PATHS : Analysis of PATH Duration Statistics and their Impact on Reactive MANET Routing Protocols

1. PATHS: Analysis of PATH Duration Statistics and their Impact on Reactive MANET Routing Protocols Narayanan Sadagopan*, Fan Bai+, Bhaskar Krishnamachari*+, Ahmed Helmy+ * Computer Science Department + Electrical Engineering Department University of Southern California

2. Outline • Introduction and Motivation • Background on Mobility Models • Link/Path Duration Metrics • Results & Observations • Distributions at low and high mobility • Is it exponential?! • Models: Path Duration, Throughput & Overhead • Conclusions and Future Work

3. Introduction and Motivation • Mobility affects performance of MANET protocols significantly [IMPORTANT ‘Infocom BSH03’] • Mobility affects connectivity, and in turn protocol mechanisms and performance • In this study: • Closer look at the mobility effects on connectivity metrics (statistics of link duration (LD) and path duration (PD)) • Develop approximate expressions for LD & PD distributions (Is it really exponential? When is it exponential?) • Develop first order models for Tput & Overhead as f(PD) Protocol Mechanisms Performance (Throughput, Overhead) Mobility Connectivity

4. Mobility Models • Used the IMPORTANT framework and tools[BSH’03] • Rich set of mobility models that exhibit various spatial correlation and relative velocities • Four main models: • Random Waypoint (RW) [CMU Monarch, BMJHJ’98] • Reference Point Group Mobility (RPGM) [UCLA, HGPC’99] • Freeway (FW) • Manhattan (MH)

5. Mobility Models (contd.) • Random Waypoint Model (RWP) • A node picks random destination & random velocity [0, Vmax] • After reaching the destination, it stops for the “pause time”. • This procedure is repeated until simulation ends • Reference Point Group Mobility (RPGM) • A group’s general movement is determined by a logical reference point • Each node in a group follows the reference point with small deviation: • Angle Deviation Ratio(ADR) and Speed Deviation Ratio(SDR). • In our study ADR=SDR=0.1 • Two scenarios: Single Group (SG) and Multiple Group (MG)

6. Mobility Models (contd.) • Freeway Model (FW) • A node is restricted to its lane on the freeway • Velocity of a node is temporally dependent on its previous velocity • If two mobile nodes on the same freeway lane are within the Safety Distance (SD), the velocity of the following node cannot exceed the velocity of preceding node • Manhattan Model (MH) • Similar to Freeway model • Allows nodes to make turns at intersections Map for FW Map for MH

7. Connectivity Metrics • Link Duration (LD): • For nodes i,j, the duration oflink i-j is the longest interval in which i & j are directly connected • LD(i,j,t1)=t2-t1 • iff t, t1  t  t2,   > 0 : X(i,j,t)=1,X(i,j,t1-)=0, X(i,j,t2+)=0 • Path Duration (PD): • Duration of path P={n1,n2,…,nk} is the longest interval in which all k-1 links exist

8. Simulation Scenarios in NS-2 • Path duration computed for the shortest path (at graph level) until it breaks.Validated later via protocol paths. • Mobility Models (IMPORTANT tool) • Vmax= 1,5,10,20,30,40,50,60 m/s, • RPGM: 4 groups (called RPGM4) • Speed/Angle Deviation Ratio=0.1 • 40 nodes, in 1000mx1000m area • Radio range (R)=50,100,150,200,250m • Simulation time 900sec

9. Link Duration (LD) PDFs • At low speeds (Vmax < 10m/s) link duration has multi-modal distribution for FW and RPGM4 • In FW due to geographic restriction of the map • Nodes moving in same direction have high link duration • Nodes moving in opposite directions have low link duration • In RPGM4 due to correlated node movement • Nodes in same group have high link duration • Nodes in different groups have low link duration • At higher speeds (Vmax > 10m/s) link duration does not exhibit multi-modal distribution

10. Nodes moving in opposite directions FW model Vmax=5m/s R=250m Nodes moving in the same direction/lane Multi-modal Distribution of Link Duration for Freeway model at low speeds

11. RPGM w/ 4 groups Vmax=5m/s R=250m Nodes in different groups Nodes in the same group Multi-modal Distribution of Link Duration for RPGM4 model at low speeds

12. RW RPGM (4 groups) Vmax=30m/s R=250m FW

13. Path Duration (PD) PDFs • At low speeds (Vmax < 10m/s) and for short paths (h2) path duration has multi-modal forFW and RPGM4 • At higher speeds (Vmax > 10m/s) and longer path length (h2) path duration can be reasonably approximated using exponential distribution for RW, FW, MH, RPGM4.

14. Nodes moving in opposite directions FW Vmax=5m/s h=1 hop R=250m Nodes moving in the same direction Multi-modal Distribution of Path Duration for Freeway model at low speeds, low hops

15. Nodes in different groups RPGM4 Vmax=5m/s h=2 hops R=250m Nodes in the same group Multi-modal Distribution of Path Duration for RPGM4 model at low speeds, low hops

16. RW RPGM4 h=2 h=4 100 Vmax=30m/s R=250m FW h=4

17. Exponential Model for Path Duration (PD) • Let path be the parameter for the exponential PD distribution: PD PDF f(x)= pathe- path x • As path increases average PD decreases (and vice versa) • Intuitive qualitative analysis: • PD=f(V,h,R); V is relative velocity, h is path hops & R is radio range • As V increases, average PD decreases, i.e., path increases • As h increases, average PD decreases, i.e., path increases • As R increases, average PD increases, i.e., path decreases

21. Exponential Model for PD But, PD PDF f(x)= pathe- path x

22. RW h=2 RGPM4 h=4 FW h=4 Vmax=30m/s R=250m FW h=4 - Correlation: 94.1-99.8%

23. RW h=2 RGPM4 h=4 Vmax=30m/s R=250m - Goodness-of-fit Test FW h=4

24. Effect of Path Duration (PD) on Performance (in-progress): Case Study for DSR • PD observed to have significant effect on performance • (I) Throughput: First order model • T: simulation time, D: data transferred,Tflow: data transfer time,Trepair: total path repair time, trepair: av. path repair time,f: path breakfrequency  

25. Effect of PD on Performance (contd.) • (II) Overhead: First order model • Number of DSR route requests= • p: non-propagating cache hit ratio, N: number of nodes • Evaluation through NS-2 simulations for DSR • RPGM exhibits low , due to relatively low path changes/route requests  Pearson coefficient of correlation () with

26. Conclusions • Detailed statistical analysis of link and path duration for multiple mobility models (RW,FW,MH,RPGM4): • Link Duration: multi-modal FW and RPGM4 at low speeds • Path Duration PDF: • Multi-modal FW and RPGM4 at low speeds and hop count • Exponential-like at high speeds & med/high hop count for all models • Developed parametrized exponential model for PDPDF, as function of relative velocity V, hop count h and radio range R • Proposed simple analytical models for throughput & overhead that show strong correlation with reciprocal of average PD

27. Future Work • Apply path duration analysis to various ad hoc protocols • Attempt to explain: Why does path duration distribution become exponential? • Analyze convergence time and cache performance to account for varying performance between different protocols. Use it to extend first order models. • Analysis of effects of mobility on protocol mechanisms • Extend and release the IMPORTANT mobility tool: • URL: http://nile.usc.edu/important

28. Backup/Extra Slides

29. Rel vel. (V) prop to max vel (Vmax)

30. D: total data transferred during simulation • T: simulation time • Tflow: data transfer time • Trepair: total time spent in repairing paths • trepair: time to repair path each time • PD: average path duration • f: frequency of path breakage, • r: is constant data rate=D/Tflow • N: number of of nodes

31. Number of path repairs=T/(PD+trepair)

32. Expression for cache hit ratio (Hit): [FW model] Hit=

33. Non-propagating Cache Hit Ratio in DSR (independent of velocity!)