Object level traffic patterns mining

Traffic network consists of a set of network objects, each of which is either a link or an intersection where traffic congestions only occur on some network objects by which the traffic demand cannot be fully serviced. Unfortunately, the demand of the network objects is

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never known in advance and the capacity of the network objects is hardly available, which makes the identification and prediction of network objects congestion impracticable.

According to the expert’s heuristic, the ratio of average speed and speed limit of a network object has a negative impact to the ratio of the demand and its capacity. The lower of the former ratio value indicates that the network object is in the higher congested situation. Thus traffic status of a spatiotemporal object (STO, notated by Oi^j, network object i in time zone Tj) can be calculated by dividing the average speed of all the TISs during the same time zone Tj by the speed limit of the network object. Let traffic index factor (TIF), θ(O_i^j), denote the normalized traffic status of O_i^j, as listed in Equation (5.1), where V_i^j, Li are the average speed and speed limit of the object O_i^j respectively. The higher the θ, the more serious congestion level of the object is, for example, θ=1 indicates the object is in a serious congestion status and θ near around zero means the object is in a free flow status.

i

The traffic status of urban network can be aggregated to snapshot by spatial and temporal domains, where spatial domain groups the TISs by spatial area of the network object and temporal domain groups the TISs by time zone, for example, 15 minutes. Let a traffic network snapshot (TNS) be composed of a set of a spatiotemporal network objects during a 15-minute period. Therefore, the traffic status of urban network in morning workday peak hour (7~9 AM) includes eight snapshots. All the spatiotemporal traffic network objects and snapshots generated in this phase are stored in TIDB as the data source of the subsequent

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phases.

5.1.1 Spatiotemporal Aggregation Pattern (SAP)

The spatiotemporal aggregation pattern (SAP), also named as congested object item (COI), represents the network object which fulfils two threshold criteria: (1) traffic congestion threshold (Hө), and (2) congestion confidence threshold (Hc). STP are mined from historical traffic database by aggregating the TISs by spatial, temporal, and event dimensions, classifying the congestion level of the link by the attributes and traveling speed of that link, and calculating the support and confidence for each SAP. Spatial dimension stands for the link identification attribute in the urban road network, and temporal dimension is the classified indices of time domain (identified by Pk), which includes: AM peak or PM peak hour, holiday or workday, etc. Congestion level is determined by the ratio of average speed and speed limit of the link in the same spatial and temporal condition. For example, average speed of 40 km/hr in the PM peak hour in workday is classified as free flow state in urban street, but will be classified as strongly congestion in freeway. Support and confidence can be calculated by aggregating the TISs at the same spatiotemporal conditions. The format of SAP is listed as in Equation (5.2): Sid, stands for link id, Tid is temporal id, Eid means the event condition of the pattern, such as normal, car accident, road construction, etc. Cg stands for congestion level, which is normalized by the link attribute (speed limit, link type) of target link (Sid); Sup and Con stand for support and confidence of the SAP respectively. An example of SAP (‘L1’, ‘W,N’, ‘N’, 9, 0.3%, 65%) means that the link [L1] is in free flow state (congestion level 9) at non-peak hours of workday and the confidence of this pattern is 65%, support is 0.3%.

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[SAP]: (Sid, Tid, Eid, Cg, Sup, Con) … (5.2)

For the network objects where the TIF (θ) larger than the threshold (Hө), which are named as spatiotemporal congested object (STCO), congestion confidence threshold filter is then applied to each STCO to discover the SAP, as illustrated in Equation (5.3). The confidence of network object O_i^j at temporal period Pk is calculated by the ratio of the congested samples of the spatiotemporal network object O_i^j over total samples in the temporal period Pk.

For the SAP, some traffic regulation actions can be taken to alleviate the congestion, such as extend the green time signal control, enforce the reversible lane, etc.

5.1.3 Congestion Drop Pattern (CDP)

The basic idea of CDP is to calculate the significant congestion difference between an object and its downstream objects, which indicates the bottleneck level of the object. In an typical intersection, an object usually has three downstream objects, as illustrated in Figure 5-1, {Oi,1, Oi,2, Oi,3} are the downstream objects of Oi (upstream object), which are the three candidate moving directions while a vehicle leaving out the object Oi.

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Figure 5-1 Congestion drop pattern concept

The definition of congestion drop ratio (CDR, notated as τ) is illustrated in Equation (5.4), which calculates the difference of TIF(θ) between object O_i^j and the average θ of its m downstream objects (

{

}

j

j O O

O'₁, '₂,..., ' ).

If the CDR (τ) of an object is closed to 1, it indicates the traffic congestion of the object is more serious than its downstream objects. On the other side, the traffic congestion is more serious in downstream objects than itself if the CDR of the object is smaller than 0. When the CDR of an object is larger than the congestion drop threshold (Hd), then this object is regarded as a CDP object

5.1.4 Intersection Delay Pattern (IDP)

Intersection delay is the delay between two consecutive links (i.e, upstream object and downstream object), as illustrated in Figure 5-1, which is mostly caused by signal delay and

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queuing delay. Intersection delays are categorized by through delay (TD), right-turn delay (RTD), and left-turn delay (LTD), which indicate the three possible directions from one link connected to its downstream links respectively. The IDP samples can be retrieved from two consecutive TISs of a journey with different link by calculating the link travel time and intersection delay. As illustrated in Equation (5.5), P is the pattern type (TD/LTD/RTD), SOid

and SIid are the two consecutive links ID from the link SOid to the link SIid, Tid is the temporal id, Davg denotes the average delay time of this intersection, and Sup, Con are the support and confidence of the pattern, respectively. For example, (‘RTD’, ‘L1’, ‘L2’, ‘W,P’, 40, 0.2%, 75%) represents that in the peak hours of workday (‘W,P’), it takes 40 seconds to do a right turn from link ‘L1’ to link ‘L2’, and the support is 0.2% , confidence is 75%.

IDP : (P, SOid, SIid, Tid, Davg, Sup, Conf) …(5.5)

Figure 5-2 Intersection delay example: RTD

Intersection delay patterns can be discovered by sequential pattern mining on spatial and temporal sequences in TIDB. Each sample of intersection delay must be in a journey which

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contains two consecutive TISs with different links. Figure 5-2 illustrates an example of RTD pattern: a probing vehicle driving north and then turn right to east, it reports TIS at location A of Link La and consecutively reports TIS at location B of Link Lb. The symbols used in the TIS format (T,L,X,Y,D,V) in Figure 5-2 stand for timestamp (T), link id (L), coordinates (X,Y), direction (D) and speed (V) respectively. The distances da, db in Figure 5-2 stand for the distance from A, B to the intersection of links La and Lb respectively. Assuming that in the short period time interval between Tb and Ta, the vehicle is driving at the speed of Va at link La and Vb at the link Lb. There are at most twelve intersection delays in a two way cross intersection object, including TD/LTD/RTD for each E/W/S/N direction. For example, the right turn delay (RTD) time from the La to Lb can be estimated by subtracting travel time of da

and db from elapsed time between two TIS (Tb-Ta).