Analysis of Hop Limit in Opportunistic Networks by

Analysis of Hop Limit in Opportunistic Networks by Suzan Bayhan*, Esa Hyytiä, Jussi Kangasharju* and Jörg Ott *University of Helsinki and Aalto University, Finland, Bayhan et al., 17:15-18:00 IEEE ICC 2015 ICC Static and Capital Time-Aggregated Hall Graphs Interactive 2

Mobile opportunistic networks Many mobile devices with different types of content stored locally

Mobile opportunistic networks Carried by users

Mobile opportunistic networks Short range radio, e.g., Bluetooth, Wifi Direct

Opportunistic communication store-carry-forward Mobility is the enabler Opportunistic short-range transmission

Hop limitations are applied to keep routing scalable and resource-efficient. Source node Destination node Relaying nodes Hop limit

Hop-Limited Routing A message can be forwarded to at most h hops Hop=1 Hop=2 Hop=h

Hop = 0 Destination Message created hop=0

Hop = 1 Message received by direct neighbors

Hop = 2 destination reached

Hop = 3 Other nodes may not be aware of the delivery of the message to the destination.

Hop = 10 Waste of resources

How does hop limit affect opportunistic routing? 1 2 3 average time to send a packet fraction of nodes reachable delivery ratio

analysis approaches http://www.lettercult.com/archives/3196 Static graph Time-aggregated graphs Simulations

Human contact trace Corresponding network topology Contact trace Static graph Time-aggregated graphs Capacity Analysis for h=1,,h or simulate!

Network topology generation A B C B C E D B T=0 t1 t2 t3 t4 T

Network topology generation A B C B C E D B T=0 t1 t2 t3 t4 T Approach 1: Aggregate all contacts in the trace, and create a static graph to represent network topology à Static graph A Observation point B D C E

Network topology generation A B C B C E D B T=0 t1 t2 t3 t4 T Approach 1: Aggregate all contacts in the trace, and create a static graph to represent network topology à Static graph Approach 2: Instead of one single graph, observe the network in several time points, and create the network topology à Time-aggregated graph C A Observation point B D C E Time interval 1 Time interval 2 A t1 D B E t2 C A t3 B t4 E D

Static vs. Time-Aggregated graphs Static graph A B D C E D! B! C! E in static graph

Static vs. Time-Aggregated graphs Static graph A B D C E D! B! C! E in static graph Time interval 1 Time interval 2 A B A B C D E C E Only D! B in this second graph B! C link is missing D

Static vs. Time-Aggregated graphs Static graph B A C D D! B! C! E in static graph E Time-aggregation results in loss of temporal dynamics but simplistic Static graph overestimates the connectivity and hence the capacity Time interval 1 Time interval 2 A B A B How much does it affect? C D E C E Only D! B in this second graph B! C link is missing D

AHOP All Hops Optimal Paths All Hops Optimal Path (AHOP) Problem: For a given source node and maximal hop count,, find, for each hop count value,, and destination node, an -hop constrained optimal path between and.

AHOP for capacity analysis Q1: Average time to send a packet s w1 w2 Path length w3 d Q2: Fraction of nodes reachable 2 3 Size of the connected component 1 s 4 Q3: Delivery ratio 7 6 5 Probability of the existence of a path s w1 w2 w3 d

AHOP analysis w(a,b) w(b,c) w(c,d) A B C D p: A à B à C à D o Optimal path p* from A to D is the path with minimum w(p) among all paths from A to D. o Hop-limited optimal path p* is p h * where length(p h *) <= h o Given the edge weights, what is the weight of p, w(p)?

Edge weights o o w(p) = w(a,b) + w(b,c) + w(c,d) à Additive weights w(p) = max{w(a,b), w(b,c), w(c,d)} à Bottleneck weights Additive weight: Path weight = routing delay weight of an edge: inter-contact time between the corresponding nodes Bottleneck weight (capacity): A routing scheme should choose the paths that will highly probably exist à most probable paths. weight of an edge: the inverse of the number of encounters between the corresponding nodes

Human contact trace Corresponding network topology Contact trace Static graph Time-aggregated graphs AHOP for h=1,,h Bottleneck Additive or simulate!

Nume ical Evaluation R for graphs and AHOP (timeordered package Benjamin Blonder) ONE for simulations

TABLE I HUMAN CONTACT TRACES USED IN THE ANALYSIS. Trace Duration # of devices (n) Context Infocom05 3 days 41 Conference participants Cambridge 11 days 36 1st and 2nd year undergraduate students Infocom06 4 days 78 (and 20 stationary devices) Conference participants http://crawdad.cs.dartmouth.edu/ Community Resource for Archiving Wireless Data At Dartmouth

Static analysis: hop limit vs. capacity Normalized delivery success Normalized delay Bottleneck capacity 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Infocom05 Cambridge Infocom06 1 2 3 4 5 6 7 8 Hop count (h) Additive weight 0.2 0.4 0.6 0.8 1.0 Infocom05 Cambridge Infocom06 1 2 3 4 5 6 7 8 Hop count (h)

Bottleneck capacity 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Static analysis: hop limit vs. capacity Normalized delivery success Infocom05 Cambridge Infocom06 1 2 3 4 5 6 7 8 Hop count (h) Additive weight 0.2 0.4 0.6 0.8 1.0 Normalized delay Infocom05 Cambridge Infocom06 1 2 3 4 5 6 7 8 Hop count (h) Delivery ratio increases while delay decreases with increasing h

Bottleneck capacity 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 2 3 4 5 6 7 8 Hop count (h) Static analysis: hop limit vs. capacity Normalized delivery success Marginal changes Infocom05 Cambridge after Infocom06 these points Additive weight 0.2 0.4 0.6 0.8 1.0 Normalized delay Infocom05 Cambridge Infocom06 1 2 3 4 5 6 7 8 Hop count (h) Delivery ratio increases while delay decreases with increasing h

Static analysis: optimal hop Optimal hop (bottleneck) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Infocom05 Cambridge Infocom06 1 2 3 4 5 6 7 8 Hop count (h) Optimal hop (additive) 1.0 1.5 2.0 2.5 3.0 Infocom05 Cambridge Infocom06 1 2 3 4 5 6 7 8 Hop count (h)

Static analysis: optimal hop Optimal hop (bottleneck) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1 2 3 4 5 6 7 8 Hop count (h) Infocom05 Cambridge Infocom06 Optimal hop (additive) 1.0 1.5 2.0 2.5 3.0 Very low hop counts Infocom05 Cambridge Infocom06 1 2 3 4 5 6 7 8 Hop count (h)

Revisiting our research questions 1 2 3 average time to send a packet o Nodes can be reached faster by relaxing hop count o Improvement vanishes after several hops o Optimal hop counts (total path delay): 2-3 hops fraction of nodes reachable The first two hops are sufficient to reach every node from every other node. delivery ratio increases significantly if at least two hops are allowed, and stabilizes after h approx. 4.

Time-aggregated graphs Three aggregation windows Short : 1 h Medium: 6 h Long: 24 h

Time-aggregated graphs Optimal hop count over time Infocom05, short Optimal hop count (bottleneck) 1.0 1.5 2.0 2.5 3.0 3.5 Time aggregated, h=3 Time aggregated, h=8 Static, h=3 Static, h=8 0 10 20 30 40 50 60 70 Snapshot index

Optimal hop count (bottleneck) 1.0 1.5 2.0 2.5 3.0 3.5 http://imnotyouami.weebly.com/ http://commons.wikimedia.org Time-aggregated graphs Optimal hop count over time Time aggregated, h=3 Time aggregated, h=8 Static, h=3 Static, h=8 0 10 20 30 40 50 60 70 Snapshot index Day Night Dependency on the time of the day Lower than static optimal hop count

Time-aggregated graphs Hop vs. reached fraction Reached fraction 0.2 0.4 0.6 0.8 1.0 Short Medium Long Static 1 2 3 4 5 6 7 8 Hop count (h) Larger time-window, higher reached fraction Acc. to static analysis, 2 hops are enough to reach all. But lower connectivity for others. Trend is the same (h=2 achieves most of the gains of multi-hop routing).

Network snapshots Hop count vs. capacity Bottleneck capacity 0.5 0.6 0.7 0.8 0.9 1.0 Short Medium Long Static 1 2 3 4 5 6 7 8 Hop count (h) Optimal hop count (bottleneck) 1.0 1.5 2.0 2.5 3.0 3.5 Short Medium Long Static Simulation 1 2 3 4 5 6 7 8 Hop count (h) Highest increase from h=1 to h=2 After h=4, vanishingly small gain

Network snapshots Hop count vs. capacity Bottleneck capacity 0.5 0.6 0.7 0.8 0.9 1.0 1 2 Short Medium Long Static 1 2 3 4 5 6 7 8 Hop count (h) Optimal hop count (bottleneck) 1.0 1.5 2.0 2.5 3.0 3.5 Short Medium Long Static Simulation 1 2 3 4 5 6 7 8 Hop count (h) 1 Highest increase from h=1 to h=2 2 After h=4, vanishingly small gain

Network snapshots Hop count vs. capacity Bottleneck capacity 0.5 0.6 0.7 0.8 0.9 1.0 Short Medium Long Static 1 2 3 4 5 6 7 8 Hop count (h) Optimal hop count (bottleneck) 1.0 1.5 2.0 2.5 3.0 3.5 Short Medium Long Static Simulation 1 2 3 4 5 6 7 8 Hop count (h) Short and medium aggregation windows closer to reality

Simulations AHOP analysis Delivery ratio 0.2 0.4 0.6 0.8 Infocom05, ttl=1 hour Infocom06, ttl=1 hour Infocom05, ttl=6 hours Infocom06, ttl=6 hours Infocom05, ttl=24 hours Infocom06, ttl=24 hours 2 4 6 8 10 Hop count (h) Bottleneck capacity 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Infocom05 Cambridge Infocom06 1 2 3 4 5 6 7 8 Hop count (h) Bottleneck capacity: inverse of number of encounters

Simulations Delivery ratio 0.2 0.4 0.6 0.8 Infocom05, ttl=1 hour Infocom06, ttl=1 hour Infocom05, ttl=6 hours Infocom06, ttl=6 hours Infocom05, ttl=24 hours Infocom06, ttl=24 hours 2 4 6 8 10 Hop count (h) Agrees our previous analysis Trend is the same h=2 highest improvement h>4 stability Bottleneck capacity 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Infocom05 Cambridge Infocom06 1 2 3 4 5 6 7 8 Hop count (h)

Simulations Delivery delay and path lengths AHOP analysis Delivery delay (s) 5000 15000 25000 Infocom05, ttl=1 hour Infocom06, ttl=1 hour Infocom05, ttl=6 hours Infocom06, ttl=6 hours Infocom05, ttl=24 hours Infocom06, ttl=24 hours Additive weight 0.2 0.4 0.6 0.8 1.0 Infocom05 Cambridge Infocom06 1 2 3 4 5 6 7 8 Hop count (h) 2 4 6 8 10 Hop count (h) Additive weight: inter-contact time

Summary Effect of hop count Capacity of the studied human contact networks increases significantly with h>=2 Improvement vanishes after h=4 Effect of analysis approach Static graph approach overestimates connectivity and performance Time window of the aggregation should be paid attention to

http://www.netlab.tkk.fi/tutkimus/pdp/ bayhan@hiit.fi jakangas@helsinki.fi esa@netlab.tkk.fi jo@netlab.tkk.fi Source node Destination node Relaying nodes Hop limit Thank you

Reading list Guérin, Roch, and Ariel Orda, "Computing shortest paths for any number of hops." IEEE/ACM Transactions on Networking (TON) 10.5 (2002): 613-620. M. Vojnovic and A. Proutiere, Hop limited flooding over dynamic networks, in Proceedings IEEE INFOCOM, 2011, pp. 685 693. M. Vojnovic and A. Proutiere, Hop limited flooding over dynamic networks, in Proceedings IEEE INFOCOM, 2011, pp. 685 693. B. Blonder, T. W. Wey, A. Dornhaus, R. James, and A. Sih, Temporal dynamics and network analysis, Methods in Ecology and Evolution, vol. 3, no. 6, pp. 958 972, 2012. A. Casteigts, P. Flocchini, W. Quattrociocchi, and N. Santoro, Time-varying graphs and dynamic networks, Int. Journal of Parallel, Emergent and Distributed Systems, vol. 27, no. 5, pp. 387 408, 2012. Burdakov, Oleg P., et al. Optimal placement of communications relay nodes. Department of Mathematics, Linköpings universitet, 2009. Available at http://www.hiit.fi/u/bayhan/