Traffic Speed Modeling Using Delta-Gamma Distribution
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Solution Overview
Problem
Current traffic speed modeling technologies fail to accurately represent traffic conditions on road segments, especially during congested conditions where vehicles may be stationary, leading to inaccuracies in route planning and estimated time of arrival, as they rely on Gaussian distributions that do not account for zero speeds and variability in traffic flow.
Innovation Solution
A server processes traffic data by separating it into zero speed and non-zero speed data, determining characteristic values for each, and generating a representative traffic value using a Delta-Gamma distribution that combines a spike at zero speed with a positive-skewed distribution for non-zero speeds, effectively modeling arterial traffic conditions by blending recent and historical data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If Gaussian distribution is used to model traffic speeds, then the modeling process is simple and computationally efficient, but the accuracy deteriorates because Gaussian distribution cannot account for zero speeds and variability in traffic flow
Solution Approach 1:
The patent segments the traffic speed data into two distinct components: zero speed data (representing stopped vehicles) and non-zero speed data (representing moving vehicles). This segmentation allows each component to be modeled separately with appropriate distributions, resolving the contradiction between modeling simplicity and accuracy by avoiding the misuse of Gaussian distribution for mixed data types.
Solution Approach 2:
The patent creates a composite probability distribution model that combines a Dirac delta function (for zero speed) with a Gamma distribution (for non-zero speeds). This composite approach maintains computational efficiency while significantly improving accuracy by accounting for both stationary and moving vehicles, eliminating the fundamental flaw of using Gaussian distribution for this mixed data.
2Measurement precision
If traffic data is separated into zero speed and non-zero speed components, then the modeling accuracy improves by accounting for stationary and moving vehicles separately, but the device complexity increases due to additional processing steps
Solution Approach 1:
The patent applies segmentation by dividing the traffic speed dataset into two subsets: zero speed observations and non-zero speed observations. This segmentation is implemented through straightforward filtering operations that separate data points based on their speed values, achieving improved modeling accuracy without requiring complex computational algorithms.
Solution Approach 2:
The patent changes the distributional parameters by using a Dirac delta function for zero speed data (which has all its mass at zero) and a Gamma distribution for non-zero speed data (which models positive continuous values). This parameter change approach allows accurate modeling of the different characteristics of stopped and moving vehicles while maintaining relatively simple computational operations.
3Reliability
If recent traffic data is combined with historical data, then the representativeness of traffic modeling improves by capturing both current conditions and long-term patterns, but the processing time increases due to data aggregation requirements
Solution Approach 1:
The patent applies preliminary action by pre-processing and storing historical traffic data in a structured format before it is needed for current modeling. Historical data is aggregated and prepared in advance, allowing rapid retrieval and combination with recent data without requiring time-consuming processing during the actual modeling operation.
Solution Approach 2:
The patent implements a dynamic data processing approach where the weighting between recent and historical data can be adjusted based on current conditions. The system can dynamically select the appropriate mix of recent and historical data points, allowing efficient processing by focusing computational resources on the most relevant data sources at any given time.
Data Source
AI summary
A method and apparatus for traffic modeling comprising: receiving by a server, traffic data generated by one or more devices configured to record data indicating speeds of vehicles traveling a road segment. The server separates, with a processor, the traffic data into zero speed data and non-zero speed data. The server determines, with the processor, a zero speed data characteristic value of the zero speed data. The server determines, with the processor, at least one non-zero speed data characteristic value of the non-zero speed data. The server generates, with the processor, a representative traffic value for the road segment as a function of the zero speed characteristic value and the non-zero speed characteristic value.