Adaptive Reliable Shortest Path in Discrete Stochastic Networks

2014 ◽  
Vol 587-589 ◽  
pp. 1854-1857
Author(s):  
Yi Yong Pan
Keyword(s):  
Shortest Path ◽  
Stochastic Networks ◽  
Shortest Path Problem ◽  
Successive Approximations ◽  
Stochastic Network ◽  
Route Guidance ◽  
Travel Times ◽  
Routing Policy ◽  
The Face ◽  
Stochastic Travel Times

This paper addresses adaptive reliable shortest path problem which aims to find adaptive en-route guidance to maximize the reliability of arriving on time in stochastic networks. Such routing policy helps travelers better plan their trips to prepare for the risk of running late in the face of stochastic travel times. In order to reflect the stochastic characteristic of travel times, a traffic network is modeled as a discrete stochastic network. Adaptive reliable shortest path problem is uniformly defined in a stochastic network. Bellman’s Principle that is the core of dynamic programming is showed to be valid if the adaptive reliable shortest path is defined by optimal-reliable routing policy. A successive approximations algorithm is developed to solve adaptive reliable shortest path problem. Numerical results show that the proposed algorithm is valid using typical transportation networks.

Approximating the Stochastic Network by its M Shortest Paths

1989 ◽  
Vol 3 (3) ◽  
pp. 435-451
Author(s):  
Bajis Dodin
Keyword(s):  
Monte Carlo ◽  
Shortest Path ◽  
Probability Distributions ◽  
Shortest Paths ◽  
Monte Carlo Sampling ◽  
Stochastic Networks ◽  
Mean Value ◽  
Stochastic Network ◽  
Distributional Properties ◽  
Deterministic Methods

Given a stochastic activity network in which the length of some or all of the arcs are random variables with known probability distributions. This paper concentrates on identifying the shortest path and the M shortest paths in the network and on using the M paths to identify surrogate stochastic networks which are amenable for deriving analytical solutions. First, it identifies the M shortest paths using a certain form of stochastic dominance. Second, it identifies the M shortest paths by applying the deterministic methods to the network resulting from replacing the random length of every arc by its mean value. The two sets of the M paths are compared with those obtained by Monte Carlo sampling. Finally, the paper investigates how the distributional properties of the shortest path in the surrogate network compare with those of the shortest path in the original stochastic network.

A shortest path problem in a stochastic network with exponential travel time

2021 ◽  
Vol 13 (3) ◽  
pp. 179
Author(s):  
S.K. Peer ◽  
Dinesh K. Sharma ◽  
B. Chakraborty ◽  
R.K. Jana
Keyword(s):  
Travel Time ◽  
Shortest Path ◽  
Shortest Path Problem ◽  
Stochastic Network

A shortest path problem in a stochastic network with exponential travel time

2021 ◽  
Vol 13 (3) ◽  
pp. 179
Author(s):  
S.K. Peer ◽  
Dinesh K. Sharma ◽  
B. Chakraborty ◽  
R.K. Jana
Keyword(s):  
Travel Time ◽  
Shortest Path ◽  
Shortest Path Problem ◽  
Stochastic Network

STOCHASTIC SCENARIO-BASED TIME-STAGE OPTIMIZATION MODEL FOR THE LEAST EXPECTED TIME SHORTEST PATH PROBLEM

2013 ◽  
Vol 21 (supp01) ◽  
pp. 17-33 ◽  
Author(s):  
LIXING YANG ◽  
XIAOFEI YANG ◽  
CUILIAN YOU
Keyword(s):  
Shortest Path ◽  
Optimization Model ◽  
Optimal Solution ◽  
Shortest Path Problem ◽  
Travel Times ◽  
Expected Time ◽  
Second Stage ◽  
Time Threshold ◽  
Proposed Model ◽  
Time Invariant

Focusing on finding a pre-specified basis path in a network, this research formulates a two-stage stochastic optimization model for the least expected time shortest path problem, in which random scenario-based time-invariant link travel times are utilized to capture the uncertainty of the realworld traffic network. In this model, the first stage aims to find a basis path for the trip over all the scenarios, and the second stage intends to generate the remainder path adaptively when the realizations of random link travel times are updated after a pre-specified time threshold. The GAMS optimization software is introduced to find the optimal solution of the proposed model. The numerical experiments demonstrate the performance of the proposed approaches.

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