CN111209966B - Path travel time determining method and system based on Markov chain - Google Patents
Path travel time determining method and system based on Markov chain Download PDFInfo
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Abstract
The invention discloses a method and a system for determining path travel time based on a Markov chain, wherein the method comprises the following steps: determining the corresponding travel time of each road section; taking the travel time of two adjacent road sections as a group to form a plurality of two-dimensional arrays; clustering all the two-dimensional arrays based on the Gaussian mixture model to obtain a path traffic state; determining path state probabilities under various path traffic states based on a Markov theory; determining path travel time distribution under various path traffic states based on a convolution theory; the total path travel time is determined according to the path state probability and the path travel time distribution under various path traffic states, so that the accuracy of determining the total path travel time is further improved, effective path induction of travelers is realized, traffic pressure is relieved, traffic jam is improved, and urban management is assisted.
Description
Technical Field
The invention relates to the technical field of travel time determination, in particular to a path travel time determination method and system based on a Markov chain.
Background
The path travel time is one of the most important reference indexes for measuring the traffic state of the urban road path. On one hand, the route travel time provides effective traffic information for traffic managers in cities, is convenient for the induction and organization of traffic flow, and ensures safe and smooth traffic environment. On the other hand, the traveler selects the current optimal driving route according to the predicted value of the route travel time, avoids the road section where traffic congestion and accidents happen, and assists in travel decision. Therefore, path travel time estimation is of great significance to solving the traffic congestion problem.
Researchers have conducted intensive research into the estimation of path travel time and have established many models. Predictions based on mathematical methods, traffic flow model theory, neural network model and machine learning theory have achieved research results. (1) The mathematical method is the earliest method for travel time prediction, and based on the existing travel time sequence, a time sequence model, ARIMA and other models are established for prediction. (2) The traffic flow theory-based path travel time prediction method introduces three parameters of traffic flow, speed and occupancy, models and identifies the evolution process of the travel time based on the three parameters, and predicts the path travel time. (3) The neural network model constructs a complex network system consisting of a large number of nodes, and constructs a travel time prediction model by adjusting weights among the nodes. Most of the above studies are to estimate and predict the path travel time from a time or space point of view, and how to consider the travel time distribution of the next stage by using the space-time correlation is still a problem to be solved at present.
Disclosure of Invention
Based on the above, the invention aims to provide a method and a system for determining the path travel time based on a Markov chain so as to improve the accuracy of determining the total path travel time.
To achieve the above object, the present invention provides a method for determining path travel time based on a markov chain, the method comprising:
determining the corresponding travel time of each road section;
taking the travel time of two adjacent road sections as a group to form a plurality of two-dimensional arrays;
clustering all the two-dimensional arrays based on the Gaussian mixture model to obtain a path traffic state;
determining path state probabilities under various path traffic states based on a Markov theory;
determining path travel time distribution under various path traffic states based on a convolution theory;
and determining the total path travel time according to the path state probability and the path travel time distribution under various path traffic states.
Optionally, the determining the path state probability under various path traffic states based on the markov theory specifically includes:
the method comprises the steps of arranging path traffic states obtained by clustering two adjacent road segments according to time sequence, and equally dividing the path traffic states into an initial state data set and a transfer state data set;
constructing a Markov model according to the initial state data set and the transition state data set to obtain a Markov chain;
determining the state transition probability of each Markov chain;
determining a connection probability between two Markov chains;
and determining the path state probabilities under various path traffic states according to the state transition probabilities and the connection probabilities.
Optionally, the determining the route travel time distribution under various route traffic states based on the convolution theory specifically includes:
determining the road section travel time distribution corresponding to each road section;
based on convolution theory, determining the route travel time distribution under various route traffic states according to the corresponding route travel time distribution of each route.
Optionally, the determining the total path travel time according to the path state probability and the path travel time distribution in various path traffic states includes the following specific formulas:
wherein RTTD is total path travel time, RTTD q For the route travel time distribution in the q-th route traffic state, RP q The probability of the path state in the Q-th path traffic state is Q, and the total number of the path traffic states is Q.
The invention also provides a path travel time determining system based on the Markov chain, which comprises:
the travel time determining module is used for determining travel time corresponding to each road section;
the two-dimensional array determining module is used for forming a plurality of two-dimensional arrays by taking the travel time of two adjacent road sections as a group;
the path traffic state determining module is used for clustering all the two-dimensional arrays based on the Gaussian mixture model to obtain a path traffic state;
the path state probability determining module is used for determining path state probabilities under various path traffic states based on a Markov theory;
the path travel time distribution determining module is used for determining path travel time distribution under various path traffic states based on convolution theory;
and the total path travel time determining module is used for determining the total path travel time according to the path state probability and the path travel time distribution under various path traffic states.
Optionally, the path state probability determining module specifically includes:
the data set determining unit is used for arranging the path traffic states obtained by clustering two adjacent road segments in time sequence and equally dividing the path traffic states into an initial state data set and a transfer state data set;
a Markov chain determining unit, configured to construct a Markov model according to the initial state data set and the transition state data set, and obtain a Markov chain;
a state transition probability determining unit configured to determine a state transition probability of each of the markov chains;
a connection probability determining unit for determining a connection probability between the two Markov chains;
and the path state probability determining unit is used for determining path state probabilities under various path traffic states according to the state transition probabilities and the connection probabilities.
Optionally, the path travel time distribution determining module specifically includes:
the road section travel time distribution determining unit is used for determining the road section travel time distribution corresponding to each road section;
and the path travel time distribution determining unit is used for determining the path travel time distribution under various path traffic states according to the path travel time distribution corresponding to each path based on the convolution theory.
Optionally, the determining the total path travel time according to the path state probability and the path travel time distribution in various path traffic states includes the following specific formulas:
wherein RTTD is total path travel time, RTTD q For the route travel time distribution in the q-th route traffic state, RP q The probability of the path state in the Q-th path traffic state is Q, and the total number of the path traffic states is Q.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses a method and a system for determining path travel time based on a Markov chain, wherein the method comprises the following steps: determining the corresponding travel time of each road section; taking the travel time of two adjacent road sections as a group to form a plurality of two-dimensional arrays; clustering all the two-dimensional arrays based on the Gaussian mixture model to obtain a path traffic state; determining path state probabilities under various path traffic states based on a Markov theory; determining path travel time distribution under various path traffic states based on a convolution theory; the total path travel time is determined according to the path state probability and the path travel time distribution under various path traffic states, so that the accuracy of determining the total path travel time is further improved, effective path induction of travelers is realized, traffic pressure is relieved, traffic jam is improved, and urban management is assisted.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for determining path travel time based on a Markov chain according to an embodiment of the present invention;
FIG. 2 is a schematic view of the travel of adjacent road segments according to an embodiment of the present invention;
FIG. 3 is a Gaussian mixture clustering chart according to an embodiment of the invention;
fig. 4 is a block diagram of a system for determining path travel time based on a markov chain according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a method and a system for determining path travel time based on a Markov chain so as to improve the accuracy of determining total path travel time.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Fig. 1 is a flowchart of a method for determining path travel time based on a markov chain according to an embodiment of the present invention, and as shown in fig. 1, the present invention provides a method for determining path travel time based on a markov chain, where the method includes:
step S1: determining the corresponding travel time of each road section;
step S2: taking the travel time of two adjacent road sections as a group to form a plurality of two-dimensional arrays;
step S3: clustering all the two-dimensional arrays based on the Gaussian mixture model to obtain a path traffic state;
step S4: determining path state probabilities under various path traffic states based on a Markov theory;
step S5: determining path travel time distribution under various path traffic states based on a convolution theory;
step S6: and determining the total path travel time according to the path state probability and the path travel time distribution under various path traffic states.
The steps are discussed in detail below:
step S1: determining the travel time corresponding to each road section specifically comprises the following steps:
step S11: selecting a starting point and an ending point;
step S12: the urban road takes an intersection as a dividing point, a highway or an urban expressway is generally divided into a road section every 1 km, and a path between the starting point and the ending point is divided to obtain a plurality of road sections;
step S13: and determining the corresponding travel time of each road section.
Step S2: taking the travel time of two adjacent road sections as a group to form a plurality of two-dimensional arrays; fig. 2 is a schematic view of the travel of adjacent road segments according to the embodiment of the present invention, and travel time of each road segment obtained by traveling in fig. 2 is shown in table 1, where TT represents travel time, t represents sampling time, and n represents the total number of sampling intervals.
Step S3: clustering all two-dimensional arrays based on the Gaussian mixture model to obtain a path traffic state, wherein the method specifically comprises the following steps:
step S31: determining an initial cluster number, and acquiring related parameters of the Gaussian mixture model through an EM (Expectation-Maximization algorithm) maximum expected algorithm, wherein the related parameters comprise the mean value and the variance of the Gaussian mixture model of each item; in the mixed Gaussian model, each Gaussian model represents a type of traffic state, and the mean value and the variance represent probability distribution characteristics of travel time in the type of path traffic state.
Step S32: and (5) increasing the clustering number or the path traffic state number, repeating the process, and calculating the error term square sum (Sum of Squared Errors, SSE for short) adopting different clustering numbers or path traffic state numbers according to the clustering result.
The SSE value is calculated as follows:
wherein K is the number of clusters, c k Is the cluster center of the kth class, and x is a two-dimensional array of adjacent road segment travel times belonging to the class k.
Step S33: selecting the clustering number corresponding to the minimum SSE value as the optimal clustering number, namely the path traffic state; the smaller the sum of squares of error terms SSE value indicates the better clustering effect.
Taking road segment 1 and road segment 2 in fig. 2 as examples, i.e., x= (TT) 1 (t+n),TT 2 (t+n)), fig. 3 shows the classification effect when the optimal clustering number, i.e., the number of traffic states is 3, based on the travel time data of the adjacent link 1 and link 2. Each cluster may be described by a polynomial gaussian function, wherein the two parameters, mean and variance, characterize the distribution of the gaussian functions.
Step S4: the method for determining the path state probability under various path traffic states based on the Markov theory comprises the following specific steps:
step S41: the method comprises the steps of arranging path traffic states obtained by clustering two adjacent road segments according to time sequence, and equally dividing the path traffic states into an initial state data set and a transfer state data set;
step S42: constructing a Markov model according to the initial state data set and the transition state data set to obtain a Markov chain;
step S43: the state transition probability of each Markov chain is determined, and the specific formula is as follows:
wherein ,from the initial state data +/for the n-1 th Markov chain>Transition to initial State data->State transition probability, X n-1 (t) is the state variable of the (n-1) th Markov chain during period t,/->For the initial state data of the n-1 th Markov chain within the period t, X n-1 (t+1) is the state variable of the n-1 th Markov chain within the period t+1,/L>Is the initial state data of the (n-1) th Markov chain in the period t+1, K n-1 Traffic state numbers divided for the n-1 th Markov chain.
Step S44: the connection probability between two Markov chains is determined, and the specific formula is as follows:
wherein ,Xn (t) is the state variable of the nth markov chain for period t,for the initial state data of the nth Markov chain within period t, X n+1 (t) is the state variable of the (n+1) th Markov chain during period t,/>For the initial state data of the n+1th Markov chain within the period t +.>For counting the n-th Markov chain initial state data as +.>And the n+1th Markov chain initial state data is +.>Number, K of n The state total number of the nth Markov chain is 1-N-1, and N is the total number of the Markov chain.
Step S45: determining path state probabilities under various path traffic states according to the state transition probabilities and the connection probabilities, wherein the specific formulas are as follows:
wherein ,RPq The probability of the path state in the Q-th path traffic state is equal to or more than 1 and equal to or less than Q, Q is the total number of the path traffic states,initial state data for the n-1 th Markov chain +.>Probability of->From the initial state data +/for the n-1 th Markov chain>Transition to initial State data->State transition probability of>Representing the probability of connection between the n-2 th Markov chain and the n-1 th Markov chain.
Step S5: the method for determining the path travel time distribution under various path traffic states based on the convolution theory specifically comprises the following steps:
step S51: the road section travel time distribution corresponding to each road section is determined, and the specific formula is as follows:
wherein ,TTDn-1 For initial state data ofInitial status data is +.>Under the condition, the travel time distribution formed by the travel time data of the n-1 th road section.
Step S52: based on convolution theory, determining path travel time distribution under various path traffic states according to the path travel time distribution corresponding to each path, wherein the specific formula is as follows:
RTTD q ＝TTD 1 *TTD 2 *…*TTD n ；
wherein RTTD q TTD for the route travel time distribution in the q-th route traffic state n The travel time distribution of the road section corresponding to the nth road section is represented by a convolution formula.
Step S6: determining total path travel time according to path state probability and path travel time distribution under various path traffic states, wherein the specific formula is as follows:
wherein RTTD is total path travel time, RTTD q For the route travel time distribution in the q-th route traffic state, RP q The probability of the path state in the Q-th path traffic state is Q, and the total number of the path traffic states is Q.
Fig. 4 is a schematic diagram of a system for determining path travel time based on a markov chain according to an embodiment of the present invention, and as shown in fig. 4, the present invention further provides a system for determining path travel time based on a markov chain, where the system includes:
the travel time determining module 1 is used for determining travel time corresponding to each road section;
the two-dimensional array determining module 2 is used for forming a plurality of two-dimensional arrays by taking the travel time of two adjacent road sections as a group;
the path traffic state determining module 3 is used for clustering all the two-dimensional arrays based on the Gaussian mixture model to obtain a path traffic state;
a path state probability determining module 4, configured to determine path state probabilities in various path traffic states based on a markov theory;
the path travel time distribution determining module 5 is used for determining path travel time distribution under various path traffic states based on convolution theory;
the total path travel time determining module 6 is configured to determine a total path travel time according to the path state probabilities and the path travel time distributions in various path traffic states.
The various modules are discussed in detail below:
the travel time determining module 1 specifically includes:
the selecting unit is used for selecting a starting point and an ending point;
a road section determining unit for dividing the paths between the starting point and the ending point based on the positions of the microwave detectors to obtain a plurality of road sections;
a history speed detection unit, configured to detect a history speed corresponding to each road section by using each of the microwave detectors;
and the travel time determining unit is used for determining the travel time corresponding to each road section according to the historical speed acquired by each microwave detector.
The path state probability determining module 4 specifically includes:
the data set determining unit is used for arranging the path traffic states obtained by clustering two adjacent road segments in time sequence and equally dividing the path traffic states into an initial state data set and a transfer state data set;
a Markov chain determining unit, configured to construct a Markov model according to the initial state data set and the transition state data set, and obtain a Markov chain;
a state transition probability determining unit configured to determine a state transition probability of each of the markov chains;
a connection probability determining unit for determining a connection probability between the two Markov chains;
and the path state probability determining unit is used for determining path state probabilities under various path traffic states according to the state transition probabilities and the connection probabilities.
The path travel time distribution determining module 5 specifically includes:
the road section travel time distribution determining unit is used for determining the road section travel time distribution corresponding to each road section;
and the path travel time distribution determining unit is used for determining the path travel time distribution under various path traffic states according to the path travel time distribution corresponding to each path based on the convolution theory.
The total path travel time is determined according to the path state probability and the path travel time distribution under various path traffic states, and the specific formula is as follows:
wherein RTTD is total path travel time, RTTD q For the route travel time distribution in the q-th route traffic state, RP q The probability of the path state in the Q-th path traffic state is Q, and the total number of the path traffic states is Q.
The invention comprehensively considers the time-space evolution law of the path travel time, classifies the two-bit array by utilizing the Gaussian mixture model to determine the path traffic state, and based on the correlation between the travel time of the adjacent road sections described by the Markov theory, estimates the total travel time distribution of the path by utilizing the convolution theory, thereby effectively inducing the traveler by accurate total path travel time estimation, relieving the traffic pressure, improving the traffic jam and assisting the urban management.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (2)
1. A method for determining path travel time based on a markov chain, the method comprising:
determining the corresponding travel time of each road section;
taking the travel time of two adjacent road sections as a group to form a plurality of two-dimensional arrays;
clustering all the two-dimensional arrays based on the Gaussian mixture model to obtain a path traffic state;
determining path state probabilities under various path traffic states based on a Markov theory;
determining path travel time distribution under various path traffic states based on a convolution theory;
determining total path travel time according to path state probability and path travel time distribution under various path traffic states;
clustering all two-dimensional arrays based on the Gaussian mixture model to obtain a path traffic state, wherein the method specifically comprises the following steps:
determining an initial cluster number, and acquiring related parameters of the Gaussian mixture model through an EM maximum expected algorithm, wherein the related parameters comprise the mean value and the variance of each sub-Gaussian mixture model; in the mixed Gaussian model, each Gaussian model represents a type of path traffic state; the mean and variance of each Gaussian model represent probability distribution characteristics of travel time in a type of path traffic state;
increasing the clustering number or the path traffic state number, repeatedly determining the initial clustering number, and calculating error term square sum SSE adopting different clustering numbers or path traffic state numbers according to the clustering result;
the SSE value is calculated as follows:
wherein K is the number of clusters, c k Is the clustering center of the kth class, x is a two-dimensional array formed by the travel time of adjacent road sections belonging to the class k;
selecting the clustering number corresponding to the minimum SSE value as the path traffic state;
the method for determining the path state probability under various path traffic states based on the Markov theory comprises the following steps:
the method comprises the steps of arranging path traffic states obtained by clustering two adjacent road segments according to time sequence, and equally dividing the path traffic states into an initial state data set and a transfer state data set;
constructing a Markov model according to the initial state data set and the transition state data set to obtain a Markov chain;
determining the state transition probability of each Markov chain; the specific formula is as follows:
wherein ,from the initial state data +/for the n-1 th Markov chain>Transition to initial State dataState transition probability, X n-1 (t) is the state variable of the (n-1) th Markov chain during period t,/->For the initial state data of the n-1 th Markov chain within the period t, X n-1 (t + 1) is the state variable of the n-1 th markov chain for period t +1,is the initial state data of the (n-1) th Markov chain in the period t+1, K n-1 A traffic state number divided for the n-1 th Markov chain;
determining a connection probability between two Markov chains; the specific formula is as follows:
wherein ,Xn (t) is the state variable of the nth markov chain for period t,for the initial state data of the nth Markov chain within period t, X n+1 (t) is the state variable of the (n+1) th Markov chain during period t,/>For the initial state data of the n+1th Markov chain within the period t +.>For counting the n-th Markov chain initial state data as +.>And the n+1th Markov chain initial state data is +.>Number, K of n N is not less than 1 and not more than N-1 which are the total number of states of the nth Markov chain, wherein N is the total number of the Markov chain;
determining path state probabilities under various path traffic states according to the state transition probabilities and the connection probabilities; the specific formula is as follows:
wherein ,RPq The probability of the path state in the Q-th path traffic state is equal to or more than 1 and equal to or less than Q, Q is the total number of the path traffic states,initial state data for the n-1 th Markov chain +.>Is a function of the probability of (1),from the initial state data +/for the n-1 th Markov chain>Transition to initial State data->State transition probability of>Representing the probability of connection between the n-2 th Markov chain and the n-1 th Markov chain;
the determining the path travel time distribution under various path traffic states based on the convolution theory specifically comprises the following steps:
determining the road section travel time distribution corresponding to each road section; the specific formula is as follows:
wherein ,TTDn-1 For the initial state data within the period tAnd the initial state data is +.>Travel time distribution composed of travel time data of the n-1 th road section under the condition;
based on a convolution theory, determining path travel time distribution under various path traffic states according to the path travel time distribution corresponding to each path; the specific formula is as follows:
RTTD q ＝TTD 1 *TTD 2 *…*TTD n ；
wherein RTTD q TTD for the route travel time distribution in the q-th route traffic state n The travel time distribution of the road section corresponding to the nth road section is represented by a convolution formula;
the total path travel time is determined according to the path state probability and the path travel time distribution under various path traffic states, and the specific formula is as follows:
wherein RTTD is total path travel time, RTTD q For the route travel time distribution in the q-th route traffic state, RP q The probability of the path state in the Q-th path traffic state is Q, and the total number of the path traffic states is Q.
2. A markov chain based path travel time determination system, the system comprising:
the travel time determining module is used for determining travel time corresponding to each road section;
the two-dimensional array determining module is used for forming a plurality of two-dimensional arrays by taking the travel time of two adjacent road sections as a group;
the path traffic state determining module is used for clustering all the two-dimensional arrays based on the Gaussian mixture model to obtain a path traffic state;
the path state probability determining module is used for determining path state probabilities under various path traffic states based on a Markov theory;
the path travel time distribution determining module is used for determining path travel time distribution under various path traffic states based on convolution theory;
the total path travel time determining module is used for determining total path travel time according to path state probability and path travel time distribution under various path traffic states;
clustering all two-dimensional arrays based on the Gaussian mixture model to obtain a path traffic state, wherein the method specifically comprises the following steps:
determining an initial cluster number, and acquiring related parameters of the Gaussian mixture model through an EM maximum expected algorithm, wherein the related parameters comprise the mean value and the variance of each sub-Gaussian mixture model; in the mixed Gaussian model, each Gaussian model represents a type of path traffic state; the mean and variance of each Gaussian model represent probability distribution characteristics of travel time in a type of path traffic state;
increasing the clustering number or the path traffic state number, repeatedly determining the initial clustering number, and calculating error term square sum SSE adopting different clustering numbers or path traffic state numbers according to the clustering result;
the SSE value is calculated as follows:
wherein K is the number of clusters, c k Is the clustering center of the kth class, x is a two-dimensional array formed by the travel time of adjacent road sections belonging to the class k;
selecting the clustering number corresponding to the minimum SSE value as the path traffic state;
the path state probability determining module specifically comprises:
the data set determining unit is used for arranging the path traffic states obtained by clustering two adjacent road segments in time sequence and equally dividing the path traffic states into an initial state data set and a transfer state data set;
a Markov chain determining unit, configured to construct a Markov model according to the initial state data set and the transition state data set, and obtain a Markov chain;
a state transition probability determining unit configured to determine a state transition probability of each of the markov chains; the specific formula is as follows:
wherein ,from the initial state data +/for the n-1 th Markov chain>Transition to initial State dataState transition probability, X n-1 (t) is the state variable of the (n-1) th Markov chain during period t,/->For the initial state data of the n-1 th Markov chain within the period t, X n-1 (t + 1) is the state variable of the n-1 th markov chain for period t +1,is the initial state data of the (n-1) th Markov chain in the period t+1, K n-1 A traffic state number divided for the n-1 th Markov chain;
a connection probability determining unit for determining a connection probability between the two Markov chains; the specific formula is as follows:
wherein ,Xn (t) is the state variable of the nth markov chain for period t,for the beginning of the nth Markov chain within time period tInitial state data, X n+1 (t) is the state variable of the (n+1) th Markov chain during period t,/>For the initial state data of the n+1th Markov chain within the period t +.>For counting the n-th Markov chain initial state data as +.>And the n+1th Markov chain initial state data is +.>Number, K of n N is not less than 1 and not more than N-1 which are the total number of states of the nth Markov chain, wherein N is the total number of the Markov chain;
a path state probability determining unit, configured to determine path state probabilities in various path traffic states according to the state transition probabilities and the connection probabilities; the specific formula is as follows:
wherein ,RPq The probability of the path state in the Q-th path traffic state is equal to or more than 1 and equal to or less than Q, Q is the total number of the path traffic states,initial state data for the n-1 th Markov chain +.>Is a function of the probability of (1),ma Erke as n-1Fuff chain from initial State data->Transition to initial State data->State transition probability of>Representing the probability of connection between the n-2 th Markov chain and the n-1 th Markov chain;
the path travel time distribution determining module specifically comprises:
the road section travel time distribution determining unit is used for determining the road section travel time distribution corresponding to each road section; the specific formula is as follows:
wherein ,TTDn-1 For the initial state data within the period tAnd the initial state data is +.>Travel time distribution composed of travel time data of the n-1 th road section under the condition;
the path travel time distribution determining unit is used for determining path travel time distribution under various path traffic states according to the path travel time distribution corresponding to each path based on a convolution theory; the specific formula is as follows:
RTTD q ＝TTD 1 *TTD 2 *…*TTD n ；
wherein RTTD q TTD for the route travel time distribution in the q-th route traffic state n For the nth road section pairThe corresponding road section travel time distribution is a convolution formula;
the total path travel time is determined according to the path state probability and the path travel time distribution under various path traffic states, and the specific formula is as follows:
wherein RTTD is total path travel time, RTTD q For the route travel time distribution in the q-th route traffic state, RP q The probability of the path state in the Q-th path traffic state is Q, and the total number of the path traffic states is Q.
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