Temporally Adaptive A* Algorithm on Time Dependent Transportation Network

Transcription

1 Temporally Adaptive A* Algorithm on Time Dependent Transportation Network Nianbo Zheng, Feng Lu Institute of Geographic Sciences and Natural Resources Research Chinese Academy of Sciences Beijing, , P.R. China

2 Outline Introduction Time dependent network model Temporally adaptive A* (TAA*) algorithm Experiment Conclusions

3 Introduction There is an increasing trend for route planners to calculate fastest paths by using dynamic traffic information. This problem is named dynamic shortest path problem (DSPP). Start 1 Origin Destination Route Planning 2 Guidance information Detour guidance Congestions Current point Destination Route guidance End Digital map Dynamic traffic Sensors Road network information +

4 Introduction (cont.) Traditional solution: path re optimization models the transportation network as dynamic graph with link weights changed periodically computes or re computes shortest paths immediately according to the graph state of the present time Obviously, this method ignores the time dependency of transportation network, and so it is not good at evaluating the travel time of a trip in advance. Time dependency refers to that the travel time through a link depends on the time to enter it.

5 Introduction (cont.) Alternative solution: time dependent SPP (TDSPP) considers the time dependency can be solved by label setting algorithms (e.g., Dijkstra) if the FIFO condition is satisfied (Kaufman & Smith, 1993) Our contributions: Proposed a time dependent network model with FIFO condition satisfied Adapted the heuristic A* shortest path algorithm to the timedependent network

6 Definition of time dependent network A transportation network G is composed of a node set N = {0, 1,, n 1} and a directed link set A {(i, j) (i, j) N N}. Time interval dependent link speeds: segment continuous time into multiple intervals [t 0, t 1 ),..., [t k, t k+1 ), and consider the speed of a link in each interval constant: f () t = v, t [ t, t ) ij (,) i j k k k+ 1 Link travel time function w ij (t) Link arrival time function T ij (t): refers to the time from node i to node j along link (i, j) with departure time t T () t = t+ w () t ij ij

7 Definition of FIFO condition FIFO (first in first out) condition: For each link (i, j) A, if the following inequality is satisfied, we call this link FIFO satisfied: T () s T () t s t ij ij Illustration of FIFO condition: Non overtaking

8 Computation of link arrival time Compute and update the arrival time iteratively and progressively for each time interval until the trip s end. Cases of a link travel covering several sequent time intervals

9 FIFO condition satisfaction: According to the time interval dependency of link speeds, two different trip trajectories departing at different time will be parallel. Link l T(s) T(t) 0 s t t k t k+1 t k+2 t k+3 t k+4 Time

10 Temporally adaptive A* algorithm A* algorithm: reduces search space by heuristic evaluation function: F i = L i + e (i,d), where, L i : travel time of current evaluated path from origin node to current node i e (i,d) : estimated travel time from current node i to destination node d

11 Temporally adaptive A* algorithm (cont.) F i (t) = T i (t) + e (i,d) (T i (t)), where, t: departure time from origin node T i (t): arrival time from origin node to current node i along the evaluated path e (i,d) (T i (t)): evaluated travel time from current node i to destination node d e (, id) D ( T( t))= id i D (i,d) : Euclidean distance between node i and node d V max : maximum possible travel speed in the network Admissibility: guarantees the accuracy of TAA* algorithm (, ) V max

12 Flow of TAA* algorithm

13 Experiment Data preparation Road network data within the Beijing s Fourth Ring Speed data in July, August and September, 2007 with 5 minute period Main roads are covered by traffic data on the whole Roads not covered by traffic data are given default speed values

14 Experiment Algorithm preparation TAA* algorithm: implements scan eligible node set with quad heap priority queue sets maximum possible travel speed (V max ) = 60km/h RTA* (Real time A*) algorithm refers to the A* algorithm only considering traffic information at departure time RTA*_M algorithm refers to the sum of multiple callings of RTA* algorithm during the whole navigation process

15 Experimental results (a) RTA* (b) TAA* From: Beichendong Road To: Cuiwei Road Departure time: 7:00 o clock Result: TAA* algorithm foresees and bypasses the forthcoming traffic congestion on the Third Ring Road. Departure time: 8:00 o clock Result: TAA* algorithm predicts the disappearance of current traffic congestion on the Third Ring Road at entrance time, and avoids an unwanted detour.

16 Experimental results (cont.) We select 30 OD pairs randomly, and compute fastest paths for every OD pair using three algorithms separately. Travel Time (min) RTA*_M TAA* 1. Path travel times of TAA* algorithm are shorter than those of RTA*_M algorithm on the whole. 2. The differentiation is limited due to the non high quality of traffic data and the simplicity of traffic prediction model.

17 Experimental results (cont.) Computational Time (s) RTA* TAA* 0 1. TAA* algorithm will cost about 10 percent more computational time than RTA* algorithm. 2. The extra time is consumed mainly by the computation of link travel time, whose time complexity is O(m), where m denotes the number of time intervals.

18 Experimental results (cont.) Computational Time (s) RTA*_M TAA* 1. TAA* algorithm cost much less computational time than RTA*_M algorithm. 2. The reason is that TAA* algorithm only need to run once due to its predictability, but comparatively, RTA*_M algorithm must run again and again.

19 Conclusions & future researches We suggest a novel time dependent network model with FIFO condition satisfied. We develop a temporally adaptive A* shortest path algorithm, which is able to foresee and bypass traffic congestions in advance, and avoid frequent path re optimization effectively. In order to improve the practicability of the algorithm, we should explore accurate traffic prediction models in the future. In order to further the efficiency of the algorithm, we should consider combining other heuristic strategies (e.g., hierarchical strategy) in the future.

20 Questions & Answers