Stochastic Route Planning for On-Time Arrival Probability
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Solution Overview
Problem
Current navigation systems fail to determine optimal routes and departure times to maximize the probability of arriving at a destination by a specified time, due to inefficiencies in handling uncertainty in road traffic conditions, leading to wasted time and sub-optimal route selection.
Innovation Solution
A stochastic route-planning algorithm that uses traffic delay probability distributions and parametric optimization to identify routes that maximize the probability of reaching a destination by a given deadline, implemented in a web site or GPS navigation device, employing pruning methods for efficient computation even in large road networks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional navigation systems use deterministic routing algorithms, then the routing computation is simple and fast, but the system cannot handle uncertainty in traffic conditions and leads to sub-optimal route selection
Solution Approach 1:
The patent transforms the deterministic routing problem into a stochastic optimization problem by changing the parameters from fixed travel times to probability distributions of travel times. The algorithm optimizes based on expected cost functions that incorporate uncertainty, allowing it to select routes that maximize the probability of arriving by the deadline rather than simply minimizing average travel time.
Solution Approach 2:
The patent introduces dynamic elements by using time-varying probability distributions for travel delays and implementing an iterative optimization process. The algorithm dynamically adjusts route selections based on stochastic models of traffic conditions and uses binary search to adaptively find optimal departure times, making the system responsive to uncertainty rather than static.
2Reliability
If navigation systems leave early to ensure on-time arrival, then the probability of meeting the deadline increases, but wasted time and fuel consumption increase
Solution Approach 1:
The patent performs preliminary stochastic analysis of traffic conditions and route options before making the departure decision. By pre-computing probability distributions and expected costs for various routes and departure times, the system can identify the optimal departure time that maximizes on-time arrival probability without excessive early departure, avoiding both late arrivals and wasted time.
Solution Approach 2:
The patent changes the optimization criterion from minimizing average travel time to maximizing the probability of meeting a deadline. This parameter change allows the system to find departure times and routes that achieve high on-time arrival probabilities without the excessive early departure that characterizes traditional deterministic approaches, which lack the ability to quantify and optimize for deadline satisfaction probability.
3Measurement precision
If navigation systems compute optimal routes using stochastic modeling, then the route selection accuracy improves, but the computational time and complexity increase
Solution Approach 1:
The patent segments the computation into distinct phases: pre-computation of probability distributions for road segments, calculation of expected costs for candidate routes, and iterative optimization using binary search. This segmentation allows the system to manage computational complexity by breaking down the stochastic optimization into smaller, more efficient sub-tasks that can be executed systematically.
Solution Approach 2:
The patent implements a practical optimization approach by considering a limited set of candidate routes and using iterative methods that converge to satisfactory solutions rather than exhaustively exploring all possible routes. The binary search on departure times and the expected cost optimization provide sufficiently precise results with reasonable computational effort, avoiding the need for excessively complex computations that would yield diminishing returns.
4Ease of manufacture
If drivers follow sub-optimal routes from traditional GPS systems, then the routing system is simple to implement, but fuel consumption and environmental pollution increase
Solution Approach 1:
The patent changes the optimization objective from minimizing average travel time to maximizing the probability of meeting a deadline, which directly addresses the user's need to arrive on time. This parameter change naturally leads to more efficient route and departure time selections that reduce unnecessary early departure and idle time in traffic, thereby reducing fuel consumption and emissions without significantly complicating the system implementation.
Data Source
AI summary
In some embodiments, a method of providing a user with a roadway route to a destination that maximizes the probability of reaching the destination by a deadline includes providing a database of traffic delay probability distributions based on historical traffic delay information, performing route-planning using at least one of the traffic delay probability distributions and parametric optimization to determine at least one route to the destination that maximizes the probability of reaching the destination by the deadline, and displaying the at least one route to the user. In some embodiments, the database includes a mean value and a variance value associated with each route from a plurality of routes stored at the database, and the performing includes the following steps: defining a first set of routes from the plurality of routes, selecting a first route from the plurality of routes as a current optimal route, defining a second set of routes and a third set of routes based on the first route, and discarding the second set of routes.