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. Conclusions & Future Research 7. Q&A 2
1. Overview
Internet of Things Definition Network of physical devices, vehicles, buildings and other items that enable these objects to collect and exchange data 1 Applications Media Healthcare systems Industry 4.0 … Challenges Safety Security Correctness Complex dependencies Cyber-Physical-Systems Requirements Specification 2 Verification 1 https://en.wikipedia.org/wiki/Internet_of_things 4 2 https://www.mobinius.com/industry-4-0-iot/
Motivation Probability in IoT Nondeterministic behavior of each devices Complex Non-predictable Analysis and design are difficult 1 1 https://www.acmicpc.net/problem/13405 5
Motivation 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 1 https://blog.storagecraft.com/business-continuity-statistics-tech/ 6
Approach Process algebra Specify IoT systems Analyze IoT systems Specify probability density function Probabilistic analysis 7
2. dTP-Calculus
dTP-Calculus Geographical Space - Processes - Actions δ - Interactions - Space Movements - Time - Probability τ ρ Communication Control Synchrony 9
Syntax 10
Syntax Probability Probabilities specification Discrete distribution Probability density function specification Normal distribution Exponential distribution Uniform distribution 11
Syntax Probabilistic choice Discrete distribution 𝑄 𝑑 + 𝐸 𝑅 𝑑 𝑑 : Probability Example 𝑄 0.2 + 𝐸 𝑅 0.5 + 𝐸 𝑆{0.3} 1 1 https://en.wikipedia.org/wiki/Probability_distribution 12
Syntax 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} 1 1 https://en.wikipedia.org/wiki/Normal_distribution 13
Syntax 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} 1 1 https://en.wikipedia.org/wiki/Exponential_distribution 14
Syntax 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} 1 1 https://en.wikipedia.org/wiki/Uniform_distribution_(continuous) 15
Syntax Probabilistic choice Summation of the probabilities should be 1 Discrete distribution 𝑄 1 𝑑 1 + 𝐸 𝑄 2 𝑑 2 + 𝐸 ⋯ + 𝐸 𝑄 𝑜 {𝑑 𝑜 } 𝑜 𝑑 𝑗 = 1 𝑗=1 Normal distribution, uniform distribution 𝑄 1 𝑑 1 + 𝐺 𝑄 2 𝑑 2 + 𝐺 ⋯ + 𝐺 𝑄 𝑜 {𝑑 𝑜 } 𝑜 𝑑 𝑗 = ℝ 𝑗=1 ∀𝑗, 𝑘 ∈ 𝑦 𝑦 ∈ ℕ, 1 ≤ 𝑦 ≤ 𝑜 𝑢ℎ𝑓𝑜 𝑑 𝑗 ∩ 𝑑 𝑘 = ∅ (𝑔𝑝𝑠 𝑗 ≠ 𝑘) Exponential distribution 𝑄 1 𝑑 1 + 𝐺 𝑄 2 𝑑 2 + 𝐺 ⋯ + 𝐺 𝑄 𝑜 {𝑑 𝑜 } 𝑜 𝑑 𝑗 = 𝑦 𝑦 ≥ 0, 𝑦 ∈ ℝ} 𝑗=1 ∀𝑗, 𝑘 ∈ 𝑦 𝑦 ∈ ℕ, 1 ≤ 𝑦 ≤ 𝑜 𝑢ℎ𝑓𝑜 𝑑 𝑗 ∩ 𝑑 𝑘 = ∅ (𝑔𝑝𝑠 𝑗 ≠ 𝑘) 16
Syntax Probabilistic choice Error Summation of the probabilities is less than 1 𝑄 𝑑 1 + 𝐺 𝑅 𝑑 2 Undefined area 𝑑 1 𝑑 2 17
Syntax Probabilistic choice Error Summation of the probabilities is greater than 1 𝑄 𝑑 1 + 𝐺 𝑅 𝑑 2 Overlapped area 𝑑 1 𝑑 2 18
Syntax Probabilistic choice Error Summation of the probabilities is greater than 1 𝑄 𝑑 1 + 𝐺 𝑅 𝑑 2 𝑄 𝑑 1 𝑄 𝑑 1 ∥ 𝑅 𝑑 2 𝑅 𝑑 2 𝑑 1 𝑑 2 19
3. SAVE
SAVE SAVE Specification, Analysis, Verification, and Evaluation Based on ADOxx meta-modeling platform 21
Specification - Visualization Graphic language System View In-the-Large (ITL) Model Representation Interactions of each processes Process View In-the-Small (ITS) Model Representation Detailed actions of each processes 22
System View 23
System View 24
Process View 25
Process View 26
Analysis Analysis Path analysis All possible execution path Generate simulation model Simulation Simulate the system based on a path 27
Simulation model 28
Verification Verification Behavior analysis Analyze the system behavior Generate geo-temporal space model Requirements Verification Verify a set of system requirements 29
Analysis model 30
4. Example
Example Smart Emergency Evacuation System Sensors Fire detection Control System Evacuation alarm Rescue request Evacuation route notification 1 1 http://www.arpel.com/business-services/fire-detection/ 32
Example Control System Building Sensor A Sensor B 33
Example Textual Specification 34
Example Textual Specification 35
Example Textual Specification 36
Example Textual Specification 37
Example 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 38
Example 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 different. 39
5. Analysis
Analysis Execution path 8 paths 41
Analysis 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 42
Analysis 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 43
Analysis Simulation Simulate the system based on the probabilities 44
Analysis Simulation Simulate the system based on the probabilities Probability Number of Simulation 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 45
Analysis Simulation Simulate the system based on the probabilities Probability Number of Simulation 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 Simulation results 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 Mathematical analysis 46
Analysis 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 47
6. Conclusions
Approach Geographical Space - Processes - Actions δ - Interactions - Space Movements - Time - Probability τ ρ Communication Control Synchrony 49
Approach Various probability specification Discrete distribution Normal distribution Exponential distribution Uniform distribution 50
SAVE 51
SAVE Simulation 52
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