Minkowski Distance for Geographical Routing in VANETs
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Transcript of Minkowski Distance for Geographical Routing in VANETs
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Empirical Analysis of the Minkowski Distance Order in GeographicalRouting Protocols for VANETs
13th International Conference on Wired & Wireless Internet Communications
Luis Urquiza-Aguiar1 Carolina Tripp-Barba2 Jos Estrada-Jimnez3
Mnica Aguilar Igartua1
1Department of Network Engineering, Universitat Politcnica de Catalunya, Barcelona, SpainEmail: [ luis.urquiza, monica.aguilar]@entel.upc.edu
2Faculty of Informatics, Autonomic University of Sinaloa, Mazatlan, MexicoEmail: [email protected]
3Department of Electronics and Telecommunications, Escuela Politcnica Naciona, Quito, EcuadorEmail: [email protected]
Mlaga, Spain, May 25-27th.
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Introduction
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Agenda
Introduction
Minkowski distance in geographical distance routing metric
Empirical Analysis of Minkowski order r
Conclusions and Future work
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2 Introduction
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Introduction
Vehicular ad hoc networks (VANETs)VANETs are seen as a special case of mobile ad hoc networks (MANETs), wherenodes are vehicles.I Faster topology changes.I Short link lifetime.I Greater number of nodes. (Non-uniformly distributed)I Nodes (vehicles) follow roads and respect traffic signals
Geographical routing protocolsA routing paradigm based only on local information.I Typically based on distance between nodes.I Position of destination and neighbors have to be known .
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3 Introduction
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Introduction
Greedy Perimeter Stateless Routing (GPSR)
(a) Greedy forwarding. (b) Perimeter mode.
Greedy Buffer Stateless Routing (GBSR)
I It uses a buffer instead of perimeter mode. (Delay Tolerant applications)I It uses more information to improve the position estimation. (e.g. speed, time)I GBSR improves packet delivery ratio but introduces delay.
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4 Introduction
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Introduction
ObjectiveTo test if the Euclidean distance is the most suitable function for VANET routingpurposes.
Why not using other distances?
(a) Manhattan distanced = x + y .
(b) Euclidean distance.d =
x2 + y2(c) Dominant distance.d = max(x , y)
All these cases are particular case from Minkowski distance function.
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Minkowski Distance in Geographical VANET routing
Distance functionA distance function (x , y) for two n-dimensional points x and y satisfies:
(x , y) = (y , x) (1a)
(x , y) 0 (1b)(x , x) = 0 (1c)
Minkowski distanceThe Minkowski distance [1] of order r between the points x and y is:
r (x , y) =
(n
i=1
|xi yi |r)1/r
(2)
When r < 0, the Minkowski distance function (2) can be seen as a similaritymeasure
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Minkowski Distance in Geographical VANET routing
Minkowski circles of radius = 1
1.0 0.5 0.0 0.5 1.0
1.0
0.5
0.0
0.5
1.0
r = 0.5
x
y O
1.0 0.5 0.0 0.5 1.0
1.0
0.5
0.0
0.5
1.0
r = 1
x
y O
1.0 0.5 0.0 0.5 1.0
1.0
0.5
0.0
0.5
1.0
r = 1.5
x
y O
1.0 0.5 0.0 0.5 1.0
1.0
0.5
0.0
0.5
1.0
r = 2
x
y O
1.0 0.5 0.0 0.5 1.0
1.0
0.5
0.0
0.5
1.0
r = 4
x
y O
1.0 0.5 0.0 0.5 1.0
1.0
0.5
0.0
0.5
1.0
r = infinite
x
y O
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Minkowski Distance in Geographical VANET routing
Effects of Minkowski order r in routing decision
1. The size and form of the searching area to find a the next forwarding node.
2. The decision of which neighbor is the closest to destination.
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Empirical Analysis of Minkowski order r in VANET geo routing
Simulation SettingsI The mobility of vehicles was obtained with SUMO [4]/C4R [3]I 100 and 150 vehicles, 1 Access PointI IEEE 802.11p. Estinet simulator [2].I GBSR [5] in the routing layer.I Inter-packet time TU(2,6) s E(T ) = 4 s. Packets of 1000 bytes
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Empirical Analysis of Minkowski order r in VANET geo routing
Percentage of packet losses vs r
Packet losses increase when r < 2 and almost constant with r > 2.
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Empirical Analysis of Minkowski order r in VANET geo routing
Average end-to-end packet delay vs r
Notice that average delay for r < 2 is similar to the obtained r = 2, but thepercentage of packet losses are different.
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Empirical Analysis of Minkowski order r in VANET geo routing
Average number of hops vs r
Manhattan distance (r = 1) has the worst performance.When r > 2 the number of hops decrease.
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Empirical Analysis of Minkowski order r in VANET geo routing
Statistical test results
Vehicle Pairwise Standardized p-ValueIs the Difference Median of
Density (r,2) Test Statistic 1 SideSignificant Differences(p-Value < 0.025)?
Percentage packet losses
150 2.5 2.091 0.018 Yes 2.549%+ 2.24 0.012 Yes 3.096 %
Average end-to-end delay
2.5 2.427 0.007 Yes 0.500 s150 3 2.763 0.002 Yes 0.584 s
4 2.203 0.013 Yes 0.409 s+ 1.269 0.108 No 0.186 s
Average number of hops
100 2.5 2.837 0.002 Yes 0.367 hops+ 3.173 0.0005 Yes 0.515 hops
3 2.165 0.015 Yes 0.0136 hops150 4 1.979 0.024 Yes 0.66 hops
+ 3.323 0.0005 Yes 0.11 hops
Table: p-values of Wilcoxon signed rank test for a pairwise comparison of the effect of theMinkowski distance order r
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Conclusions and Future work
ConclusionsOur results in a realistic grid urban scenario, indicate:I The use of the Minkowski order (r < 2) is not a good idea. (higher packet
losses)I The use of the dominant distance (r +) in the routing decision leads to
better performance than the one obtained Euclidean distance (r = 2). (shorterpaths, lower packet losses, same delay)
I The performance differences between euclidean distance are not far from thebest ones obtained by other Minkowski r value. Euclidean distance is always agood choice.
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Conclusions and Future work
Future work include:I To this same comparison in other city topologiesI To develop a geographical routing protocol that combines some Minkowski
distances.I A distance function to select candidates nodes and other distance function to
compute the best forwarding node.I A linear combination of distances in the selection of next forwarding nodes.
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Thanks for your attentionif Questions then
if Time WWIC15_limit thenPlease ask
elseemail to: [email protected]
return Answer & Thanks
Luis Urquiza Aguiarwww.lfurquiza.com
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References
[1] Borg, I., Groenen, P.: Modern Multidimensional Scaling - Theory andApplications. Springer New York, New York, second edn. (2005)
[2] Estinet-Technologies: EstiNet 7 Network Simulator and Emulator (2015),http://www.estinet.com/products.php?lv1=13&sn=15
[3] Fogue, M., Garrido, P., Martinez, F.J., Cano, J.C., Calafate, C.T., Manzoni, P.: Arealistic simulation framework for vehicular networks. In: 5th International ICSTConference on Simulation Tools and Techniques. pp. 3746. ACM, Brussels,Belgium (2012), http://dl.acm.org/citation.cfm?id=2263019.2263025
[4] Krajzewicz, D., Erdmann, J., Behrisch, M., Bieker, L.: Recent development andapplications of SUMO - Simulation of Urban MObility. International Journal OnAdvances in Systems and Measurements 5(3&4), 128138 (2012)
[5] Tripp Barba, C., Urquiza Aguiar, L., Aguilar Igartua, M.: Design and evaluationof GBSR-B, an improvement of GPSR for VANETs. IEEE Latin AmericaTransactions 11(4), 1083 1089 (2013)
IntroductionVANET routingWork objective
Minkowski distance in geographical distance routing metricMinkowski distanceEffects of Minkowski order ``r''
Empirical Analysis of Minkowski order ``r''Simulation SettingsSimulation Results
Conclusions and Future workConclusionsFuture work