Process Model to Predict Nondeterministic Behavior of IoT Systems - - PowerPoint PPT Presentation
Process Model to Predict Nondeterministic Behavior of IoT Systems Yeongbok Choe and Moonkun Lee 31 October 2018 Chonbuk National University Republic of Korea Contents 1. Overview 2. dTP-Calculus 3. SAVE 4. Example 5. Analysis 6.
31 October 2018 Chonbuk National University Republic of Korea
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Definition
Network of physical devices, vehicles, buildings and other items that enable these objects to collect and exchange data1
Applications
Media
Healthcare systems
Industry 4.0
…
Challenges
Safety
Security
Correctness
Complex dependencies
Cyber-Physical-Systems
Requirements
Specification
Verification
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1 https://en.wikipedia.org/wiki/Internet_of_things 2 https://www.mobinius.com/industry-4-0-iot/
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Probability in IoT
Nondeterministic behavior of each devices
Complex Non-predictable
Analysis and design are difficult
1 https://www.acmicpc.net/problem/13405
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Probability in IoT
Probability
In design step, statistics data is used
Error occurred Route selection
Probability is used to analyze
Risk management Behavior prediction 1 https://blog.storagecraft.com/business-continuity-statistics-tech/
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Process algebra
Specify IoT systems Analyze IoT systems Specify probability density function Probabilistic analysis
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δ Movements τ Communication ρ Control Geographical Space
Synchrony
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Probability
Probabilities specification
Discrete distribution
Probability density function specification
Normal distribution Exponential distribution Uniform distribution
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Probabilistic choice
Discrete distribution
𝑄 𝑑 +𝐸 𝑅 𝑑
𝑑 : Probability
Example
𝑄 0.2 +𝐸 𝑅 0.5 +𝐸 𝑆{0.3}
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1 https://en.wikipedia.org/wiki/Probability_distribution
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Probabilistic choice
Normal distribution
𝑄 𝑑 +𝑂(𝜈,𝜏) 𝑅 𝑑
𝑑 : Variable area (Condition) 𝜈 : Mean 𝜏 : Standard deviation
Example
𝑄 𝑤 > 52 +𝑂(50,5) 𝑅{𝑤 ≤ 52}
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1 https://en.wikipedia.org/wiki/Normal_distribution
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Probabilistic choice
Exponential distribution
𝑄 𝑑 +𝐹(𝜇) 𝑅 𝑑
𝑑 : Variable area (Condition) 𝜇 : Frequency
Example
𝑄 𝑤 > 2.5 +𝐹(0.33) 𝑅{𝑤 ≤ 2.5}
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1 https://en.wikipedia.org/wiki/Exponential_distribution
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Probabilistic choice
Uniform distribution
𝑄 𝑑 +𝑉(𝑚, 𝑣) 𝑅 𝑑
𝑑 : Variable area (Condition) 𝑚 : Lower bound 𝑣 : Upper bound
Example
𝑄 𝑤 > 5 +𝑉(3,7) 𝑅{𝑤 ≤ 5}
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1 https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)
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Probabilistic choice
Summation of the probabilities should be 1 Discrete distribution
𝑄
1 𝑑1 +𝐸 𝑄2 𝑑2 +𝐸 ⋯ +𝐸 𝑄 𝑜{𝑑𝑜}
𝑑𝑗
𝑜 𝑗=1
= 1 Normal distribution, uniform distribution
𝑄
1 𝑑1 +𝐺 𝑄2 𝑑2 +𝐺 ⋯ +𝐺 𝑄 𝑜{𝑑𝑜}
𝑑𝑗
𝑜 𝑗=1
= ℝ
∀𝑗, 𝑘 ∈ 𝑦 𝑦 ∈ ℕ, 1 ≤ 𝑦 ≤ 𝑜 𝑢ℎ𝑓𝑜 𝑑𝑗 ∩ 𝑑
𝑘 = ∅ (𝑔𝑝𝑠 𝑗 ≠ 𝑘)
Exponential distribution
𝑄
1 𝑑1 +𝐺 𝑄2 𝑑2 +𝐺 ⋯ +𝐺 𝑄 𝑜{𝑑𝑜}
𝑑𝑗
𝑜 𝑗=1
= 𝑦 𝑦 ≥ 0, 𝑦 ∈ ℝ}
∀𝑗, 𝑘 ∈ 𝑦 𝑦 ∈ ℕ, 1 ≤ 𝑦 ≤ 𝑜 𝑢ℎ𝑓𝑜 𝑑𝑗 ∩ 𝑑
𝑘 = ∅ (𝑔𝑝𝑠 𝑗 ≠ 𝑘)
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Probabilistic choice
Error
Summation of the probabilities is less than 1
𝑄 𝑑1 +𝐺 𝑅 𝑑2
𝑑1 𝑑2 Undefined area
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Probabilistic choice
Error
Summation of the probabilities is greater than 1
𝑄 𝑑1 +𝐺 𝑅 𝑑2
𝑑1 𝑑2 Overlapped area
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Probabilistic choice
Error
Summation of the probabilities is greater than 1
𝑄 𝑑1 +𝐺 𝑅 𝑑2
𝑑1 𝑑2 𝑄 𝑑1 ∥ 𝑅 𝑑2 𝑄 𝑑1 𝑅 𝑑2
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SAVE
Specification, Analysis,
Based on ADOxx meta-modeling platform
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Graphic language
System
In-the-Large (ITL) Model Representation
Interactions of each processes
Process View
In-the-Small (ITS) Model Representation
Detailed actions of each processes
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Analysis
Path analysis
All possible execution path Generate simulation model
Simulation
Simulate the system based on a path
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Verification
Behavior analysis
Analyze the system behavior Generate geo-temporal space model
Requirements
Verify a set of system requirements
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Smart Emergency Evacuation System
Sensors
Fire detection
Control System
Evacuation alarm Rescue request Evacuation route
notification
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1 http://www.arpel.com/business-services/fire-detection/
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Building
Sensor A Sensor B
Control System
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Textual Specification
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Textual Specification
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Textual Specification
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Textual Specification
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Probabilistic choice
Building
𝑇𝐵 𝐺𝑗𝑠𝑓
0.5 +𝐸 𝑇𝐶 𝐺𝑗𝑠𝑓 {0.5}
Discrete distribution
P1
∅ ⋅ … ⋅ 𝑤 < 2.5 +𝑂 5,3 𝑝𝑣𝑢 2𝑜𝑒 ⋅ … ⋅ 𝑤 ≥ 2.5 Normal distribution
P2
∅ ⋅ … ⋅ 𝑤 < 2.5 +𝑂 5,8 𝑝𝑣𝑢 2𝑜𝑒 ⋅ … ⋅ 𝑤 ≥ 2.5 Normal distribution
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Probabilistic choice
Building
𝑇𝐵 𝐺𝑗𝑠𝑓
0.5 +𝐸 𝑇𝐶 𝐺𝑗𝑠𝑓 {0.5}
Discrete distribution
P1
∅ ⋅ … ⋅ 𝑤 < 2.5 +𝑂 5,𝟒 𝑝𝑣𝑢 2𝑜𝑒 ⋅ … ⋅ 𝑤 ≥ 2.5 Normal distribution
P2
∅ ⋅ … ⋅ 𝑤 < 2.5 +𝑂 5,𝟗 𝑝𝑣𝑢 2𝑜𝑒 ⋅ … ⋅ 𝑤 ≥ 2.5 Normal distribution
P1 and P2 have same type’s choice, but parameters are
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Execution path
8 paths
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Execution path
8 paths
Fire: The location where the fire occurred Stay: P1 or P2, confined in Building Out: P1 or P2, escaped from Building
Path 1 Path 2 Path 3 Path 4 Path 5 Path 6 Path 7 Path 8 Fire Stair A Stair A Stair A Stair A Stair B Stair B Stair B Stair B P1 Stay Stay Out Out Stay Stay Out Out P2 Stay Out Stay Out Stay Out Stay Out
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Probability
Mathematical analysis
Calculate the probability
∅ ⋅ … ⋅ 𝑤 < 2.5 +𝑂 5,𝟒 𝑝𝑣𝑢 2𝑜𝑒 ⋅ … ⋅ 𝑤 ≥ 2.5
∅ ⋅ … ⋅ 0.2023 +𝐸 𝑝𝑣𝑢 2𝑜𝑒 ⋅ … ⋅ 0.7977
∅ ⋅ … ⋅ 𝑤 < 2.5 +𝑂 5,𝟗 𝑝𝑣𝑢 2𝑜𝑒 ⋅ … ⋅ 𝑤 ≥ 2.5
∅ ⋅ … ⋅ 0.3773 +𝐸 𝑝𝑣𝑢 2𝑜𝑒 ⋅ … ⋅ 0.6227
Path 1 Path 2 Path 3 Path 4 Path 5 Path 6 Path 7 Path 8 % 3.82 6.3 15.05 24.83 3.82 6.3 15.05 24.83
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Simulation
Simulate the system based on the probabilities
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Simulation
Simulate the system based on the probabilities
Number of Simulation Probability Path 1 Path 2 Path 3 Path 4 Path 5 Path 6 Path 7 Path 8 1,000 3.5 6.2 14.2 25 3.5 7.5 14.4 25.7 1,000,000 3.79 6.32 15.04 24.86 3.82 6.32 14.98 24.87
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Simulation
Simulate the system based on the probabilities
Number of Simulation Probability Path 1 Path 2 Path 3 Path 4 Path 5 Path 6 Path 7 Path 8 1,000 3.5 6.2 14.2 25 3.5 7.5 14.4 25.7 1,000,000 3.79 6.32 15.04 24.86 3.82 6.32 14.98 24.87 Path 1 Path 2 Path 3 Path 4 Path 5 Path 6 Path 7 Path 8 % 3.82 6.3 15.05 24.83 3.82 6.3 15.05 24.83
Simulation results Mathematical analysis
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Prediction of occurrence probability
In complex system, mathematical analysis is difficult. Through the simulation, paths and probabilities are derived.
Automation
SAVE tool
Specify and analyze the system Generate all possible paths Simulation based on probability
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δ Movements τ Communication ρ Control Geographical Space
Synchrony
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Various probability specification
Discrete distribution Normal distribution Exponential distribution Uniform distribution
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Simulation
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Theory
Requirement analysis methods for probability Requirement verification methods for probability
System
Apply to real IoT examples