Haiming Jin, He Huang, Lu Su and Klara Nahrstedt University of Illinois at Urbana-Champaign State University of New York at Buffalo October 22, 2014 Cost-minimizing Mobile Access Point Deployment in Workflow-based Mobile Sensor Networks

Motivation 2 Presenter: Haiming Jin Emerging mission-driven workflow-based mobile sensor networks Airplane maintenance Mobile devices collect data Workflow gives mobility information image or video text note 1:00 PM Check right engine 1:00 PM Check right engine 1:30 PM Check left engine 1:30 PM Check left engine 2:00 PM Check stabilizers 2:00 PM Check stabilizers 2:30 PM Go to Gate 7 2:30 PM Go to Gate 7

Motivation 3 Presenter: Haiming Jin Emerging mission-driven workflow-based mobile sensor networks Airplane maintenance Industrial production line management Infrastructure monitoring Mobile Diagnostic Robot Cameras Microphones etc. Railway Inspecti on Pipeline Inspecti on Pipeline Inspecti on

Motivation 4 Presenter: Haiming Jin Sensory data collection using APs (relays or base stations) Stationary APs: [Huang et al., SECON’10], [Misra et al., ToN’10] and … Resource overprovisioning! 1:00 PM Location A 1:00 PM Location A 1:30 PM Location B 1:30 PM Location B 2:00 PM Location C 2:00 PM Location C

Motivation 4 Presenter: Haiming Jin Sensory data collection using APs (relays or base stations) Stationary APs: [Huang et al., SECON’10], [Misra et al., ToN’10] and … Resource overprovisioning! Mobile APs: 1:00 PM Location A 1:00 PM Location A 1:30 PM Location B 1:30 PM Location B 2:00 PM Location C 2:00 PM Location C

Motivation 4 Presenter: Haiming Jin Sensory data collection using APs (relays or base stations) Stationary APs: [Huang et al., SECON’10], [Misra et al., ToN’10] and … Resource overprovisioning! Mobile APs: Minimize energy consumption: [Xing et al., Mobihoc’08] and … Maximize network life time: [Xie et al., Infocom’13] and … Minimize deployment cost: this paper

Problem Description 5 Presenter: Haiming Jin Objective Minimize total AP deployment cost Purchasing cost (#) Movement cost (moving distance) Constraints Lower bound bandwidth for sensors Upper bound bandwidth for APs Moving speed of APs

Model and Assumptions 6 Presenter: Haiming Jin Mobile users (MUs) Time slots, MUs move according to predefined trajectories Extracted from workflows APs stay only at grid intersections Move between grid intersections along shortest paths Obstacles occlude wireless signal Time Slot t Time Slot t+1

Mathematical Formulations-Overview 7 Presenter: Haiming Jin Sub-problem I: Minimum AP Deployment (MinAD) Calculate the minimum number AP deployment in every time slot that satisfies MUs’ bandwidth requirement Sub-problem II: Cost Minimization (CMin) Given output from MinAD, calculate minimum cost AP deployment

Mathematical Formulations-MinAD 8 Presenter: Haiming Jin Extract network topology graphs Trajectory discretization Network Topology Graph in Time Slot t

Mathematical Formulations-MinAD 9 Presenter: Haiming Jin Sub-problem I: MinAD Variables: : whether there should be an AP at location in time slot : amount of data sent from SU at position to AP at location in time slot

Mathematical Formulations-MinAD 9 Presenter: Haiming Jin Sub-problem I: MinAD Objective: Minimize the number of APs Constraints: Lower bound bandwidth for sensors Upper bound bandwidth for APs

Mathematical Formulations-CMin 10 Presenter: Haiming Jin AP Position Transition Graph Sub-problem II: CMin AP purchasing cost

Mathematical Formulations-CMin 10 Presenter: Haiming Jin AP Position Transition Graph Sub-problem II: CMin Total moving cost

Mathematical Formulations-CMin 10 Presenter: Haiming Jin AP Position Transition Graph Sub-problem II: CMin Total AP deployment cost

Solution and Analysis-NP-hardness 11 Presenter: Haiming Jin Theorem 1: The MinAD problem is NP-hard. Proof: We prove the NP-hardness of the MinAD problem by showing that the set cover problem (NP-complete) is polynomial time reducible to MinAD. Theorem 2: The CMin problem is NP-hard. Proof: We prove the NP-hardness of the CMin problem by showing that the minimum cost three dimensional perfect matching problem (NP-complete) is polynomial time reducible to CMin.

Solution and Analysis-Approximation Algorithm 12 Presenter: Haiming Jin Linear programming relaxation and iterative rounding (LR-IR)

Solution and Analysis-Approximation Algorithm 13 Presenter: Haiming Jin Theorem 3: LR-IR for MinAD has linear approximation ratio w.r.t. maximum node degree of the network connectivity graph. Theorem 4: LR-IR for CMin has constant approximation ratio.

Performance Evaluation 14 Presenter: Haiming Jin Simulation Settings

Performance Evaluation 14 Presenter: Haiming Jin Scenario I Scenario II

Performance Evaluation 15 Presenter: Haiming Jin LR-IR for MinAD LR-IR for CMin

Conclusion 15 Presenter: Haiming Jin We formulate the cost-minimizing mobile AP deployment problem as meaningfully solvable (mixed) integer optimization problems and prove that the formulated optimization problems are NP-hard. Further, we design efficient approximation algorithms with guaranteed approximation ratios.

Incomplete Information Workflows 18 Presenter: Haiming Jin Durations that MUs stay at mission locations are not a priori known. Shared-AP trajectory Stationary APs Dedicated-AP trajectory Mobile APs

Performance Evaluation 19 Presenter: Haiming Jin Percentage of Selected Trajectory Segments

Performance Evaluation 20 Presenter: Haiming Jin