic-
tiondecisionthatisblindtothepopularityofthedataitems
and the previous history of the data item requests. Hence,
fortheremainderofthepaper,therandomreplacementpol-
icy is used as the representative of the local policies.
Lesson 3: In order to separate out the variation of N
and ®, we next present results capturing the variation of N
while keeping ® constant (case 1) and vice-versa (case 2).
Here we set T = 25. Figure 2 shows the variation in ±
agg
when ® is ¯xed to 2 and N is increased from 25 to 400 (en-
vironment 1). There are two main observations from these
0 50 100 150 200 250 300 350 400
0
1
2
3
4
5
6
Number of cars
no−replacements
random−replacement
Aggregate availability latency (δ
agg
)
2.a
0 50 100 150 200 250 300 350 400
0
10
20
30
40
50
60
Number of cars
% Improvement in δ
agg
wrt no−replacements (ω)
2.b
Figure 2: Figure 2.a and Figure 2.b show ±
agg
and !
as a function of the car density when ® is ¯xed at 2.
Here T =25 and the map is a 5x5 Torus.
¯gures in support of lesson 3 which indicates the existence
of a peak that marks the highest improvement in latency
that can be obtained with the replacement policies. First,
keeping ® constant, increase in car density has higher ben-
e¯ts because increasing N introduces more zebroids in the
system as observed with lesson 1. Second, the curves that
indicate the % improvement in ±
agg
as compared to the no-
replacementscase(!)showaninvertedU-shape. Thereason
that! reducesisbecauseincreasing N alsoincreasestheto-
tal storage in the system. Hence, the number of replicas per
data item goes up thereby increasing the number of servers.
Consequently, the number of zebroids decreases. Hence, the
replacement policy cannot ¯nd a zebroid as often to trans-
port the requested data item to the client earlier than any
of the servers. On the other hand, the increased number
of servers bene¯ts the no-replacements case in bringing ±agg
down. The net e®ect results in reduction in ! for larger
values of N.
Figure3depictsthevariationin±
agg
whenN is¯xedto50
while ® is increased from 1 to 10 in steps of 1 (environment
1). This ¯gure further supports lesson 3 in that it indicates
that given a data item repository, for a constant car den-
sity if we keep increasing the storage per C2P2 device the
enhancements in latency with the replacement policies ¯rst
increase and then go down. This is because the number of
zebroids shows a similar trend as ® is increased.
0 2 4 6 8 10
0
1
2
3
4
5
6
Storage per car (α)
no−replacements
random−replacement
Aggregate availability latency (δ
agg
)
3.a
0 2 4 6 8 10
0
10
20
30
40
50
60
Storage per car (α)
% Improvement in δ
agg
wrt no−replacements (ω)
3.b
Figure 3: Figure 3.a and Figure 3.b show ±
agg
and !
as a function of ® when N is¯xed at 50. Here T =25
and the map is a 5x5 Torus.
Lesson 4: The next set of results elaborate on lesson 4
which applies for environment 2. Here, we present a repre-
sentative scenario that shows that with reduced predictabil-
ity replacement policies still show improvements in ±
agg
. A
probabilistic error is associated with the prediction of the
future path of the C2P2 equipped cars. We use a single
metric to quantify the accuracy of these predictions. Fig-
ure 4 shows the variation in ±agg as a function of this route
prediction accuracy metric. We observe a smooth reduction
50 60 70 80 90 100
0
0.5
1
1.5
2
2.5
3
3.5
4
Prediction percentage
no−replacements
random−replacement
Aggregate availability latency (δ
agg
)
Figure 4: Figure 4 shows ±
agg
as a function of the
prediction accuracy metric with a 5x5 torus. Here
N =100, ®=2 and T =50.
in the improvement in ±
agg
as the prediction accuracy
metric reduces. Note that here as in the other cases only a
maximum of one zebroid per client request may be used by
thereplacementpolicyeventhoughthecarroutesprediction
information is not perfect. In order to provide higher gains
in latency a policy may choose to employ multiple zebroids
as data carriers in order to adapt to the lower accuracy in
the route predictions. We intend to consider such variants
as part of our future work.
Lesson 5: The following set of results elaborate on les-
son 5 which indicates that the improvement in latencies are
obtained at the cost of a replacement overhead. Figure 5
shows the number of replacements for the various policies
as a function of the di®erent (N:®) values. As N increases
and ® reduces, the replacement policies perform a larger
number of replacements thereby enabling the latency to be
reduced. Note that a policy only performs a replacement
when it leads to an improvement in the latency. Hence,
higher replacements lead to higher improvements in ±
agg
.
When the storage is so scarce that only one replica per
data item exists in the C2P2 network, the number of re-
placements will be zero since any replacement will cause a
data item to be lost from the database. The dispatchers
along with the control plane prevent any data loss. At the
other end of the spectrum, when the storage is so abun-
dant that the entire database can be replicated on every
car then number of replacements is again zero since each
request can be satis¯ed locally. However, there is a stor-
age spectrum in the middle where performing replacements
results in improvements in ±agg. Figure 6 shows the num-
ber of replacements for the two cases 1 and 2 mentioned
above. These ¯gures indicate an inverted U-shape. This
behavior is similar to that seen with !. This is because
0 20 40 60 80 100
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Number of cars
random
lfu_global
lfu_local
lru_global
lru_local
rep_global
No of replacements
Figure 5: Figure 5 shows the number of replace-
ments incurred by the various replacement policies
as a function of (N,®) values when the total storage
in the system is kept ¯xed, ST = 200. Here T = 50
and the map is a 5x5 Torus.
initially as storage is increased the bene¯ts obtained with
the replacements policies increase as more replacements can
be performed thereby reducing latency. Eventually a peak
is hit where suitable zebroids that can carry the requested
dataitemtotheclientbecomeavailablemorereadilyresult-
ing in a higher replacements giving a higher !. Thereafter,
as the storage is increased further more data item replicas
are allocated, hence number of zebroids decreases resulting
in a lower number of replacements.
Withenvironment3,recallthatinadditiontothecars,we
have an additional type of vehicle, `buses' which carry the
entire data item repository. Since the buses always have a
copyofeverydataitemtheycannotbezebroids. Exceptfor
theadditionalpresenceofbusesthesimulationsetupforthe
environment3 is similar to that of the other environments.
Here, we study the variation in the system performance,
namely, ±
agg
and replacement overhead as we increase the
number of buses in the system.
Figure 7.a and 7.b show the variation in ±
agg
as a func-
tion of the number of buses for a 5x5 torus when N = 50.
The performance is compared against the no-replacements
case. Increase in number of buses reduces availability la-
tency, trends seen are similar to that seen with lesson 3.
Figure 7.c shows the trend in the number of replacements
as a function of the number of buses.
These results support lesson 5. The same behavior is ob-
tained by increasing the number of buses as was obtained
by varying N and keeping ® constant and vice-versa. Here,
however, as we increase the number of buses the number of
serversgoesupbutdoesnotchangethenumberofzebroids.
Note that every bus increases the total number of replicas
per data item by 1. The possibility of ¯nding a suitable
zebroid that can transport the requested data item to the
client sooner becomes more di±cult as the number of buses
goes up, since the number of servers increases.
The results for the various swap policies have not been
presented here since they provide similar improvements in
0 50 100 150 200 250 300 350 400
0
500
1000
1500
2000
2500
3000
3500
4000
Number of cars
No of replacements
6.a) ®=2
0 2 4 6 8 10
0
500
1000
1500
2000
2500
3000
3500
4000
Storage per car (α)
No of replacements
6.b) N =50
Figure6: Figure6.aandFigure6.bshowthenumber
of replacements as a function of N keeping ® and
vice-versa respectively. Here T = 25 and the map is
a 5x5 Torus.
latency but the number of replacements incurred is twice
thatofthenon-swappolicies. Thisisbecause, asmentioned
earlier with the swap policies, whenever there is an eviction
two replacements are incurred by the swap.
Finally, if we remove the constraint that at least one copy
ofeverydataitemmustbepresentinthesystematalltimes
then we get the following main observation. When storage
is scarce, the global policies (lru-global, lfu-global) produce
the lowest latency and lowest replacement overhead but at
thecostofahigherlossofdata. Thelocalpolicies(lfu-local,
lru-local) produce the highest latency and incur higher re-
placement overhead but lose less data. The random policy's
performanceisbetweenthelocalandtheglobalones. When
systemstorageisaboveacertainthreshold,noneofthepoli-
cies lose any data. Due to lack of adequate space we have
not shown these results here.
0 5 10 15 20
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Number of buses
no−replacements
random−replacement
Aggregate Availability latency (δ
agg
)
7.a
0 5 10 15 20
0
5
10
15
20
25
30
35
40
45
50
Number of buses
% Improvement in δ
agg
wrt no−replacements (ω)
7.b
0 5 10 15 20
0
500
1000
1500
2000
2500
3000
3500
4000
Number of buses
No of replacements
7.c
Figure 7: Figure 7.a and Figure 7.b show ±
agg
and
! as a function of the number of buses with frame-
work3 with a 5x5 torus for the random replacement
policy. Figure 7.c shows the overhead of this policy
in terms of the number of replacements as a func-
tion of the number of buses with N =50. Here ®=2
and T =50.
6. ANALYTICAL EV ALUATION
In this section, we provide a simple probabilistic analy-
sis that gives an upper bound on the latency improvements
obtained using carrier-based replacements. We consider the
movement of N cars as an unbiased random walk on a 2D
torus consisting of G total cells. At the moment that a data
item i is requested by a single client, we assume that there
are ri servers with replicas of that data item. Let N
c
i
be the
expected total number of nodes that are in the same cell as
the servers, which is given by the following expression:
N
c
i
=(N¡r
i
)¢
1¡
1¡
1
G
r
i
(1)
Consider¯rstthescenariowherenoreplacementsaremade.
In this case, the expected availability latency for the data
item is the expected meeting time of the random walk un-
dertaken by the client with one of random walks by any of
theservers. Aldouset al.[1]showthatthethemeetingtime
oftworandomwalksinsuchasettingcanbemodelledasan
exponential distribution with the mean cGlogG, where the
constant c' 0:34 for G¸ 25. The meeting time, or equiv-
alently the availability latency ±i, for the client requesting
dataitemiisthetimetillitencountersanyofthese ri repli-
casforthe¯rsttime. Thisisalsoanexponentialdistribution
with the following expected value (we should note that this
formulation is valid only for sparse cases when G >> r
i
):
±i =
cGlogG
r
i
The aggregate availability latency of the no-replacement
case is then this expression averaged over all data items,
weighted by their frequency of access:
±agg(no¡repl)=
T
X
i=1
f
i
cGlogG
ri
(2)
Nowconsiderwhenreplacementsaremade. Intheanalyt-
icalmodel, weassumethatthat N
c
i
newreplicasarecreated
through replacements, so that the total number of replicas
is increased to r
i
+ N
c
i
. The available latency is reduced
since the client is more likely to meet a replica earlier. The
aggregated expected availability latency over all data items,
with replacements, is then:
±
agg
(repl)=
T
X
i=1
f
i
cGlogG
r
i
+N
c
i
(3)
Notethatinobtainingthisexpression,foreaseofanalysis,
we have assumed that the new replicas start from random
locations in the torus (not necessarily from the same cell
as the original ri servers). It thus treats all the N
c
i
carri-
ers independently, just like the ri original servers. As we
shall show below by comparison with simulations, this ap-
proximation provides an upper-bound on the improvements
that can be obtained because it results in a lower expected
meeting time between the client.
It should be noted that the performance of the scheme
with replacements is similar to an oracle-based algorithm
that is aware of all future movement of cars in terms of
latency. Theoracle-basedalgorithmwouldonlytransferthe
requesteddataitemonasinglezebroid,ifitdeterminesthat
thezebroidwillmeettheclientearlierthananyotherserver.
In the replacements scheme this selected zebroid is included
in the N
c
i
new replicas.
To get the fractional di®erence (labelled !) in the latency
betweentheno-replacementsandreplacementscasewetake
the di®erence between equations 2 and 3 and divide it by
theformer. Thiscapturesthefractionalimprovementinthe
availability latency obtained by performing replacements.
! =
P
T
i=1
f
i
¢C
r
i
¡
P
T
i=1
f
i
¢C
r
i
+(N¡r
i
)¢(1¡(1¡
1
G
)
r
i
)
P
T
i=1
f
i
¢C
r
i
(4)
10
1
10
2
10
3
10
−1
10
0
10
1
10
2
Number of cars
no−replacements
anal

no−replacements
sim

replacements
anal

replacements
sim
Aggregate Availability latency (δ
agg
)
δ
agg
=1
8.a) ±agg
10
1
10
2
10
3
0
10
20
30
40
50
60
70
80
90
100
Number of cars
% Improvement in δ
agg
wrt no−replacements (ω)
analytical upper−bound
simulation
8.b) !
Figure 8: Figure 8.a shows ±agg obtained through
simulations as a function of car density with the no-
replacements and replacement policies respectively
for a 10x10 Torus. Figure 8.b shows the % improve-
ment in ±agg obtained wrt the no-replacements pol-
icy via simulations as well as the analytical approx-
imation for a 10x10 Torus. Here T =10.
Figure 8.a shows the variation in ±agg as a function of N
for T = 10 with a 10x10 torus. Both the x-axis and y-axis
are drawn to a log-scale. Figure 8.b show the % improve-
mentin±
agg
obtainedwithdynamicreplicationforthe10x10
torus respectively. In this case, only the x-axis is drawn to
a log-scale. The analysis and simulation curves match quite
well until the point where ±agg starts becoming less than
1. Also, initially, when the network is sparse the analytical
approximation given by Equation 4 is close to the simula-
tionresults. However, as N increasesthetwocurvesrapidly
diverge since then N becomes greater than G and the net-
workisnolongersparse. Moreover,asmentionedearlier,the
analysisprovidesinanupperboundonthelatencyimprove-
ments, as it treats the carriers given by N
c
independently
while the simulations do not have that constraint.
7. CONCLUSIONS AND
FUTURE RESEARCH DIRECTIONS
This study introduces a zebroid framework in which ze-
broids are used as data carriers to transport data items to
clients thereby reducing their observed latency. Various re-
placementpolicies areconsidered to determine whichcandi-
datedataitemreplicastoevictfromthezebroidsduringthe
replacement process. We have quanti¯ed the performance
improvement of these policies using availability latency as
the metric of interest. The base line for comparison is a
static no-replacements scheme. Moreover, the overhead in-
curred by a replacement policy is captured in the number of
replacements incurred by it. The primary conclusion is that
for a given database repository using more cars each with
lower storage provides higher gains in latency as compared
to using a few with more storage. We present an analytical
formulation of the improvements in latency with a replace-
ment policy in a sparse network.
Weintendtoextendthisstudyinseveraldirections. First,
we intend to explore alternate de¯nitions for the route pre-
dictionaccuracyparameter(seeSection 4.1, environment3)
aspartofourfuturework. Second,insteadofusingonlyone
zebroidperclientrequest,multiplezebroidscanbeemployed
thereby making it possible to improve the latency even fur-
ther. However, this will lead to a higher replacement over-
head. We intend to study such replacement schemes that
employ multiple zebroids. Third, to better re°ect reality we
would like to validate the lessons from this study with some
real world simulation traces of vehicular movements.
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Description

Shahram Ghandeharizadeh, Shyam Kapadia, Bhaskar Krishnamachari. "Zebroids: Carrier-based replacement policies to minimize availability latency in vehicular ad-hoc networks." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 862 (2005).

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Creator Ghandeharizadeh, Shahram (author), Kapadia, Shyam (author), Krishnamachari, Bhaskar (author)

Core Title USC Computer Science Technical Reports, no. 862 (2005)

Alternative Title Zebroids: Carrier-based replacement policies to minimize availability latency in vehicular ad-hoc networks (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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