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This paper establishes a mathematical model of the empty load rate to help customers analyze the empty load rate of taxis, thus explaining whether the taxi subsidy policy can improve the actual load rate during peak hours and alleviate the difficulty of taking a taxi(Click “Read the original text” at the end of the article to get the complete code data).
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Analysis ideas
1. Using the data of so many days, first calculate the average daily load rate of this year according to the algorithm, and draw it into a curve
2 Use a smoothing forecast model to calculate the forecast daily average empty load rate for so many days, and the smoothing constants in it are respectively brought into the three values I assumed, and the forecast and actual mean square deviations are calculated, and finally the corresponding one with the smallest mean square deviation is selected. The smoothing constant is what we want.
3. Use the quadratic smoothing index forecasting model to predict the daily average no-load rate from April 25 to May 31 and draw it into a curve (the initial value is the actual daily average no-load rate on April 23, and the smoothing constant is 2 the one you want in
Choose three locations in Nanjing: Drum Tower Park, Sipailou, and Xuanwu Lake Park. Because of the distance and the traffic conditions are similar, measure the taxi demand of these three locations every day from April 1 to April 30. Taxi total.
Data
The data is obtained from the Didi platform:
Analysis method
Take Gulou Park as an example:
Then the empty load rate on April 1st is:
Note: Regardless of the carpooling status, it is assumed that a taxi can only take one order.
By analogy, on April 2, April 3, April 4…April 30, the empty load ratios are:
Using the smoothing exponential formula:
For example: the forecasted empty load rate on April 1st is k, then the forecasted empty load rate on April 2nd
We use the algorithm of quadratic smoothing index prediction to predict the short-term empty load rate which is not affected by seasonal factors.
Quadratic Smoothing Exponential Forecasting Model: Formula:
Find the empty load ratio
kongzailv=function(datat){
sum(as.numeric(datat[,2]))/sum(as.numeric(datat[,1]))
}
Location: Gulou Park
for(i in 1:27){
datat=data[((i-1)*4 + 1):(i*4),3:4]
kongzailvdata[i]=kongzailv(datat)
Set the alpha parameter to 0.3
alpha <- 0.3
See model parameters
Calculate the mean square error value
RMSE1=mean((model$fitted-model$x)^2)
Set the alpha parameter to 0.5
alpha <- 0.5
Set the alpha parameter to 0.7
Find the smallest RMSE value
min(RMSE1,RMSE2,RMSE3) [1] 0.2712489
Therefore, the alpha is 0.5, and then the algorithm of quadratic smoothing index prediction is used to predict the short-term empty load rate which is not affected by seasonal factors.
See model parameters
Forecast value
Predicted image
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Spatial and temporal visualization analysis of taxi driving trajectory data in Hangzhou
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District: Four Pailou
which.min(c(RMSE1,RMSE2,RMSE3)) ## [1] 3 ###From the results, it can be seen that when alphaha is 0.7, the minimum RMSE value of the channel
Therefore, the alpha is 0.7, and then the algorithm of quadratic smoothing index prediction is used to predict the short-term no-load rate that is not affected by seasonal factors.
See model parameters
Location: Xuanwu Lake Park
############################### Find the minimum RMSE value min(RMSE1,RMSE2,RMSE3) ## [1] 0.01964692 which.min(c(RMSE1,RMSE2,RMSE3)) ## [1] 1 ###From the results, it can be seen that when alphaha is 0.3, the minimum RMSE value of the channel
See model parameters
Click “Read the original text” at the end of the article
Get the full text and complete code data materials.
This article is selected from “R Language Exponential Smoothing Forecasting Method to Analyze the Feasibility of Subsidy Policies for No-load Rate of Nanjing Taxi Hailing Software”.
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