CN112927508B - Traffic accident space-time influence range estimation method considering multiple congestion levels - Google Patents

Traffic accident space-time influence range estimation method considering multiple congestion levels Download PDF

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CN112927508B
CN112927508B CN202110160138.8A CN202110160138A CN112927508B CN 112927508 B CN112927508 B CN 112927508B CN 202110160138 A CN202110160138 A CN 202110160138A CN 112927508 B CN112927508 B CN 112927508B
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王正礼
郑振杰
陈哲
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Beijing Jiaotong University
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Abstract

The invention provides a traffic accident space-time influence range estimation method considering multiple congestion levels. The method comprises the following steps: the speed data provided by the floating car is used for constructing a space-time congestion level map, and the speed s of the road section j and the time interval m under the accident-free condition and after the accident occurs are respectively obtainedj，mAnd velocity
Figure DDA0002936214170000011
According to the speed
Figure DDA0002936214170000012
And speed sj，mCalculating the congestion level of each space-time cell based on the number of the congestion levels, setting a basic rule which is required to be met by the shape of a space-time area affected by an accident according to a propagation rule of traffic waves, establishing an integer programming optimization model of a traffic accident influence range according to the basic rule, constraint conditions and an objective function, and solving the integer programming optimization model to obtain the optimized congestion level of each space-time cell. The method can distinguish a plurality of congestion levels, and improves the accuracy and precision of estimation. The estimation result meets the propagation rule of the traffic wave, and the reasonability of the estimated space-time influence range is ensured.

Description

Traffic accident space-time influence range estimation method considering multiple congestion levels
Technical Field
The invention relates to the technical field of traffic accident management, in particular to a traffic accident time-space influence range estimation method considering multiple congestion levels.
Background
Sudden traffic accidents on roads can block the normal running of vehicles and reduce the operating efficiency of a road system, and inconvenience is brought to people's trips. Because the time and the position of the traffic accident are random, no rule can be followed, if the traffic accident is not conducted in time, serious traffic jam or even local traffic paralysis can be caused. The estimation of the space-time influence range caused by the traffic accident can provide a guidance function for traffic emergency treatment, and the estimation method can be used for not only quantifying the vehicle delay caused by the accident, but also determining the maximum congestion duration and the maximum congestion distance caused by the accident. In addition, regression or machine learning models can also be used to predict the spread in time and space of congestion caused by an accident, combining factors such as the type of accident, road structure, time and location of the incident, weather, etc.
At present, the method for estimating the space-time influence range of the traffic accident in the prior art comprises the following steps: the speed data provided by the floating cars or the detectors is used for distinguishing the congestion level from the non-congestion level. The disadvantages of this method are: the method can only distinguish two grades of congestion and non-congestion, and the estimation accuracy and precision of the space-time influence range of the traffic accident are not high.
Disclosure of Invention
The invention provides a traffic accident space-time influence range estimation method considering multiple congestion levels, so as to effectively estimate the traffic accident space-time influence range.
In order to achieve the purpose, the invention adopts the following technical scheme.
A traffic accident space-time influence range estimation method considering multiple congestion levels comprises the following steps:
constructing a space-time congestion level map by using speed data provided by a floating car, and corresponding to a space-time unit cell in the space-time congestion level map for a given road section j and a time interval m;
using the speed data provided by the floating body, the speed s of the section j and the time interval m in the accident-free case is obtainedj，mAnd speed at road section j and time interval m after the occurrence of the accident
Figure BDA0002936214150000021
According to said speed
Figure BDA0002936214150000022
And said speed sj，mCalculating a congestion level of each spatiotemporal cell in the spatiotemporal congestion level map based on a given congestion level number;
setting a basic rule which is required to be met by the shape of a space-time area affected by an accident according to a propagation rule of traffic waves, establishing an integer programming optimization model of a traffic accident influence range according to the basic rule, a set constraint condition and an objective function, and solving the integer programming optimization model to obtain the optimized congestion level of each space-time cell.
Preferably, the building of the spatiotemporal congestion level map using the speed data provided by the floating car corresponds to a spatiotemporal cell in the spatiotemporal congestion level map for a given road section j and time interval m, and comprises:
dividing a researched road into J road sections with equal length, sequentially marking the road sections as 1, … J and … J from upstream to downstream, dividing a researched time interval into M intervals with equal length, sequentially marking the road sections as 1, … M, … and M according to the time sequence, taking the road sections as a horizontal axis and the time as a vertical axis, establishing a space-time congestion level graph comprising M multiplied by J cells, and for a given road section J and a given time interval M, corresponding to a space-time cell < J, M > in the space-time congestion level graph, wherein the numerical value marked in each space-time cell represents the congestion level of the space-time cell.
Preferably, the speed data provided by the floating car are used to obtain the speed s of the section j and the time interval m in the accident-free case respectivelyj，mAnd speed at road section j and time interval m after the occurrence of the accident
Figure BDA0002936214150000023
The method comprises the following steps:
the speed s of the non-accident road section j and the time interval m is calculated by using the speed data provided by the floating carj，mAnd speed at road section j and time interval m after the occurrence of the accident
Figure BDA0002936214150000024
Using historical speed data under the condition of no accident occurrence to calculate sj，mAverage value of (2)
Figure BDA0002936214150000025
And standard deviation σj，mAnd further obtaining a space-time velocity matrix and a standard deviation matrix under the accident-free condition.
Preferably, said speed is dependent on said speed
Figure BDA0002936214150000031
And said speed sj，mThe comparing result of (a) calculating a congestion level of each spatiotemporal cell in the spatiotemporal congestion level map based on a given congestion level number, comprising:
when the condition is satisfied
Figure BDA0002936214150000032
Where α is a parameter having a value greater than 0, the cell is determined<j，m>The accident is not influenced; otherwise, the cell is determined<j，m>Is affected by accidents;
the unit cells affected by the accident correspond to the smallest and largest
Figure BDA0002936214150000033
Are respectively marked as
Figure BDA0002936214150000034
And
Figure BDA0002936214150000035
calculating a speed interval for distinguishing individual congestion levels
Figure BDA0002936214150000036
Congestion level for each cell Pj，mExpressed, the calculation is as follows:
Figure BDA0002936214150000037
wherein K is more than or equal to 1 and less than or equal to K and is an integer.
Preferably, the basic rule that the shape of the space-time region affected by the accident should meet is set according to the propagation rule of the traffic wave includes:
the 3 basic rules that the shape of the accident-affected spatio-temporal region should satisfy are set as follows:
rule 1: the propagation of traffic waves in space and time is uninterrupted, and each row and each column of affected cells are continuous in a space-time congestion level map;
rule 2: as time goes on, the spatial boundary of the traffic wave moves to the upstream road section against the traffic flow direction;
rule 3: the boundaries of the accident-affected spatio-temporal regions are continuous.
Preferably, the integer programming optimization model for establishing the traffic accident influence range according to the basic rule, the set constraint conditions and the objective function comprises:
defining an integer decision variable:
Figure BDA0002936214150000038
defining a binary decision variable ζj，mIf the impact of an accident is in a cell<j，m>Dissipation then ζj，m1 is ═ 1; otherwise, ζj，mThe cell is a termination cell, which is mathematically defined as:
Figure BDA0002936214150000041
the method for setting the constraint conditions of the integer programming optimization model comprises the following steps:
after the occurrence time interval and the road section position of the accident are known, the corresponding cell is the initial cell of the accident<js，ms>The constraints are as follows:
Figure BDA0002936214150000042
the space-time region affected by the accident has a termination cell, and the corresponding constraint conditions are as follows:
Figure BDA0002936214150000043
when the termination cell affected by the accident is < j, m >, the congestion level is at least 1, and the corresponding constraint conditions are as follows:
Figure BDA0002936214150000044
when the accident affects the termination cell is<j，m>Then cell<j-1，m>And<j，m+1>no longer affected by accident, i.e. kj-1，m＝κj，m+1The corresponding constraint is as follows:
Figure BDA0002936214150000045
Figure BDA0002936214150000046
when cell<j，m>When affected by an accident, κj，mNot less than 1, cell<j，m-1>And<j+1，m>at least one being affected by the accident, kj，m-1Not less than 1 or kappaj+1，m1Not less than 1, with the corresponding constraint conditions as follows
Figure BDA0002936214150000047
When k isj，m-1Kappa of not less than 1j+1，m1When the cell is more than or equal to 1<j，m>Is also affected by accidents, κj，mMore than or equal to 1, and the corresponding constraint conditions are as follows:
Figure BDA0002936214150000048
Figure BDA0002936214150000049
Figure BDA00029362141500000410
λ1+λ2+λ3constraint no more than 2 (10)
λ1，λ2，λ3E {0, 1} constraint (11)
Given time interval m-1, when the congestion level of segment j is lower than the congestion level of its immediately upstream cell j-1, i.e., κj，m-1＜κj-1，m-1Then cell<j，m>Congestion level of not higher than cell<j，m-1>Congestion level of, i.e. kj，m≤κj，m-1The corresponding constraint conditions are as follows:
Figure BDA0002936214150000051
Figure BDA0002936214150000052
λ4+λ5constraint of ≦ 1 (14)
λ4，λ5E {0, 1} constraint (15)
Given time interval m-1, when the congestion level of segment j is higher than the congestion level of its immediately upstream cell j-1, i.e., κj，m-1≥κj-1，m-1At the next time interval m, cell<j，m>Congestion level of not lower than cell<j，m-1>Congestion level of, i.e. kj，m≥κj，m-1The corresponding constraint conditions are as follows:
Figure BDA0002936214150000053
Figure BDA0002936214150000054
λ6+λ7constraint no more than 1 (18)
λ6+λ7E {0, 1} constraint (19)
When cell < j, m-1> is a termination cell, then constraints (16) and (17) are no longer valid;
the constraints on the decision variables are expressed as follows:
Figure BDA0002936214150000055
Figure BDA0002936214150000056
Figure BDA0002936214150000057
Figure BDA0002936214150000058
the objective function of the integer programming optimization model is set as follows:
Figure BDA0002936214150000059
converting the objective function into a linear model, and then rewriting the objective function as:
Figure BDA00029362141500000510
Figure BDA0002936214150000061
Figure BDA0002936214150000062
and establishing an integer programming optimization model of the traffic accident influence range according to the basic rule, the set constraint conditions and the objective function.
Preferably, the obtaining of the optimized congestion level of each spatiotemporal cell by solving the integer programming optimization model includes:
inputting the occurrence position and the occurrence time of the researched accident and historical speed data of the road into the integer programming optimization model, solving the integer programming model by using a branch-and-bound method, gradually dividing a feasible solution space into smaller and smaller subsets, calculating a target lower bound for the feasible solution in each subset, and outputting the space-time influence range of the accident and the optimized congestion level of each space-time unit cell by the integer programming optimization model after the solution process is finished, wherein the subsets exceeding the target value of the known feasible solution set are not further branched.
According to the technical scheme provided by the embodiment of the invention, the method for estimating the space-time influence range of the traffic accident considering multiple congestion levels can distinguish the multiple congestion levels, so that the estimation accuracy and precision are improved. The estimation result of the method meets the propagation rule of traffic waves, and the reasonability of the estimated space-time influence range is ensured.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a processing flow chart of a method for estimating a space-time impact range of a traffic accident considering multiple congestion levels according to an embodiment of the present invention.
Fig. 2 is a space-time congestion level map obtained based on real speed data of a floating car according to an embodiment of the present invention.
FIG. 3 is a block diagram of a congestion level variable P according to an embodiment of the present inventionj，mExamples of (2) are shown.
Fig. 4 is a schematic diagram of a result obtained after optimization of an air-time congestion level map based on an integer programming model according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
For the convenience of understanding of the embodiments of the present invention, the following description will be further explained by taking specific embodiments as examples with reference to the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
In actual life and application, the congestion level is often further subdivided, for example, a high-grade map divides the congestion level into 4 levels of smooth congestion, light congestion, medium congestion and severe congestion. The space-time influence range of the accident is estimated by considering multiple congestion levels, the estimation result is more accurate, and the traffic management department can also more accurately estimate the influence of the accident, so that a more appropriate traffic emergency treatment strategy is provided.
The processing flow of the method for estimating the space-time influence range of the traffic accident considering the multiple congestion levels, which is provided by the embodiment of the invention, is shown in fig. 1 and comprises the following processing steps:
step 1, constructing a space-time congestion level map by using speed data provided by a floating car.
Step 1.1 the invention first divides the road under study into J sections of equal length, which are labeled 1, …, J, …, J in sequence from upstream to downstream. The time interval under study is then divided into M intervals of equal length, labeled sequentially in chronological order 1, … M, …, M. FIG. 2 is a space-time congestion level map obtained based on actual speed data of a floating car according to an embodiment of the present invention, and FIG. 3 is a congestion level variable Pj，mExamples of (2) are shown. In fig. 2 and 3, a spatiotemporal congestion level map including M × J cells is constructed with a road section as a horizontal axis and time as a vertical axis, and for a given road section J and time interval M, one spatiotemporal cell in the spatiotemporal congestion level map is corresponding to<j，m>And the numerical value marked in each space-time cell represents the congestion level of the space-time cell. Since the accident occurrence section and time can be known through the accident record, the corresponding space-time cell is generally regarded as the starting cell of the accident influence range.
The floating car mainly comprises a taxi provided with a vehicle-mounted GPS device.
Step 1.2 Using the speed data provided by the floating car (mainly a taxi equipped with a vehicle GPS device), the speed of the vehicle traveling on the road section j and the time interval m can be calculated and recorded as sj，m. After the accident occurs, s affected by the accident can be obtainedj，mIs given as
Figure BDA0002936214150000081
Therefore, the space-time velocity matrix under the accident occurrence condition can be obtained. And s can be calculated by using historical speed data under the condition of no accidentj，mThe average and standard deviation of (1) are respectively recorded as
Figure BDA0002936214150000082
And σj，m。
Step 1.3 when
Figure BDA0002936214150000091
Is not significantly less than
Figure BDA0002936214150000092
When is like
Figure BDA0002936214150000093
(where α is a parameter with a value greater than 0, typically 4.2) may be initially considered as a cell<j，m>Is not affected by accidents. Otherwise, the cell is considered<j，m>May be affected by an accident. Cells that may be affected by an accident may be further differentiated into different congestion levels. Given a number of differentiated congestion levels of K, the cells affected by the accident correspond to the smallest and largest
Figure BDA0002936214150000094
Are respectively marked as
Figure BDA0002936214150000095
And
Figure BDA0002936214150000096
may be calculated to distinguish between the singlesSpeed interval of congestion level
Figure BDA0002936214150000097
Thereby, the space-time speed matrix under the accident occurrence condition can be converted into a discrete matrix with a plurality of congestion levels, and the congestion level of each cell is Pj，mExpressed, the calculation is as follows:
Figure BDA0002936214150000098
wherein K is more than or equal to 1 and less than or equal to K and is an integer. From Pj，mThe higher the defined congestion level is, the more serious the congestion caused by the accident is, and P is given in figure 3j，mExamples of values are presented.
And 2, researching the shape of the accident space-time influence range.
The shape of the accident influence range should satisfy the propagation law of traffic waves: 1) after an accident occurs, congestion caused by the accident can be gradually spread to an upstream road section along with the time; 2) after the accident is cleared, the congestion caused by the accident gradually dissipates to an upstream road section along with the time. According to the propagation rule and the continuity of the traffic wave propagation, the invention provides 3 basic rules which are satisfied by the shape of the time-space region affected by the accident:
rule 1: the propagation of traffic waves in space and time must be uninterrupted, that is, each row and each column of affected cells in the space-time congestion level map should be continuous and form a single cluster.
Rule 2: over time, the spatial boundaries of traffic waves must move upstream segments against the direction of traffic flow. For a given time interval, the spatial boundaries of the traffic waves caused by the accident correspond to the most downstream and most upstream road segments affected by the accident.
Rule 3: the boundaries of the accident-affected spatiotemporal region must be continuous, i.e. the shape of the accident spatiotemporal region of influence should be connected and not be able to be divided into a plurality of independent sub-regions.
As the bold black line in fig. 2 represents the boundary of the spatiotemporal region actually affected by the accident, it is easy to verify that the boundary satisfies 3 basic rules for traffic wave propagation.
And 3, establishing an integer programming optimization model.
Step 3.1. the invention first defines the decision variables used by the optimization model. Because the speed data provided by the floating car has errors, the congestion in the space-time congestion level map can be caused by other accidental factors except accidents. Therefore, errors may exist in cells affected by an accident based on the speed data, that is, the shape of the accident spatiotemporal influence range obtained based on the speed data may not meet the propagation rule of traffic waves, and fig. 4 is a result schematic diagram obtained after the spatiotemporal congestion level diagram is optimized based on the integer programming model provided by the embodiment of the present invention. To obtain the spatio-temporal regions really affected by the accident and to differentiate their congestion levels, we define the following integer decision variables:
Figure BDA0002936214150000101
in addition to this, to determine the location and time of dissipation of the impact of the incident, a binary decision variable ζ is definedj，m. If the impact of an accident is in a cell<j，m>Dissipation then ζj，m1 is ═ 1; otherwise, ζ j，m0. For convenience of discussion, the cell is referred to as the termination cell, which is mathematically defined as follows:
Figure BDA0002936214150000102
step 3.2 constraint conditions of the model
Step 3.2.1 after the occurrence time interval and the road segment position of the accident are known, as described in step 1.1, the corresponding cell is the initial cell of the accident<js，ms>It is inevitably affected by accidents, so the corresponding constraints can be obtained as follows:
Figure BDA0002936214150000103
step 3.2.2 the space-time area affected by the accident has a termination cell, and the corresponding constraint conditions are as follows:
Figure BDA0002936214150000111
when the termination cell affected by the accident is < j, m >, it must be affected by the accident, i.e. the congestion level is at least 1. The corresponding constraints are as follows:
Figure BDA0002936214150000112
when the accident affects the termination cell is<j，m>Then cell<j-1，m>And<j，m+1>must not be affected by the accident, i.e. kj-1，m＝κj，m+1The corresponding constraint is as follows:
Figure BDA0002936214150000113
Figure BDA0002936214150000114
step 3.2.3 current cell<j，m>When affected by an accident, the effect must be either propagated from the downstream segment adjacent to the cell or a reservation of the cell at an affected time interval. That is, when the cell is<j，m>When affected by accident (kappa)j，m≧ 1), cell<j，m-1>And<j+1，m>at least one of which is affected by the accident (k)j，m-1Not less than 1 or kappaj+1，m1Not less than 1), the corresponding constraint conditions are as follows
Figure BDA0002936214150000115
In addition, when the cell<j，m-1>And<j+1，m>all affected by accident (k)j，m-1Kappa of not less than 1j+1，m1≧ 1) rule cell<j，m>Is also necessarily affected by accidents (k)j，mNot less than 1), and the corresponding constraint conditions are as follows:
Figure BDA0002936214150000116
Figure BDA0002936214150000117
Figure BDA0002936214150000118
λ1+λ2+λ3less than or equal to 2; restraint (10)
λ1，λ2，λ3E {0, 1}. constraint (11)
Step 3.2.4 since the vehicle moves from upstream to downstream, the congestion level of the downstream road segment may be affected by the traffic conditions of the upstream road segment. Given time interval m-1, when the congestion level of segment j is lower than the congestion level of its immediately upstream cell j-1 (κ)j，m-1＜κj-1，m-1) It is known that the average speed of the road segment j is higher than the average speed of the immediately adjacent upstream cell j-1. According to the corresponding relation between the speed and the flow, the flow of the road section j is larger than the flow of the road section j flowing into the road section j from the road section j-1. That is, at the next time interval m, the vehicles remaining on the section j may decrease. Thus, the unit cell<j，m>Does not exceed the cell<j，m-1>Congestion level (k) ofj，m≤κj，m-1) The corresponding constraint conditions are as follows:
Figure BDA0002936214150000121
Figure BDA0002936214150000122
λ4+λ5less than or equal to 1; restraint (14)
λ4，λ5E {0, 1}. constraint (15)
Given time interval m-1, when the congestion level of segment j is higher than the congestion level of its immediately upstream cell j-1 (κ)j，m-1＞κj-1，m-1) It is known that the average speed of the road segment j will be lower than the average speed of the immediately upstream cell j-1. According to the corresponding relation between the speed and the flow, the flow of the road section j is smaller than the flow of the road section j flowing into the road section j from the road section j-1. That is, at the next time interval m, the number of vehicles remaining on the section j increases. Thus, the unit cell<j，m>Does not fall below the cell level<j，m-1>Congestion level (k) ofj，m≥κj，m-1) The corresponding constraint conditions are as follows:
Figure BDA0002936214150000123
Figure BDA0002936214150000124
λ6+λ7less than or equal to 1; restraint (18)
λ6，λ7E {0, 1}. constraint (19)
It is worth noting that when cell < j, m-1> is the terminating cell, the corresponding constraints (16) and (17) are no longer valid either, since the impact of the accident has disappeared.
The constraints of step 3.2.5 on the decision variables are expressed as follows:
Figure BDA0002936214150000125
Figure BDA0002936214150000131
Figure BDA0002936214150000132
Figure BDA0002936214150000133
and 3.3, the difference value between the congestion level output by the model and the congestion level obtained by the actual data is as small as possible. Thus, for a cell<j，m>When P isj，mWhen k, the decision variable k of the modelj，mPreferably also k. Therefore, the objective function corresponding to the model is expressed as follows:
Figure BDA0002936214150000134
to convert this to a linear model, the objective function described above can be rewritten as:
Figure BDA0002936214150000135
Figure BDA0002936214150000136
Figure BDA0002936214150000137
and establishing an integer programming optimization model of the traffic accident influence range according to the 3 basic rules, the set constraint conditions and the objective function.
Step 4 solution of integer programming model
The input of the integer programming optimization model is the occurrence position and the occurrence time of the researched accident and historical speed data (obtained by GPS data provided by a floating car) of a road, and the output of the model is the space-time influence range of the accident and the congestion level of each space-time cell. The integer programming model can be solved using standard branch-and-bound methods, with the idea of gradually partitioning the feasible solution space into smaller and smaller subsets, and computing a lower target bound for the feasible solutions in each subset, and any subset that exceeds the target value of the known feasible solution set is not further branched, which makes many subsets unnecessary to consider, improving the solution efficiency. In practical application, many mathematical programming model solvers embed standard branch-and-bound methods, and for example, the model can be solved by calling a Gurobi solver through Python programming language.
Examples
In this example, an integer programming optimization model that accounts for multiple congestion levels is used to estimate the spatiotemporal reach of the accident. Firstly, real speed data provided by a floating car is used for constructing a road space-time congestion level map of an accident instance occurring on Beijing three loops, then a corresponding integer programming optimization model is established according to the rule of the shape of an accident space-time influence range, finally a Gurobi solver is called by Python to solve the model, and the space-time influence range and the specific congestion level of the accident are obtained. The method comprises the following specific steps:
step 1, constructing a space-time congestion level map by using speed data provided by a floating car
Step 1.1 in this example, the speed data of the floating car is used to construct a map of the road's spatio-temporal congestion level. The road under study is first divided into 50 segments of equal length, each segment being 100m in length and labeled 1-50 in sequence from upstream to downstream. The time interval under study (16:00PM-18:00PM) is then divided into 120 intervals of equal length, each interval being 5 minutes, and labeled sequentially in chronological order as 1-120. According to the accident record, the occurrence time of the accident is 16:50 minutes, and the accident occurs at the position of 0.7 kilometer.
Step 1.2 calculating the distance m and distance j traveled by the vehicle using the speed data provided by the floating carVelocity, denoted as sj，m. After the accident occurs, s affected by the accident can be obtainedj，mIs given as
Figure BDA0002936214150000141
Therefore, the space-time velocity matrix under the accident occurrence condition can be obtained. And s can be calculated by using historical speed data under the condition of no accidentj，mThe average and standard deviation of (1) are respectively recorded as
Figure BDA0002936214150000142
And σj，mTherefore, the space-time speed matrix and the standard deviation matrix under the accident-free condition can be obtained.
Step 1.3 when
Figure BDA0002936214150000143
Is not significantly less than
Figure BDA0002936214150000144
When is like
Figure BDA0002936214150000145
Wherein alpha is 4.2, the cell can be considered preliminarily<j，m>Is not affected by accidents. Otherwise, the cell is considered<j，m>May be affected by an accident. Cells that may be affected by an accident are further differentiated into different congestion levels. Given a number of congestion levels of 3, the cells affected by the accident correspond to the smallest and largest
Figure BDA0002936214150000146
Are respectively marked as
Figure BDA0002936214150000147
(24.63km/h) and
Figure BDA0002936214150000148
(46.67km/h), then the speed interval used to distinguish individual congestion levels can be calculated
Figure BDA0002936214150000149
To this end, the space-time velocity matrix in the case of an accident can be converted into a discrete matrix with a plurality of congestion levels, the congestion level of each cell being Pj，mExpressed, the calculation is as follows:
Figure BDA00029362141500001410
wherein k is more than or equal to 1 and less than or equal to 4 and is an integer. From Pj，mThe higher the congestion level is, the more serious the congestion caused by the accident is, and a space-time congestion level map after calculation is given in fig. 2.
Step 2, study of accident time-space influence range shape
The shape of the accident influence range should satisfy the propagation law of traffic waves: 1) after an accident occurs, congestion caused by the accident can be gradually spread to an upstream road section along with the time; 2) after the accident is cleared, the congestion caused by the accident gradually dissipates to an upstream road section along with the time. According to the propagation rule and the continuity of the traffic wave propagation, the invention provides 3 basic rules which are satisfied by the shape of the time-space region affected by the accident:
rule 1: the propagation of traffic waves in space and time must be uninterrupted, that is, each row and each column of affected cells in the space-time congestion level map should be continuous and form a single cluster.
Rule 2: over time, the spatial boundaries of traffic waves must move upstream segments against the direction of traffic flow. For a given time interval, the spatial boundaries of the traffic waves caused by the accident correspond to the most downstream and most upstream road segments affected by the accident.
Rule 3: the boundaries of the accident-affected spatiotemporal region must be continuous, i.e. the shape of the accident spatiotemporal region of influence should be connected and not be able to be divided into a plurality of independent sub-regions.
Due to congestion caused by data errors or other accidental factors such as non-accidents, the shape of the space-time influence range in the attached figure 2 does not meet the rule, and then the optimization model provided by the invention is used for estimating the real space-time influence range of the accidents and distinguishing the congestion levels of the accidents.
Step 3, establishing an integer programming optimization model
In step 3.1, from the division of the links and time intervals in step 1, it can be seen that M is 24, J is 40, and the congestion level K is 3. And establishing a corresponding integer programming model based on the integer programming model.
Step 3.2 constraint conditions of the model
Step 3.2.1 after the occurrence time interval and the road section position of the accident are known, the cell <11, 7> is the initial cell of the accident, which is inevitably affected by the accident, so that the corresponding constraint conditions can be obtained as follows:
κ11，7not less than 1. constraint (1)
Step 3.2.2 the space-time area affected by the accident has a termination cell, and the corresponding constraint conditions are as follows:
Figure BDA0002936214150000161
when the termination cell affected by the accident is < j, m >, it must be affected by the accident, i.e. the congestion level is at least 1. The corresponding constraints are as follows:
Figure BDA0002936214150000162
when the accident affects the termination cell is<j，m>Then cell<j-1，m>And<j，m+1>must not be affected by the accident, i.e. kj-1，m＝κj，m+1The corresponding constraint is as follows:
Figure BDA0002936214150000163
Figure BDA0002936214150000164
step 3.2.3 current cell<j，m>When affected by an accident, the effect must be either propagated from the downstream segment adjacent to the cell or a reservation of the cell at an affected time interval. That is, when the cell is<j，m>When affected by accident (kappa)j，m≧ 1), cell<j，m-1>And<j+1，m>at least one of which is affected by the accident (k)j，m-1Not less than 1 or kappaj+1，m1Not less than 1), the corresponding constraint conditions are as follows
Figure BDA0002936214150000165
In addition, when the cell<j，m-1>And<j+1，m>all affected by accident (k)j，m-1Kappa of not less than 1j+1，m1≧ 1) rule cell<j，m>Is also necessarily affected by accidents (k)j，mNot less than 1), and the corresponding constraint conditions are as follows:
Figure BDA0002936214150000166
Figure BDA0002936214150000167
Figure BDA0002936214150000168
λ1+λ2+λ3less than or equal to 2; restraint (10)
λ1，λ2，λ3E {0, 1}. constraint (11)
Step 3.2.4 since the vehicle moves from upstream to downstream, the congestion level of the downstream road segment may be affected by the traffic conditions of the upstream road segment. Given time interval m-1, when the congestion level of segment j is lower than the congestion level of its immediately upstream cell j-1When (k)j，m-1＜κj-1，m-1) It is known that the average speed of the road segment j is higher than the average speed of the immediately adjacent upstream cell j-1. According to the corresponding relation between the speed and the flow, the flow of the road section j is larger than the flow of the road section j flowing into the road section j from the road section j-1. That is, at the next time interval m, the vehicles remaining on the section j may decrease. Thus, the unit cell<j，m>Does not exceed the cell<j，m-1>Congestion level (k) ofj，m≤κj，m-1) The corresponding constraint conditions are as follows:
Figure BDA0002936214150000171
Figure BDA0002936214150000172
λ4+λ5less than or equal to 1; restraint (14)
λ4，λ5E {0, 1}. constraint (15)
Given time interval m-1, when the congestion level of segment j is higher than the congestion level of its immediately upstream cell j-1 (κ)j，m-1＞κj-1，m-1) It is known that the average speed of the road segment j will be lower than the average speed of the immediately upstream cell j-1. According to the corresponding relation between the speed and the flow, the flow of the road section j is smaller than the flow of the road section j flowing into the road section j from the road section j-1. That is, at the next time interval m, the number of vehicles remaining on the section j increases. Thus, the unit cell<j，m>Does not fall below the cell level<j，m-1>Congestion level (k) ofj，m≥κk，m-1) The corresponding constraint conditions are as follows:
Figure BDA0002936214150000173
Figure BDA0002936214150000174
λ6+λ7less than or equal to 1; restraint (18)
λ6，λ7E {0, 1}. constraint (19)
It is worth noting that when cell < j, m-1> is the terminating cell, the corresponding constraints (16) and (17) are no longer valid either, since the impact of the accident has disappeared.
The constraints of step 3.2.5 on the decision variables are expressed as follows:
Figure BDA0002936214150000181
Figure BDA0002936214150000182
Figure BDA0002936214150000183
Figure BDA0002936214150000184
and 3.3, the difference value between the congestion level output by the model and the congestion level obtained by the actual data is as small as possible. Thus, for a cell<j，m>When P isj，mWhen k, the decision variable k of the modelj，mPreferably also k. Therefore, the objective function corresponding to the model is expressed as follows:
Figure BDA0002936214150000185
to convert this to a linear model, the objective function described above can be rewritten as:
Figure BDA0002936214150000186
Figure BDA0002936214150000187
Figure BDA0002936214150000188
the integer programming optimization model of the step 3.4 or more can be solved by using a standard branch-and-bound method, in the example solution, a Gurobi solver is called by using Python language to carry out solution, and the space-time influence range and the congestion level estimated by the model are shown in FIG. 4. As can be seen from fig. 3 and 4, the original congestion level map in fig. 3 does not satisfy the propagation law of traffic waves, which may be caused by data errors or other non-accident contingencies. However, after the integer programming model described in the step 3 is used for optimization, an accident space-time influence range meeting the traffic wave propagation rule can be obtained, and the accident space-time influence range is divided into 4 congestion levels (including the unblocked level corresponding to the number 0).
In summary, the embodiment of the invention provides a traffic accident space-time influence range estimation method considering multiple congestion levels, and compared with the existing estimation method which can only distinguish two congestion levels and non-congestion levels, the optimization model of the invention can distinguish the multiple congestion levels, so that the estimation accuracy and precision are improved. In addition, the estimation result of the method necessarily meets the propagation rule of the traffic wave, and the reasonability of the estimated space-time influence range is ensured.
Those of ordinary skill in the art will understand that: the figures are merely schematic representations of one embodiment, and the blocks or flow diagrams in the figures are not necessarily required to practice the present invention.
From the above description of the embodiments, it is clear to those skilled in the art that the present invention can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method according to the embodiments or some parts of the embodiments.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, they are described in relative terms, as long as they are described in partial descriptions of method embodiments. The above-described embodiments of the apparatus and system are merely illustrative, and the units described as separate parts may or may not be physically separate, and the parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (2)

1. A method for estimating a space-time influence range of a traffic accident by considering multiple congestion levels is characterized by comprising the following steps:
constructing a space-time congestion level map by using speed data provided by a floating car, and corresponding to a space-time unit cell in the space-time congestion level map for a given road section j and a time interval m;
respectively obtaining on-road without accident by using speed data provided by floating carSpeed s of segment j and time interval mj，mAnd speed at road section j and time interval m after the occurrence of the accident
Figure FDA0003438580260000011
According to said speed
Figure FDA0003438580260000012
And said speed sj，mCalculating a congestion level of each spatiotemporal cell in the spatiotemporal congestion level map based on a given congestion level number;
setting a basic rule which is required to be met by the shape of a space-time area affected by an accident according to a propagation rule of traffic waves, establishing an integer programming optimization model of a traffic accident influence range according to the basic rule, a set constraint condition and an objective function, and solving the integer programming optimization model to obtain the optimized congestion level of each space-time cell;
according to the speed
Figure FDA0003438580260000013
And said speed sj，mThe comparing result of (a) calculating a congestion level of each spatiotemporal cell in the spatiotemporal congestion level map based on a given congestion level number, comprising:
when the condition is satisfied
Figure FDA0003438580260000014
Where α is a parameter having a value greater than 0, the cell is determined<j，m>The accident is not influenced; otherwise, the cell is determined<j，m>Is affected by accidents;
the unit cells affected by the accident correspond to the smallest and largest
Figure FDA0003438580260000015
Are respectively marked as
Figure FDA0003438580260000016
And
Figure FDA0003438580260000017
calculating a speed interval for distinguishing individual congestion levels
Figure FDA0003438580260000018
Congestion level for each cell Pj，mExpressed, the calculation is as follows:
Figure FDA0003438580260000019
wherein K is more than or equal to 1 and less than or equal to K and is an integer;
the basic rule that the shape of the space-time area affected by the accident should meet is set according to the propagation rule of the traffic wave, and the basic rule comprises the following steps:
the 3 basic rules that the shape of the accident-affected spatio-temporal region should satisfy are set as follows:
rule 1: the propagation of traffic waves in space and time is uninterrupted, and each row and each column of affected cells are continuous in a space-time congestion level map;
rule 2: as time goes on, the spatial boundary of the traffic wave moves to the upstream road section against the traffic flow direction;
rule 3: the boundaries of the time-space regions affected by the accident are continuous;
the integer programming optimization model for establishing the traffic accident influence range according to the basic rule, the set constraint conditions and the objective function comprises the following steps:
defining an integer decision variable:
Figure FDA0003438580260000021
defining a binary decision variable ζj，mIf the impact of an accident is in a cell<j，m>Dissipation then ζj，m1 is ═ 1; whether or notThen, ζj，mThe cell is a termination cell, which is mathematically defined as:
Figure FDA0003438580260000022
the method for setting the constraint conditions of the integer programming optimization model comprises the following steps:
after the occurrence time interval and the road section position of the accident are known, the corresponding cell is the initial cell of the accident<js，ms>The constraints are as follows:
Figure FDA0003438580260000023
the space-time region affected by the accident has a termination cell, and the corresponding constraint conditions are as follows:
Figure FDA0003438580260000024
when the termination cell affected by the accident is < j, m >, the congestion level is at least 1, and the corresponding constraint conditions are as follows:
Figure FDA0003438580260000025
when the accident affects the termination cell is<j，m>Then cell<j-1，m>And<j，m+1>no longer affected by accident, i.e. kj-1，m＝κj，m+1The corresponding constraint is as follows:
Figure FDA0003438580260000031
Figure FDA0003438580260000032
when cell<j，m>When affected by an accident, κj，mNot less than 1, cell<j，m-1>And<j+1，m>at least one being affected by the accident, kj，m-1Not less than 1 or kappaj+1，m1Not less than 1, with the corresponding constraint conditions as follows
Figure FDA0003438580260000033
When k isj，m-1Kappa of not less than 1j+1，m1When the cell is more than or equal to 1<j，m>Is also affected by accidents, κj，mMore than or equal to 1, and the corresponding constraint conditions are as follows:
Figure FDA0003438580260000034
Figure FDA0003438580260000035
Figure FDA0003438580260000036
λ1+λ2+λ3constraint no more than 2 (10)
λ1，λ2，λ3E {0, 1} constraint (11)
Given time interval m-1, when the congestion level of segment j is lower than the congestion level of its immediately upstream cell j-1, i.e., κj，m-1<κj-1，m-1Then cell<j，m>Congestion level of not higher than cell<j，m-1>Congestion level of, i.e. kj，m≤κj，m-1The corresponding constraint conditions are as follows:
Figure FDA0003438580260000037
Figure FDA0003438580260000038
λ4+λ5constraint of ≦ 1 (14)
λ4，λ5E {0, 1} constraint (15)
Given time interval m-1, when the congestion level of segment j is higher than the congestion level of its immediately upstream cell j-1, i.e., κj，m-1＞κj-1，m-1At the next time interval m, cell<j，m>Congestion level of not lower than cell<j，m-1>Congestion level of, i.e. kj，m≥κj，m-1The corresponding constraint conditions are as follows:
Figure FDA0003438580260000041
Figure FDA0003438580260000042
λ6+λ7constraint no more than 1 (18)
λ6，λ7E {0, 1} constraint (19)
When cell < j, m-1> is a termination cell, then constraints (16) and (17) are no longer valid;
the constraints on the decision variables are expressed as follows:
Figure FDA0003438580260000043
Figure FDA0003438580260000044
Figure FDA0003438580260000045
Figure FDA0003438580260000046
the objective function of the integer programming optimization model is set as follows:
Figure FDA0003438580260000047
converting the objective function into a linear model, and then rewriting the objective function as:
Figure FDA0003438580260000048
Figure FDA0003438580260000049
Figure FDA00034385802600000410
establishing an integer programming optimization model of the traffic accident influence range according to the basic rule, the set constraint conditions and the objective function;
the method for constructing the space-time congestion level map by using the speed data provided by the floating car corresponds to a space-time cell in the space-time congestion level map for a given road section j and a given time interval m, and comprises the following steps of:
dividing a researched road into J road sections with equal length, sequentially marking the road sections as 1, … J, … and J from upstream to downstream, dividing a researched time interval into M intervals with equal length, sequentially marking the road sections as 1, … M, … and M according to a time sequence, taking the road sections as a horizontal axis and the time as a vertical axis, establishing a space-time congestion level graph comprising M multiplied by J cells, and for a given road section J and a time interval M, corresponding to a space-time cell < J, M > in the space-time congestion level graph, wherein a numerical value marked in each space-time cell represents the congestion level of the space-time cell;
the speed s of the section j and the time interval m under the accident-free condition is respectively obtained by using the speed data provided by the floating carj，mAnd speed at road section j and time interval m after the occurrence of the accident
Figure FDA0003438580260000051
The method comprises the following steps:
the speed s of the non-accident road section j and the time interval m is calculated by using the speed data provided by the floating carj，mAnd speed at road section j and time interval m after the occurrence of the accident
Figure FDA0003438580260000052
Using historical speed data under the condition of no accident occurrence to calculate sj，mAverage value of (2)
Figure FDA0003438580260000053
And standard deviation σj，mAnd further obtaining a space-time velocity matrix and a standard deviation matrix under the accident-free condition.
2. The method of claim 1, wherein obtaining the optimized congestion level for each spatiotemporal cell by solving the integer programming optimization model comprises:
inputting the occurrence position and the occurrence time of the researched accident and historical speed data of a road into the integer programming optimization model, solving the integer programming optimization model by using a branch-and-bound method, gradually dividing a feasible solution space into smaller and smaller subsets, calculating a target lower bound for feasible solutions in each subset, and outputting the space-time influence range of the accident and the optimized congestion level of each space-time unit cell by the integer programming optimization model after the solution process is finished, wherein the subsets exceeding the target value of the known feasible solution set are not further branched.
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