JP2006154962A - Method for predicting travel time using status space expression method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To predict the future travel time of a road by using a travel time database in which the travel time result data of a road collected on a road network are stored. <P>SOLUTION: The deviation Δx(i, k) of a travel time at a certain time of the small section of a road is calculated, and a coefficient ϕ(i) is identified by expressing the deviation of the travel time at a certain time of the small section by prediction formula (3) of the linear sum of the product of the deviation Δz(i, k-1), ..., Δz(i, k-s) of the travel time since a time previous to the time of the small section to a time going back to the past by an s time and the coefficient ϕ(i). The deviation of the travel time at the time ahead of the current time of the small section is successively predicted by using the data of the deviation of the traveling time since the current time of the small section to the time going back to the past by the s time by prediction formula (3) including the identified coefficient ϕ, and the prediction value of the travel time is calculated by adding the deviation of the predicted travel time to the movement average value of the travel time at the same time in the past for each small section, and the travel time between two spots is predicted by adding the prediction values. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a method for predicting the future travel time of a road by using a travel time database storing road travel time performance data collected on a road network.

With the recent increase in traffic demand and the spread of information transmission media such as the Internet and mobile phones, there is an increasing need for traffic information provision. Of the traffic information, information about the time required for the traveling vehicle to travel on the road (referred to as travel time) is necessary for grasping traffic congestion, calculating the shortest route or detour route to reach the destination, and the like.
Travel time result data collected by measuring traffic is stored in a travel time database.

In urban areas, road-car information communication systems are currently being built (VICS (Vehicle Information Communication System)). If the travel time data is obtained using VICS, the actual travel time between points can be grasped.
Sagara, Akizuki, Nakamizo, Katayama “System Identification” Society of Instrument and Control Engineers, 1981

In order to predict traffic congestion on the road, it is necessary to predict not only the actual travel time but also the future travel time. Also, in calculating the shortest route and the detour route, it is preferable in terms of accuracy to predict and use the future travel time rather than the current travel time.
As a method of predicting the future travel time, a method (statistic difference method) is used to predict the future travel time by extending the time transition pattern of the travel time up to the present in the road section to be predicted. There are many.

Therefore, the inventor calculates a deviation between a travel time at a certain time in the road section and a statistical average value of the travel time at the same time in the past over a plurality of past times in the road section, and calculates these deviations. We focused on using it to predict future travel times.
The present invention provides a travel time prediction method capable of predicting a road section with high accuracy using a travel time database storing travel time performance data of each road section collected on a road network. Objective.

  The travel time prediction method of the present invention divides a road into small sections, and calculates the deviation of the travel time at a time in the small section from the travel time at the time in the small section to the same time in the past of the small section. The travel time is calculated by subtracting the statistical average value of the travel time of the travel time, and the travel time deviation at a certain time in the small section is the travel from the time immediately before the time in the small section to the time that is s times in the past. As expressed by the prediction formula of the linear sum of the product of the deviation of time and the coefficient φ, the deviation of the travel time of the obtained small section, the deviation of the travel time expressed by the prediction formula of the linear sum, The coefficient φ is identified so that the difference between the current time of the subsection and the current time of the subsection is earlier than the current time of the subsection by using the deviation data of the travel time from the current time of the subsection to the time that is s time backward in the past. The travel time deviation of the time is defined as the prediction including the identified coefficient φ. For each small section, calculate the predicted travel time by adding the deviation of the predicted travel time to the statistical average value of the travel time at the same time in the past, and from the departure point to the destination point. In this method, the predicted travel time is added to predict the travel time between two points.

The “time” is not a precise time in seconds or milliseconds, but is a time (discrete time) in units of time width in which travel time data is provided.
The “statistical average value of travel time” may be calculated using a moving average or exponential average technique, but is not limited to this. Generally, a statistical technique based on past travel time data is used. This is a value that represents the past travel time required.

In the method of the present invention, attention is paid to the deviation between the travel time at a certain time in a small section and the statistical average value of the travel time at the same time in the past. Predict travel time by finding this deviation for each time in the past for the subsection, adding these weights to the statistical average value of travel time at future times in the subsection Suggest to do.
In addition, when traffic congestion occurs, traffic congestion is derived in a small section connected upstream (referred to as upstream in the direction of travel of the vehicle) and downstream. It is preferable to process a plurality of small sections. Therefore, it is desirable to use not only the small section but also a deviation in travel time between the small section and the upstream and / or downstream small sections (claim 2). This is expected to improve the travel time prediction accuracy.

  In the travel time prediction method of the present invention, the road is divided into small sections, and the travel time at a certain time in the small section is traced back s times in the past from the time immediately preceding the time in the small section. The difference between the actually measured travel time and the travel time represented by the linear sum prediction formula is the smallest as expressed by the prediction formula of the linear sum of the product of the travel time up to the time and the coefficient φ. As described above, the coefficient φ is identified, and the travel time of the time earlier than the current time of the small section is identified by using the travel time data from the current time of the small section to the time that is s times backward in the past. Travels between two points by sequentially predicting with the prediction formula including the calculated coefficient φ, obtaining the predicted value of the travel time for each small section, and adding the predicted value of the travel time from the departure point to the destination point A method for predicting time (claim 3).

In the present invention, the travel time itself, not the deviation of the travel time, is predicted by weighting the travel time in the small section from the time immediately before the time to the time that is s times back in the past. . The prediction method is the same as that of the first aspect of the invention.
Also in the present invention, it is desirable to use not only the small section but also a deviation in travel time between the small section and the upstream and / or downstream small sections (claim 4).

  Moreover, it can be expected that the amount of information increases and the travel time prediction accuracy increases as s at the past s time increases, but if s is too large, the calculation load increases. Therefore, it is desirable to determine s based on the balance between the two (claim 5).

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
FIG. 1 is a route diagram in which a road section between a departure point A and a destination point B is composed of N (N is an integer of 2 or more) small sections (links). The starting point A is A (0), and the connection points between each subsection are 1, 2,. . . , N-1, and the destination point B is represented by B (N). Each small section is represented as [0, 1], [1, 2], and the like.

It is assumed that travel time record data for each small section is obtained for each time width Δt. In particular, the actual travel time of the small section [i−1, i] of the vehicle that has arrived at the point i immediately before the discrete time t = kΔt (k is an integer) is represented as x (i, k).
1. Prediction method 1.1 Symbols The symbols used in the prediction model are as follows.

: A predicted travel time for the small section [i-1, i] at time (k + j) Δt based on travel time data up to time kΔt.

: Variance of the same prediction error.
Y (i, k): Predicted travel time for the interval [0, i] based on travel time data up to time kΔt.
P (i, k): Variance of the prediction error.
1.2 Prerequisites
(1) The travel time predicted value for points A to B (section [0, N]) is the sum of the predicted travel time values for each small section.
(2) The travel time of each small section is predicted at each discrete time. For vehicles predicted to arrive at point i between times (k + j-1) Δt and (k + j) Δt, the predicted value

Is used as the predicted travel time for the small section [i-1, i].
(3) Predicted value

Is assumed to be statistically independent with respect to i, j. At this time, the variance of the travel time prediction error in the section [0, N] is obtained by adding the variance of the travel time prediction error in each small section.
1.3 Prediction of travel time for section [0, N] While predicting travel time for section [0, i] of a car that has departed from point A (0) at time kΔt, refer to the flowchart (Fig. 2). explain.

First, a variable i representing a section is set to 0, and a variable j representing a time of prediction of a time ahead is set to 0 (step S1). The travel time x (0, k) at time Δk (j = 0) obtained in the small section [−1,0] is set as an initial value used for prediction (step S2). Since the small section [−1,0] does not exist, the travel time x (0, k) used as the initial value is an actually measured value.
Predicted value of small interval [i-1, i] ahead of jΔt time

And its dispersion

Is calculated (step S3).
The following inequality

(Step S4), and if the inequality holds, the process proceeds to step S6. This inequality is obtained by adding the predicted value Y (i-1, k) of the travel time of the interval [0, i-1] to the predicted value of the small interval [i-1, i], that is, the interval [0, It is checked whether or not the predicted travel time of i] is within jΔt.
If the inequality does not hold, that is, if

Proceeding to step S5, j is incremented by one so that j ← j + 1, and the process returns to step S3.
In step S6, the predicted value and variance of the small section [i-1, i] are converted into the predicted value Y (i-1, k) and the variance P (i-1, k) of the section [0, i-1]. To obtain the predicted value Y (i, k) and variance P (i, k) of the interval [0, i].
In step S5, the travel time of the previous time can be sequentially predicted by incrementing j one by one.

By comparing i and N, it is checked whether or not the destination point B has been reached (step S7). If not, i ← i + 1 is set (step S8), and the process returns to step S1. If it has reached, the process is terminated. With this, the travel time of all small sections can be predicted.
2. Prediction of small sections 2.1 Introduction of deviations from average values Consider the prediction of travel time on weekdays. Moving average at the same time in the past L days including the present

And the deviation Δx (i, k) from the moving average value is predicted by the equation (1).

The moving average value is approximated by the exponential smoothing equation (2) so as to be suitable for sequential calculation.

here,

Represents an average value at a time one day before the time kΔt. d indicates the number of discrete times per day.
2.2 Prediction model of small section Travel time deviation Δx (i, k) at time kΔt of small section [i-1, i] and past time (ks) Δt of the section [i-1, i] , (k-s + 1) Δt,..., (k-1) Δt (i, ks),..., Δx (i, k-1) of travel time at Δt, upstream section [i-2, i− 1] past time (ks) Δt, (k−s + 1) Δt,..., (K−1) Δt (Δ−1 (ks−1),. k-1) and the past time (ks) Δt, (k−s + 1) Δt,..., (k−1) Δt in the downstream section [i, i + 1], the travel time deviation Δx (i + 1, ks),..., Δx (i + 1, k−1), and the “linear sum prediction formula” in formula (3) is established.

Where φ (i) is an unknown weighting factor a (i, 1), ..., a (i, s); b (i, 1), ..., b (i, s); c (i, 1), ..., c (i, s) vector, Δz (i, k-1) is the travel time at the past time (ks) Δt, (k-s + 1) Δt, ..., (k-1) Δt .DELTA.x (i, ks), ...,. DELTA.x (i, k-1); .DELTA.x (i-1, ks), ...,. DELTA.x (i-1, k-1); .DELTA.x (i + 1, ks), ..., a vector of Δx (i + 1, k-1), ξ (i, k) is a residual. s is a variable indicating how long the travel time result data is adopted retroactively (assuming s <k).

The residual ξ (i, k) is assumed to be normal white noise N [0, q (i)]. Since there is no upstream section in the small section [0, 1] and no downstream section in the small section [N-1, N], there is no corresponding term.
In the following, the dynamic model of equation (3) is used as the basis for the travel time prediction formula for one hour ahead.
2.3 Coefficient Estimation Problem Δz (i, k-1) in equation (4) is the travel time at the past time (ks) Δt, (k-s + 1) Δt, ..., (k-1) Δt The deviation was shown. Therefore, the travel time deviation vector Δz (i, k-2) at (ks-1) Δt, (ks) Δt,..., (K-2) Δt is created by shifting the time one time in the past. Similarly, the travel time deviation vector Δz (i, k-3 in (ks−2) Δt, (ks−1) Δt,. )make. In this way, the travel time deviation vector Δz (i, s) is created.

Further, the time is extended one step from (k−1) Δt, and the travel time deviation vector Δz (i, i, (k−s + 1) Δt, (k−s + 2) Δt,. k).
In this manner, travel time deviation vectors Δz (i, s) to Δz (i, k) can be obtained. These vectors are collected to form a matrix ΔZ (i, k) = [Δz (i, s),..., Δz (i, k)]. Each element of the matrix ΔZ (i, k) has already been obtained by equation (1). Therefore, ΔZ (i, k) is referred to as “information” ΔZ (i, k).

  When the information ΔZ (i, k) is given to obtain the value of the unknown coefficient φ (i) based on the information ΔZ (i, k), the sum of squared errors

Factor to minimize

Think about seeking.
As a solution suitable for online calculation of this problem, the following sequential relationships (6) to (8) hold (see Non-Patent Document 1).

However, the initial time is k = s, and the initial value of the sequential formula is

And This is the coefficient

Is obtained.
2.4 Variance of Residual Variance q (i) of residual ξ (i, k) can be estimated by equation (9) (see Non-Patent Document 1).

However, since Equation (9) is not a sequential calculation equation, the approximate calculation shown in Equation (10) is performed so as to be suitable for online calculation.

2.5 Prediction of j time ahead A prediction problem is a coefficient determined based on information ΔZ (i, k) up to time kΔt.

Is used to predict the travel time deviation j time ahead.

And distributed

Is to seek. Therefore, the travel time deviation equations are collectively expressed as a state equation.
First, N-dimensional vectors Δx (k), ξ (k), N × N-dimensional matrix φ (m)

Ns dimensional vector ΔX (k), Ξ (k), Ns × Ns dimensional matrix Φ

Then, the equation (3) can be expressed as a normal state equation.

It becomes.
Estimated travel time deviation ahead of jΔt time based on information ΔZ (k) = [ΔX (s), ΔX (s + 1), ..., ΔX (k)]

And its error covariance

From prerequisite 1.2 (3)

Therefore, it can be obtained from the following recurrence formulas (16) and (17).

here,

Is the Ns dimension,

Is Ns × Ns dimension, and each element is as follows.

3. Understanding the prediction accuracy 3.1 Verification data The 4th week of travel time data for 3 weeks when the main road of about 13.5km in the city is divided into consecutive N = 14 subsections The prediction accuracy was verified by predicting the travel time and comparing it with the actual travel time data of the fourth week. Saturdays and Sundays are excluded from the calculation target.

The travel time record data is obtained by recording the travel time of each small section every time width Δt = 5 minutes, and the value of L in the past L days when calculating the moving average is 14.
3.2 Determination of Order The order s that minimizes the information criterion AIC (Akaike's Information Criteria) in the model equation (3) is the best dynamic model (see Non-Patent Document 1). Comparison of AIC (s) of Equation (19) at the final time (k = 1728) of the verification period of the fourth week was performed. The result is shown in FIG.

From FIG. 3, AIC (s) decreases monotonously in the range of the order s = 1 to 10. Further, it is considered that an optimum value of s that minimizes AIC (s) can be found by increasing the order, but if the order increases, the prediction calculation process becomes enormous. Therefore, the order was set to s = 7, where the decreasing trend of AIC (s) began to settle.
3.3 Statistical properties of the residual If the dynamic model is appropriate, the residual becomes white noise (see Non-Patent Document 1). Therefore, the whiteness of the residual was examined for the model of order s = 7 obtained in Section 3.2. As a result, it was found that the autocorrelation coefficient of the residual is distributed within the range of ± 0.15 and the cross-correlation coefficient is within the range of ± 0.1. Therefore, it can be said that the residual has no correlation in time and space. It can be said that the precondition (3) in section 1.2 is satisfied.

3.4 Convergence of Coefficients As an example, Fig. 4 shows the weighting coefficients that make up the coefficient φ (i) in the calculation period k = 8 to 288 (one day) (see equation (4)).

Shows changes. Since the order s is set to 7, m ranges from 1 to 7. Near k = 200, the estimated value has almost converged.
3.5 Significance of the prediction method In order to grasp the significance of the present invention, the prediction error of the proposed method

And as a simple prediction, the current travel time is used as the predicted value as it is,

Prediction error when using

And compared. Table 1 shows a comparison result of the mean square of the prediction error near the average passage time jΔt of each small section. However, in the table

It is.

From Table 1, it can be seen that in the section excluding the section [9, 10], the prediction error of 5 to 26 points is less in the method of the present invention than in the simple prediction.
3.6 Validity of the prediction error calculation formula To verify the validity of the prediction error calculation formula,

The standard deviation

Contrast with.
As an example, FIG. 5 shows a comparison result in a small section [3,4] (i = 4) and 15 minutes later (j = 3). According to the figure, the error

62% of the standard deviation shown in the figure

It exists in the range. Therefore, it can be said that the calculation formula of the prediction error is appropriate.
3.7 Travel Time Prediction when Traveling in All Sections Figure 6 shows the temporal changes in travel time prediction value Y (N, k) and prediction accuracy √P (N, k) for all sections during the verification period. According to the graph of FIG. 6, the travel time varies from 25 minutes to 60 minutes from night to peak time, but the prediction accuracy is within approximately 3 minutes. Therefore, it can be proved that the prediction method is sufficiently accurate.

  Although the embodiments of the present invention have been described above, the embodiments of the present invention are not limited to the above-described embodiments. For example, in Section 2.2 “Prediction Model for Small Sections”, the past sections of the small section [i-1, i], the upstream section [i-2, i-1], and the downstream section [i, i + 1] The “prediction formula for linear sum” of Equation (3) was expressed using the travel time deviation at the time, but the equation using the travel time deviation at the past time only for the small section [i-1, i]. (3) may be expressed, and equation (3) may also be expressed using the deviation of travel time at the past times of the small section [i-1, i] and the upstream section [i-2, i-1]. The equation (3) may be expressed by using the deviation of the travel time at the past time in the small section [i−1, i] and the downstream section [i, i + 1]. Although the prediction accuracy of travel time may decrease, there is an advantage that the amount of calculation processing decreases as the number of sections decreases.

  In the explanation so far, the concept of deviation from the average value of travel time is introduced in section 2.1, the deviation is calculated for each time in the past for the small section, and these deviations are weighted. The travel time was predicted by adding to the statistical average value of the travel time at the future time of the small section. However, a method is also conceivable in which the travel time itself is obtained by weighting the travel time from the time immediately before the time in the small section to the time that is s times back in the past. In this case, “Introduction of deviation from average” in Section 2.1 is not performed. The “prediction model for small sections” in Section 2.2 is described as follows.

  Travel time x (i, k) at time kΔt in the small section [i-1, i] and past time (ks) Δt, (k-s + 1) Δt, in the section [i-1, i] ..., (k-1) Δt, travel time x (i, ks), ..., x (i, k-1), past time (ks) Δt, ( k-s + 1) Δt, ..., (k-1) Travel time x (i-1, ks), ..., x (i-1, k-1) in Δt and downstream section [i, i + 1 ] Past time (ks) Δt, (k-s + 1) Δt, ..., (k-1) travel time x (i + 1, ks), ..., x (i + 1, k-1) at Δt ), The following “linear sum prediction formula” holds.

Where φ (i) is an unknown weighting factor a (i, 1), ..., a (i, s); b (i, 1), ..., b (i, s); c (i, 1), ..., c (i, s) vector, z (i, k-1) is the travel time x at the past time (ks) Δt, (k-s + 1) Δt, ..., (k-1) Δt (i, ks), ..., x (i, k-1); x (i-1, ks), ..., x (i-1, k-1); x (i + 1, ks), ..., The vector of x (i + 1, k-1), ξ (i, k) is the residual.
After that, the coefficient φ (i) is identified by the method of minimizing the sum of squares of errors described in Section 2.3 and the following, and using this identified coefficient φ (i), the same as Expression (13) Equation of state

Can be used to determine the travel time x (i, k + j) ahead of j time points.

It is the figure on which the path | route comprised from each subsection between the departure point and the destination point was drawn. 10 is a flowchart for explaining a process p for predicting a travel time of a section [0, i] of a car that has departed from a point A (0) at time kΔt. In order to evaluate a variable s indicating how far the travel time record data is adopted retroactively, the order s is represented by a horizontal axis and AIC (s) is represented by a vertical axis. It is a graph which shows the time change of the weighting coefficient which comprises coefficient (phi) (i). It is a graph which shows the time change of prediction error. It is a graph which shows the predicted value and prediction accuracy of travel time.

Explanation of symbols

A Departure point B Destination point

Claims (5)

Using the travel time data from the current time to the past time for each subsection that forms between the starting point and the destination point, it takes for the vehicle that departed from the starting point to arrive at the destination point. A method for predicting travel time,
(A) A deviation of travel time at a certain time in a small section is obtained by subtracting a statistical average value of travel times at the same time in the past from the travel time at the corresponding time in the small section,
(B) The travel time deviation at a certain time in a small section is a linear product of the product of the deviation of the travel time and the coefficient φ from the previous time of the small section to the time s times before in the past. As represented by the sum prediction formula, the difference between the travel time deviation of the small section obtained in the procedure (a) and the travel time deviation represented by the linear sum prediction formula is the smallest. The coefficient φ is identified as follows:
(C) Using the deviation data of the travel time from the current time of the small section to the time that is s times in the past, the deviation of the travel time of the time earlier than the current time of the small section is determined as the identified coefficient. sequentially predicting by the prediction formula including φ,
(D) For each small section, add the deviation of the travel time predicted in the procedure (c) to the statistical average value of the travel time at the same time in the past to obtain the predicted value of the travel time. A travel time prediction method comprising: adding a predicted travel time value to predict a travel time between two points.   In the procedure (b), instead of “deviation of travel time of the small section from the time immediately before the time to the time that is s time in the past”, “the small section and its upstream and / or The travel time prediction method according to claim 1, wherein a deviation of travel time from a time immediately before the time in the downstream small section to a time that is s time backward in the past is used. Using the travel time data from the current time to the past time for each subsection that forms between the starting point and the destination point, it takes for the vehicle that departed from the starting point to arrive at the destination point. A method for predicting travel time,
(A) The travel time at a certain time in a small section is a prediction formula for a linear sum of products of the travel time and the coefficient φ from the previous time of the small section to a time that is s times before in the past The coefficient φ is identified so that the difference between the actually measured travel time and the travel time represented by the prediction formula of the linear sum is minimized,
(B) Using the travel time data from the current time of the small section to the time that is s times before, the travel time of the time earlier than the current time of the small section includes the identified coefficient φ. Predict sequentially using the prediction formula,
(C) For each small section, the travel time prediction value is obtained in the procedure (b), and the travel time between the two points is predicted by adding the travel time prediction value from the departure point to the destination point. A method for predicting travel time.   In the procedure (b), instead of “the travel time of the subsection from the time immediately before the time to the time that is s times in the past”, “the subsection and its upstream and / or downstream The travel time prediction method according to claim 3, wherein “travel time from a time immediately before the time in the small section to a time that is s times back in the past” is used.   The travel time prediction method according to claim 1, wherein s of the past s time is selected as an order that minimizes an information amount criterion AIC (Akaike's Information Criteria).

Images