This research examines the problem of short-term forecasting of traffic flows in conditions of incomplete information. For the task of forecasting, a mathematical model has been compiled, which makes it possible to compare the main characteristics of the traffic flow with the value of the forecast - the speed of the flow. Within the framework of this work, various forecasting algorithms have been investigated, which make it possible to analyze the influence of the number of recorded observations and similar records, as well as allowing modifications to increase the forecast accuracy. Also, a data recovery approach has been developed to eliminate noisy and missing data. Experiments of short-term forecasting were carried out on an open dataset from Yandex and confirmed the importance of the stage of preprocessing and analysis of the effectiveness of recovery algorithms. After applying the proposed approach to data processing and recovery, the predicted value turned out to be more accurate on average by 2 km / h. The results of the study showed that the combined model with weighing showed a more accurate result compared to simple models, the average error was 9.81 km / h. Among the possible directions for further research, one can single out the search for several combined methods that have equivalent algorithms using neural networks.
traffic congestions in large cities increases every year, resulting in low efficiency of transport networks and wasted time, wasted fuel, and excessive air pollution. Also, intelligent traffic management is a key issue, which is also an important tool to guide scientific decision making in traffic management. Traffic forecasting is a challenging task in intelligent traffic management.
Because traffic data has sharp nonlinearities resulting from transitions from free flow to failure, and then to congested traffic, predicting traffic flow is challenging due to rapidly changing traffic conditions. Also, processing the data before building the model can significantly affect the result of the prediction algorithm. This is due to many factors, such as speed noise, missed travel times, traffic accidents (data outliers), etc. Such phenomena affect the accuracy of the constructed forecast. In this regard, the purpose of this work is to develop a data recovery algorithm for solving the problem of short-term forecasting of traffic flow.
congestion configurations in networks (spatial congestion configurations of the entire network) is considered. As part of the development of a unified data mining system, the authors presented a description of the most typical time patterns of network traffic status and a long-term forecast of large-scale traffic dynamics. The experiments have shown the effectiveness of clustering and forecasting based on the results of tensor factorization.
the study [4]. The experiments have shown that the performance of the speed prediction model increases when the missing values are taken into account and restored in the multi-view approach.
algorithm. However, traffic congestion modeling is based on the example of a specific road, based on its spatial and temporal data, and requires generalization to large-scale networks.
The transport network is represented as a graph = ( , ), ∈ representing road segments and a set of vertexes
representing intersections. The following values can be used as the predicted traffic flows value on the edges of the road graph: flow density, average time of vehicle passing along the road section. In this paper, the average speed of a vehicle passing a road section will be used for conducting a numerical experiment. Let’s assume that data processing has been completed where is number of observations on the -th edge; are observed time points; ∈ + is speed at a time
. Taking into account the entered designations, a formal statement of the problem of
getting a forecast for a given parameter of the transport network’s traffic flows: Using the road graph
= ( , ) and current data on the traffic flows value in the form (
A prediction model based on information about nearest neighbors using = , = ( (
), ), ( ∗ + ) = ( ) { ( ∗ + ) ∈ +
, ∀ ∗ ≥
N i=1 where is the amount of traffic flow on the road at time . Then in matrix form the dependency
When building a model for predicting traffic flows, appropriate databases are needed, which often have data gaps and noise in practice. The missing information can be filled in when performing local forecasting for the road network graph in sections with gaps. The idea is to use information about traffic flow on neighboring edges to predict this value based on similar incidents in the past. The function of restoring the value of the transport flow, depending on the values on neighboring edges, can be represented as: vd,t = (vdr1,t , vdr2,t , . . . , vdrN,t ),
r where , is speed on the road in time of the day ; is some recovery function. We will use linear regression as a function. We will look for the type of function as a linear dependence on the speeds on adjacent roads: (vdr1,t , vdr2,t , . . . , vdrN,t )= b1vdr1,t + b2vdr2,t + . . . + bN vdrN,t + ε = X N i = ∑ biv di,t + ε, r where are linear regression coefficients; ε is the approximation error function .
The goal is to find the coefficients . These coefficients can be found using the least squares
method. Let there are a history of observing the road, as well as a vector of points
=
( 1, 2, . . . , )where indicates a point in time in the past. Vector of transport flow values at time
points ti on edge for which the forecast will be built we denote by . For each edge there is a certain
number of adjacent edges . Let there are a matrix of the form:
(
+ , looks like this:
= (ε1, . . ., ε ).
deviations is minimal:
where is vector of linear regression coefficients = ( 1, . . . , ); is the vector of forecast errors
It is necessary to select the coefficients = ( 1, . . . , ), so that the sum of the squares of
(
where ( )is linear combination of traffic flow values and coefficient vector at a time .
To find the coefficient vector we transform the matrix form (
= 1, 2, . . . , for which all values of traffic flows values on adjacent edges are known at given time points;
2. trecovery occurs at those points where the traffic flows value is unknown at the time +1 but on neighboring edges all traffic flows values at the predicted time are present in the observation
(
( 1( 1)+ 2( 2)+ ⋯ + ( )).
For unequal models, we will take into account their coefficients. In this method, the ensemble of models is defined as the weighted sum of
weak models (combined model II): = 1 1( )+ 2 2( )+ ⋯ + ( ). where is coefficient with which the weak model is included in the ensemble.
When predicting the amount of traffic flows on the road at some point in time t we can use where , is speed on the road at time of day . observations of this section. Then the base model I is represented in following form: , =
( −1, − , … , −1, −1, … , −1, +1, … , −1, + , −2, − , … ),
To take into account the situation with a small number of observations we will take the average value of the traffic flows value for all observations on the transport network and shift it in its direction. Then the base model II is represented as follows: , = ∗ + + ∗ ,
(
alue are traffic flows values obtained from the formula (
To account for differences in traffic flow characteristics, it is possible take into account observations that are most similar to the current behavior of the traffic flows at a given time. For this purpose we enter the similarity metric expressed by the formula: ( , )= ( 1 | | ∑
∑ ∈ ∈ | , − | | , |) −1 , known , and , . where , is speed on the road at time of day ; - day number in the history of observations; - many roads in the transport network; is a set of moments in time for which both dimensions are
= ( 1, 2, . . . , ) consisting of weak models. Then the constructed model for predicting traffic flows will have the form (combined model I):
To find linear regression coefficients 1, 2, . . . , predictions 1, 2, . . . , , are made for one of the previous days, ∗ is the forecast vector of the combined model. Then the Least Absolute
consists of two parts: a description of the city’s street network and observation data for these streets. The observations cover 31 days for the Moscow road graph. Intersections in Moscow correspond to the vertices of the graph, and street segments correspond to arcs (a two-way street corresponds to two multidirectional arcs). of the road network graph:
The metric of the average deviation of the forecast values from the observed measurements can serve as an estimation measure (15).
1 =
∑ | ∗ − ̂| , where is total number of plots; ̂ is predicted speed on the section; ∗ is observed speed on the site.
Based on the results obtained, the following conclusions can be made: 1. The approach with data recovery using information about the nearest neighbors allowed increasing the number of observations, the number of data increased by about 1.5 times. Forecasts based on the new data were more accurate.
2. The basic model III makes a significant contribution to the combined model. In this case, the coefficient 3 = 0, 92. The other models account for only 0,08.
the best model (combined model II) gives an average error of 9.81 km/h, i.e. the improvement is on average 3 km/h.
information, the purpose of which is to develop an adaptive mathematical model for predicting traffic flows with the required accuracy. A comparative analysis and selection of the optimal TP model are carried out, as well as algorithms for predicting the flow rate of the transport network are studied.
processing and clearing raw data is an important step before predicting traffic flow. So according to the processed data, the results were more accurate by an average of 2.3 km/h.