Quality of Monitoring and Optimization of Threat-based Mobile Coverage

1. Quality of Monitoring and Optimization of Threat-based Mobile Coverage David K Y Yau Department of Computer Science Purdue University

2. Introduction • Part of federal SensorNet initiative • Oak Ridge National Lab and university partners (including Purdue and UIUC) • Initial deployment of a detection, identification, and tracking sensor-cyber network (DITSCN) in the Washington D.C. and Memphis Port areas; against radiological, biological, and chemical threats. • DITSCN combining various modalities of sensors and cyber networks • Sensor network provides information about the physical space • Cyber network provides storage and computational resources to predict plume propagation based on realistic dispersion models • Decisions regarding future sensing and communications are made in cyber network and carried out in the physical space

3. Physical Space Cyber Space SensorNet Node Multi-hop communication Sensors… Control Center Actuator DITSCN Architecture

4. Research Tasks • Convergence between physical and cyber spaces • Effectively gather information about the physical space • Communicate most useful data to the cyber space given bandwidth, delay and signal attenuation constraints • Enable the cyber space to task and activate sensors to collect high-quality data • Acknowledgment of the existence of uncertainty; enable decision making processes to deal with the uncertainty in a robust fashion • Incorporate knowledge of physical environment: people, terrain, land cover, and meteorological information • Model physical phenomena adequately (e.g., plumes with respect to the absorption, propagation, and dispersion coefficients) • Support for deeply embedded operations • Integrate system components in an open, plug-and-play manner, through the use of open data, control, and communication interfaces

5. Cyber-space Analytical Results

6. Physical Space Sensing RFTrax RAD Sensor to detect the presence and intensity of the plume source WMS Wind Sensor to monitor background wind speed and direction

7. Wide-area Wireless Network Communication • Sensor data communicated through RS-485 or802.11x interfaces to the SensorNet Node • Multihop wireless mesh network for robustness and flexibility • current implementation uses Linksys routers running AODV • IEEE 1451 interface to configure sensors at runtime

8. Antenna Processor Router Modem Power Supplies Serial Interface Fan SensorNet Node Hardware

9. TEDS STIM Data Management and Storage Configuration (Web) Server Control Services for RDC and external users Auth Data Services Comm. Mode Control Legacy Legacy Codes Codes Serial E.g., Sprint 1451.1 NCAP TEDS TEDS Session USB Mux Link options: Dialup/PCS/ 802.11 Wired etc. Sensors STIM Other 1451.2 Stubs Sensors Interface Ethernet SensorNet Node Software Architecture

10. ER-1 Robots Physical Space Tasking • ER-1 robotssupporting autonomous and programmable movement are guided by the cyber center, through commands sent over 802.11x wireless network • Tasking enables sensor mobility to increase the coverage of high-threat locations

11. Detection of Radiation Threats • Stealthy bombs • Small explosions (can be dismissed as low harm), but • Exposure of population to dangerous radiation • Need detection by suitable sensors • Commercial sensors • RFTrax RAD-CZT (limited range of tens of feet) • Yankee Environmental System Inc. RAD 7001 (somewhat longer range but more expensive) • High procurement and operation costs (may not have sufficient sensors for full area coverage all the time)

12. Prior SensorNet Deployments • Washington DC deployment • Gamma radiation detection by RFTrax in urban areas • Memphis Port deployment • Chemical detection of fresh water supply to area residents by Smith APD 2000 • Lessons learned • Management of resource constraints (mobile coverage) • Importance of people protection (resource allocation) • Uncertainty management (temporal dimension)

13. Temporal Dimension of Sensing (radiation detection)

14. Other Utility Functions

15. People-centric Resource Allocation • Allocating goal of coverage time by mobile sensor • higher threats (people impact)  higher coverage • proportional to numbers of residents in subregions • Proportional sharing is well known (CPU, network, …) • but impact on sensor QoM not well understood

16. Problem Formulation • One sensor moving among n points of interest (PoI) under some maximum speed vmax • Each PoI has given threat level (no. of residents) • Road of distance dijconnects PoIs i and j • Dynamic events appear at each PoI • Stochastic event arrival, staying, and absent times (given probabilistic distributions) • Sensing quality increases with sensing time (according to utility function) • Sensing occurs when event falls within sensing range R of sensor

17. Goals and Questions • We seek to achieve proportional sharing of sensor coverage time among PoIs according to threat profile • What does it mean in terms of QoM? • Does r times coverage implies r times performance? • Questions: how should the sensor move among the PoIs to maximize the aggregate information captured? • Subject to physical constraints of movement and proportional sharing goal • What’s impact of sharing granularity? • What’s scaling law of mobile coverage? (Do we capture more information by being mobile?)

18. Periodic PoI Schedule • Analyze periodic presence/absence of sensor at given PoI • Induced by mobile coverage algorithm (feasibility and realization later) • Sensor is present for q time units every p time units (min present time is =2R/vmax) • Same q/p proportional share can be achieved at different fairness granularity • P A A A vs. P P A A A A A A (25% share) • How much information captured as a function of event dynamics and type of event?

19. Periodic PoI Coverage: Blip Events • Theorem: For independent arrivals of events that have the step utility function and do not stay, i.e. “blip events”, the QoM at any PoI is directly proportional to its share of coverage time • Corollary: For these events, the achieved QoM at a PoI is linear in the proportional share and does not depend on the fairness granularity p • r times coverage  r times QoM

20. Periodic PoI Coverage: Step Utility • Theorem : For independent arrivals of events that stay and have the step utility function, the QoM at a PoI is given by

21. Corolloraries (Step Utility) • Corollary: With the fairness granularity p kept constant, we have: • QoM is a monotonically decreasing function of the fairness granularity, i.e., Q decreases as p increases. Furthermore,

22. QoM Justification of Mobility • Theorem: For sensor moving among k PoIs, the expected fraction of events captured is an increasing function of k.

23. Periodic PoI Coverage: General Utility • Theorem: For events at a PoI that have the utility function U(・) and whose event staying time pdf is given by f(x), the achieved QoM equals

24. Exponential Staying Time Exponential utility function

25. Pareto Staying Time

26. Pareto Staying Time

27. Implications of Theorem (General Utility) • Step and Exponential Utilities: QoM decreases monotonically in p • Concave function  advantageous to move around and look for new information • But for other utility functions (e.g., Delayed Step), optimal QoM may occur at intermediate p • Competitive effects between observing existing event long enough for significant information vs. looking for new information elsewhere

28. Periodic Global Sensor Schedule • Smallest periodic sequence of PoIs visited and the visit times • S={(L1,C1) … (Lm,Cm)} (PoI L1 visited for C1 time, etc) • Not all periodic global schedules produce simple periodic PoI schedules • E.g., {(1,T) (2,3T) (1,T) (3,2T)} • When each PoI appears in S no more than once, S is called linear periodic schedule • Maximum feasible utilization of S:

29. Maximum Feasible Utilization • Theorem: The maximum feasible utilization of S is where

30. Optimization of Linear Periodic Schedules • Find linear visit schedule that minimizes  aj • TSP, but good approximation algorithms exist • Once visit schedule known, all aj’s are determined, remains to determine Cj’s • Express each Cj as function of C1(reduce problem to single dimension) • Choose C1 that optimizes Q* (one dimensional optimization depending on event utility function)

31. Illustration (Blip Events) • If  aj = 0, then any choice of C1 is optimal • Otherwise, there is no optimal choice but we can get arbitrarily close to the optimal by selecting a sufficiently large C1(hence, a sufficiently small travel overhead)

32. Linear Periodic Schedules are Sub-optimal • Consider three PoIs and Step utility events • d12 = d13 = d23 = 2R • Proportional sharing objective r12 = n/(n - 1) and r13 = n • Optimal linear periodic schedule is • However, QoM increases with finer grained sharing; hence, optimal non-linear periodic schedule is

33. Optimization of General Global Coverage • Start with some schedule of length n • Could be optimal linear schedule if it exists • Search for optimal general schedule of the same length (while respecting physical constraints) • Search space is huge: n! permutations • Use simulated annealing to guide the search and obtain global optimal with high probability

34. Optimization Algorithm

35. Simulation Results

36. QoM of Blip Events

37. QoM of Step Utility Events

38. QoM of Exponential Utility Events

39. QoM of Delayed Step Utility Events

40. Optimization of General Periodic Schedules

41. Another Proportional Share Proportional share ratios 53:29:17

42. Conclusions • Extensive analysis and supporting simulations to understand QoM of proportional-share mobile sensor coverage • Higher share  higher QoM (but not linear except for blip events) • When events stay, QoM can be much higher than proportional share due to ``extra’’ events captured • Sensor gains by moving around to look for new information • Optimal coverage depends on event utility • Step, Exponential utilities: finer granularity is better • Linear utility: initially flat, then finer granularity is better • Delayed Step and S-Shaped utilities: intermediate fairness granularity is best

43. Conclusions (continued) • Linear periodic schedules can be optimized as one dimensional optimization problem • But optimal linear periodic schedules are generally sub-optimal • General periodic schedules of given lengths can be optimized using simulated annealing • Near-global optimal schedule with high probability • Practical search time even for huge search spaces • Search terminates in seconds in our experiments

44. Discussions • Advantages of mobile coverage have been established in prior work • Bisnik, Abouzeid, Isler, ACM MOBICOM 2006 • Liu, Brass, Dousse, Nain, Towsley, ACM Mobihoc 2005 • Increased mobility is always better (ignoring costs) • Our new angles/results • Proportional sharing of coverage time, motivated by people protection • Temporal dimension of sensing, captured in event utility functions • Mobility is useful, but not always the more the better when temporal dimension is present (in terms of QoM) • Linear periodic schedules can be significantly suboptimal; solved optimization of general periodic schedules