實驗室 : 先進網路技術與服務實驗室 報告者 : 黃福銘 (Angus F.M. Huang) Adaptive Fastest Path Computation on a Road Network: A Traffic Mining Approach TMSG

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Conference – VLDB ‘07, September 23-28, 2007, Vienna, Austria Authors –Hector Gonzalez, Jiawei Han, Xiaolei Li, Margaret Myslinska, John Paul Sondag Department of Computer Science University of Illinois at Urbana-Champaign 3 Publication

Angus F.M. Huang Outline INTRODUCTION PROBLEM DEFINITION TRAFFIC DATABASE ROAD NETWORK PARTITIONING TRAFFIC MINING PRE-COMPUTATION AND UPGRADES FASTEST PATH COMPUTATION EXPERIMENTAL EVALUATION CONCLUSIONS 4

Angus F.M. Huang Introduction MapQuest, MapPoint, Google Maps –Route planning systems –MapQuest had 10 billion routes queries from 1996 to 2006 Current speed conditions are not enough for the fastest route searching –Road speed limits, average speed,… Example 1: Importance of driving patterns –Local experts will consider a multitude of important factors that are difficult to explicitly incorporate into a path finding algorithm Example 2: Importance of speed patterns –Time of departure, weather conditions, car pool lane, etc. 5

Angus F.M. Huang Introduction Solution –Traffic-mining-based path-finding method –Speed and driving patterns from historic traffic data Technical Contributions –Road hierarchy-based partitioning –Speed rule mining –Driving pattern mining –Adaptive pre-computation –Road upgrading –Adaptive fastest path algorithm 6

Angus F.M. Huang Problem Definition Def.: Road network –G(V, E) Def.: Speed pattern – –d i is a value for speed factor Di –m is an aggregate function computed on edge speed Def.: Driving pattern –A sequences s of edges e(1),e(2),…,e(l) –appears more than min_sup times –support(s), the number of paths containing the sequence –length(s), the number of edges that it contains Def.: Edge forecast model –F(edge_id, t) –Returns a tuple (d 1,d 2,…,d k ) with the expected driving conditions for edge edge_id at time t 7

Angus F.M. Huang Time-of-day D 1 = weather D 2 = vehicle-type 8 Larger roads are shown in bold 24,123 edges 18,496 nodes TIGER line files Forecast function example –At 5 pm [time], for highway 74 between Champaign and Normal [edge], Weather = rain, and Construction = no [conditions]

Angus F.M. Huang Problem Statement Given a road network G(V,E), a set of speed patterns S, an edge forecast model F, and a query q ←(s, e, start_time) Compute a fast route q r between nodes s and e starting from s at time start_time, such that q r contains a large number of frequent driving patterns 9

Angus F.M. Huang Traffic Database (edge_id, time, speed) –Basic traffic observation (car_id, edge_id, time, speed) –Radio-frequency tags (edge_id, start_time, end_time, (d 1,d 2,…,d k ):m) –Augment each traffic observation with the driving factors 10

Angus F.M. Huang Road Network Partitioning Road hierarchy –Highway, interstate road, multi-lane road, small road,… Grid-based partitioning is bad The natural partition induced by the road hierarchy itself can be used to divide the network into semantically meaningful areas –With well defined driving and speed patterns Given a road hierarchy with l levels, we can construct a hierarchy of areas as a tree of depth l-1 –Road class 1 is the largest, and road class l the smallest 11

Angus F.M. Huang San Joaquin Partitioned Map 12 a:b –a is the area number when roads of level 1 are used –b is the subarea of a when roads of level 2 are used to subdivide a The upper left !! –Quite a few strong connection

Angus F.M. Huang Area Partitioning Algorithm Generate semantically meaningful partitions –By using road hierarchy information Flood filling technique –Identify strongly connected components –class(n) > k It automatically identifies.. –Interior nodes, those with a single area in their area set –Border nodes, those with multiple areas in their area set O(n) –O(1), interior node, n nodes –O(|a|), border nodes, a areas –O(n x |a|) –|a| << n 13

Angus F.M. Huang Traffic Mining Speed pattern mining –See the mining as a classification problem Where we would like to predict edge speed based on time and feature values d 1,…,d k –“if area = a 1 and weather = icy and time = rush hour then speed =1/4 x base speed” Abstraction level, general representation –Run a preprocessing step to discretize speed factors, which will be treated as our class label –Use Decision tree induction to perform rule induction 14

Angus F.M. Huang Traffic Mining Driving pattern mining –Ask local people for route tips in an unfamiliar area –Frequent pattern mining Minimum support level –Uniform mining support level is difficult to define And it may filter many important local roads, or may keep infrequently traveled high-level roads –Use a frequent pattern mining method guided by the area and road hierarchies Frequent edges are mined according to different area level To distinguish different level-supports 15

Angus F.M. Huang Pre-computation and Upgrades To improve the performance both in terms of run time and path accuracy Area level pre-computation –A*, Floyd Warshall,… –When edge speed is a function of factors The fastest path between two nodes may be different for different times and conditions –We can check two conditions to determine pre-computing benefits How many fastest path queries will go through nodes of the pre- computed path How stable is the path –To compute certain fastest paths only within the nodes inside the area 16

Angus F.M. Huang Pre-computation and Upgrades Assumption: drivers take the largest road available to reach destination Exception !! : if there is a small road that is faster than a large road 17 Small road upgrades –If under some driving conditions small roads have a significantly higher speed –To upgrade the internal edges to upper level

Angus F.M. Huang Fastest Path Computation Properties of the (approximate) fastest routes –Be well supported by the historical driver behavior –Larger road first, significant smaller road second –Account for all relevant factors affecting driving speed Before computation… –Road network partitioning –Speed patterns are mined get_edge_speed(edge_id, t, (d 1,…,d k )) –Driving patterns are mined is_frequent(edge_seq, t, (d 1,…,d n )) –Area-level paths are pre-computed –Internal roads are upgraded get_edge_class(edge_id, t, (d 1,…,d k )) 18

Angus F.M. Huang Fastest Path Algorithm It is a variation of A* Algorithm strategies 1.Priority queue of expanded paths 2.Pick the frequent node with lowest g(n)+h(n) g(n), the current travel time cost h(n), the expected travel time cost, 3.Ascending search to find the bigger road 4.Descending search to find the smaller road 5.Simple estimation policy, h(n) = distance(n, end) / max_speed 6.Online path re-computation Lemma –The adaptive fastest path algorithm, when computing a path between (start, end) nodes, in areas a i, a j respectively will consider at most O(|a i |+|a j |+|bn|+|un|) distinct nodes 19

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Angus F.M. Huang Experimental Evaluation Comparisons –A*, basic A* –Hier, the algorithm without area pre-computation –Adapt, the algorithm Data synthesis –San Francisco Bay area, 175,343 nodes, 223,606 edges –Illinois, 831,524 nodes, 1,048,080 nodes, 24,123 edges Traffic simulator –Network-based Generator of Moving Objects by Thomas Brinkhoff –Rush hour: 10,000 objects, Non-rush: 1,000 objects –Include weather factor to slow down speeds –Two car classes: Cars with faster speeds, Trucks with slower speeds Simulation output was a list of edge observations – –Then, mine the speed patterns for each edge 21

Angus F.M. Huang Network-based Generator of Moving Objects Thomas Brinkhoff Institut für Angewandte Photogrammetrie und Geoinformatik (IAPG) 22

Angus F.M. Huang Query Length We varied the average distance between the starting and ending nodes –The longer the distance the larger the search space –The distance is as a percentage of the map diameter –20% upgraded roads –Pre-compute fastest paths in 30% of the lowest level areas Figure 5, Adapt only expands slightly more nodes than Hier Figure 6, Adapt is as good as the A*’s fastest path, efficiency & accuracy Figure 7, the same pattern as in the expanded nodes 23

Angus F.M. Huang Upgraded Paths Vary the percentage of lowest level areas that contain a path that is faster than the border paths and thus needs to be upgraded Figure 8&10: A* and Hier are significantly affected (???) Figure 8&10: Adapt suffers as having more upgraded edges but still gradual Figure 9: when no edges are upgraded both Hier and Adapt perform equally, as we increase the number of upgraded edges Adapt starts closing the gap with A* We can use a fairly aggressive edge updating strategy to improve path quality without incurring any significant performance penalty –Interior edges as long as are 80% as fast as border edges 24

Angus F.M. Huang Area Pre-computation Examine the performance gain for different levels of pre-compution –Adapt vs. Adapt_nopre The same algorithm but withourt using pre- computed areas –Select a percentage of the lowest level areas to pre- compute fastest path, 0% to 100% The performance improvement is very significant If we use higher level area, the performance would have been more noticeable 25

Angus F.M. Huang Road Network Size Compare query processing efficiency for 3 road network sizes –sj, nodes and edges –sf, nodes and edges –il, nodes and edges –sj < sf < il Adapt has excellent scalability in terms of road network size –The number of nodes usually grow much slower than the number of small roads 26

Angus F.M. Huang Conclusion We developed an adaptive fastest path algorithm, that bases routing decision on driving and speed patterns mined from historical data. The partitioning algorithm yields very natural partitions, where larger areas are observed at regions with low road densities, and much finer areas are observed at dense regions such as big cities. 27

Angus F.M. Huang Angus Comments 如果道路層級規畫不佳，此篇成效依然會很好嗎 ?? 此篇亦無解決歷史資料稀疏的問題。 The power of Number & Trajectory – 28

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