Research on Dwell Point Strategy of Compact Intelligent Parking System under Dynamic Demand

“Parking difficulty” seriously hinders urban traffic development, Therefore, itis of great theoretical and practical value to improve the operation efficiency, which study the compact intelligent parking system with high land utilization rate. Considering decentralized and random vehicle access demands, and their impact on the dwell point strategy of parking system, the selection model of dwell point strategy under dynamic demand is built. Building the operation model of compact intelligent parking system, and analysing the influence of environmental factors on the system demand, then the data set is built. Based on random forest, the selection model of dwell point strategy under dynamic demand is built, and the importance of relevant influencing factors is sorted. Finally, the research effect is verified by example. The result shows that the research can effectively improve the operation efficiency and user satisfaction, and the research has a wider scope and application value.


Introduction
In recent years, the number of cars retained has increased rapidly, and parking is increasingly difficult.To efficiently use the parking resources, and improve the access efficiency of the parking system has become an urgent problem.To develop the compact intelligent parking system, which has become an effective way to alleviate the problem of parking difficulties.Compact intelligent parking system access cars over storage lanes by straddle carrier, and completes the vertical movement by lift, which reduce the required laneway space and the time required to move to free up space in mechanical stereo garage, and effectively improves land utilization, However, there are still problems such as inefficient access and long waiting time for users.To solve such problems, scholars study the storage strategy [1], resource allocation [2], system devices operation policy [3], dwell point strategy and other related issues.Meneghetti A [4] indicated that dwell point is a location, where a handling device is moved in idle time to wait for the next task, rational dwell point can shorten the operation time of the next task probably.For warehousing systems, scholars [5] optimized dwell point for idle device by Tchebychev expected distance function.To optimize the dwell point of AVS/RS system, building a multi-class semi-open queuing network model with class switching [6].For the transporter in the stereo garage, designing dwell point for load balancing by artificial bee colony algorithm [7].For the dynamic dwell point strategy, scholars [8] built mathematical models of each working status, when the in-out storage demands of the stereoscopic warehouse were known.For dynamic adjustment of dwell point strategy in AVS/RS system, scholars built the decision tree model [9] and built interactive dynamic impact diagrams (I-DIDs) [10].For planar mobile stereo garage, scholar [11] revealed the internal law of accessing data, and optimize dwell point strategy by combining access arrival status and parking space allocation.In summary, the dwell point is related to the access demand of the next task.Compare with warehousing system, the parking demands are uncertain and randomly distributed.Therefore, it is necessary to study the dwell point strategy with its demand characteristics.Based on previous research, the research considers the impact of external environment on dynamic demand, and based on random forest, a selection model of dwell point strategy under dynamic demand is built, the impact of external environmental factors on dwell point strategy is sorted, in this way, the selection of dwell point strategy is discussed in depth.The rest of paper is organized as follows.Section 2 introduces the proposed problem, and Section 3 describes the design of the model.Finally, results and conclusions are given in Section 4 and Section 5.

Problem description
A schematic of compact intelligent parking system is shown in Figure 1.The lift is located at the input and output (I/O) point of each tier.The retrieval and storage process of the system is completely opposite.The operation steps of the retrieval processes as follows: Step1: User arrives, the car requests and waits for a straddle carrier.
Step2: The straddle carrier slides from the dwell point to the target position.
Step3: The straddle carrier loads the car, slides to tier I/O point, then unloads the car.
Step4: The car requests and waits for a lift.Step5: The lift travels from the dwell point to target tier, loads the car and move to system I/O point.
Step6: The lift unloads the car.The car leaves the system.A complete storage or retrieval task includes straddle carrier and lift operation time ( v T and l T ) for Step3 and 5, and waiting time as ( v W and l W ) for Step4 and 6.
Equations ( 1) and ( 2) are the operation time and waiting time under time period t, Equation (3) is the total time spent on a single operation.
In the system, dwell point refers to the position of the lift and straddle carrier, when task is completed or idle.The main process of device operation is related to dwell point, the total operation time spent is significantly different under different dwell point strategies.According to the dynamic demand under multi-environmental factors, the optimal dwell point strategy is selected, which can effectively reduce the device empty operation time, and improve system efficiency and device utilization.

Model building
The selection of the optimal dwell point strategy can be regarded as a pattern classification problem in essence, that is, to determine the dwell point strategy under dynamic demand of the time period.Multiple factors affect dynamic demand, the demand acts on the operation model of the compact intelligent parking system, thus affecting the selection of the optimal dwell point strategy.Therefore, based on the random forest model, the selection model of optimal dwell point strategy under dynamic demand can be built.The research analyzes the following three dwell point strategies: Return to I/O point: dwell point is at the corresponding I/O point.Return to the middle: dwell point is at the middle point of each corresponding channel.
In-place reset: dwell point is at the task completion point.

Random Forest
Random Forest (RF) is an ensemble learning algorithm for regression prediction and classification, which composed of decision trees, it has been widely used in traffic behavior research [12], traffic .the working principle of RF Each decision tree in RF is learned by random sampling with replacement, and multi-decision tree combination can get more accurate and stable results.Compared to general mathematical model, RF is not easy to overfit, good at dealing with multi -dimensional data, can mine the nonlinear relationship between features, relatively simple to implement, and has been proved applicable to small data sets.In addition, RF can quantify the relative importance of characteristic variables in the results, which increase the interpretability of the model.Equation ( 4) is importance score ( ) k VIM X of the independent variable ; The model constructs tree n decision trees, i E is the calibration error of the decision tree , ik E is the calibration error of the decision tree  after randomly replaced of the independent variable  ( ) The model will build by the classification principle of RF, and regard each dwell point strategy as different categories, then to complete the selection of the optimal dwell point strategy under dynamic demand.According to the voting results of each decision tree, the prediction results are obtained.

Operation model of compact intelligent parking system
Considering user satisfaction and operational efficiency, taking operation time and waiting time as system performance evaluation indicators, the operation time and queuing network model of compact intelligent parking system are built.
3.2.1.Operation time Model.Equation ( 5) is the operation time of the straddle carrier and lift, which consider the acceleration and deceleration process. is the transportation distance.When retrieve a car, the  of the straddle carrier and the lift from the dwell point to the target car is  *  and  * ℎ,  and  is the parking position and tier of the car,  and ℎ is the tier height and width of parking position.And the  and  is the device speed and acceleration.

Queuing Network Model.
To evaluate user satisfaction, a queue network will be built, and get user waiting time as Equation (2).Taking retrieval processes as example, as shown in Figure 3, when retrieval task arrives, the vehicle waits for system service, requests straddle carrier to be assigned (Step 2), and to complete the horizontal task (Step 3), then requests lift to be assigned (Step 4), and to complete the vertical task (Step 5), Finally, the car leaves the system and the task is completed.Since the queuing network contains some service devices, which obeying the general distribution, For avoiding excessive computation, the decomposition method [14] will be used to solve the non-product queuing network.Equation ( 6).is the average waiting time gotten by the decomposition method.
It is the sum of the current average remaining service time 0i W and the service time i Bi QT  of the task ahead of the queue.And 0 P is the device utilization rate.The Front queue length ( ) Ai c is gotten by multiple iterations of synthesis, flow, and decomposition from the initial value is 1 , it marks the end When 22 ,, () .Equation ( 7)-( 9) is the synthesis, flow and decomposition process.
Here the operation model of compact intelligent parking system is completed, gotten the evaluation performance by running the model.With the shortest operation time and queuing time, the objective function for optimal dwell point strategy selection is Equation (11).

The selection model of dwell point strategy under dynamic demand
Analysing the access vehicle dynamic demand of the compact intelligent parking system, considering the influence of its external environmental factors, and combining the operation model to establish a model data set.Based on the random forest, building the selection model of optimal dwell point strategy under dynamic demand.Then, making further accurate quantitative analysis and judgment on the model, so as to realize the reliable and fast selection of dwell point strategy under dynamic demand.

Dynamic Demand Analysis.
Comparing with the road traffic flow, the parking system flow is not dense, so take 1 h as the research interval, that is, the research object is the access vehicle data from 7 to 22 every 1 hour, a total of 15 time periods in weekdays.Parking system access car demand is affected by external environmental factors, and cyclical fluctuations over time.Therefore, the analysis of the influencing factors of dynamic demand is as follows: Time 1 x : The most important factor affecting access vehicle demand.Demands shows obvious time periodicity, so divided the time period is into five access modes: retrieval peak period, retrieval multiple periods, access balance period, storage multiple period and storage peak period.Traffic density 2 x : The car density of nearby main roads, reflecting likelihood of demand generation, is assigned by Gaode map.Green indicates unblocked, yellow indicates slow driving, red indicates congestion, dark red indicates very congestion.Weather 3 x : Weather affects the purpose and way people travel, thus affecting the demand for access to cars.The weather is assigned by the short-term weather forecast, Divided into sunny or cloudy, cloudy, light rain, moderate rain and rainstorm; Queuing situation 4 x / 5 x : Queue length affects the willingness to access.users are often impatient to leave due to excessive queuing.It divided into storage 4 x and retrieval 5 x , which is assigned to the actual queue length.According to research, when the interval between two consecutive cars is less than 45 seconds, it can be considered to have experienced queuing.The access car demand changes dynamically, which is reflected in the change of the access proportion and arrival rate.Both affect the operation time and the waiting time, thus affecting the selection of the optimal dwell point strategy in this period of time., , , , X x x x x x = , The output y is the optimal one of the three strategies studied under the demand.
2) Data balancing: If the proportion of categorical dependent variables is imbalanced in RF, he conclusion is often biased.So, the data will be analysed after pre-processing for balance.If there is unbalanced data of three dwell point strategies, the SMOTE algorithm, a few oversampling techniques, will be used.SMOTE algorithm is a common method to deal with unbalanced data.Its basic idea is to analyze and simulate a few categories of samples, and add artificially simulated new samples to the data set, so that the categories in the original data are no longer unbalanced.The algorithm sets the sampling ratio according to the unbalanced ratio, selects new samples from the nearest, and constructs new minority samples by random linear interpolation.
3) Parameter adjustment: For better selecting, RF parameters are adjusted by K-fold cross validation results, which randomly divided the training set into K portions, one portion was randomly taken out as the validation set, and the remaining was the training set.And using the grid search method, to gradually shorten the step length and search range to adjust the parameter values, until the optimal value is approached.4) Model analysis: Model analysis: Regarding the optimal dwell point strategy gotten under dynamic demand as hybrid strategy.For measuring selection effect of hybrid strategy, three quantitative indicators are recorded by Recall as R, Precision as P and F1 value.Recall rate: It refers to is the proportion of predicted positive samples to actual positive samples, the performance is better when the recall rate is greater.Precision rate: It refers to the proportion of actual positive samples to predicted positive samples, the performance is better when the precision rate is greater.F1 value: It refers to harmonic average of precision and recall rate.The precision rate and recall rate are mutually influential, so the F1 value can be used to comprehensively reflect the classification effect of the model.The calculation equation is

Example data description
Taken a parking system in Wuhan as an example, 255 valid data were collected and a data set was built.Processed the data set, eliminated a useless data, and then did descriptive statistics on the data set, which found that there is sample imbalance, so the SMOTE algorithm is used for oversampling.
The data set characteristics are shown in Table 1.

Analysis of model results
Based on RF, the selection model of the optimal dwell point strategy under dynamic demand is built.75% of the data in the data set is used for model training, and 25% is used for model testing.Ten-fold cross validation is used to improve the classification accuracy and generalization ability.The number of decision trees tree n is 100, because the model accuracy does not increase significantly as the tree n increases.And optimize remaining parameters, the maximum depth of the decision tree is set to 50, and The rest is the default, the model can achieve better prediction results.

Model result.
From the selection model of the optimal dwell point strategy under dynamic demand, the classification results of the test set can be gotten.For analysis, the classification results are reordered as shown in Figure 5.The model effect is evaluated by the three indicators described in Section 3.2.2, and the results are shown in Table 2.As shown in Figure 5 and Table 2, the model after debugging has a good effect on the training set, and the F1 value on the test set is also higher than 80%.Most of the strategy values of the decision results fall on the actual dwell point strategy scatter, which shows that the selection model of the optimal dwell point strategy under dynamic demand has been well applied.The main reasons affecting the accuracy are as follows: For selecting inaccurate periods, most of them fall on the dwell point strategy which is not much different from its operation performance.It suggested that the judgment ability of the critical point still needs to be improved.The collected sample data is limited, and few data of different environmental factor combinations, resulting in insufficient model training and still need to be improved.
The selection of the dwell point strategy affected by the dynamic demand of the access car, which is not only related to environmental factors, but also to some other unmeasurable human factors.So, it still needs to be improved.

Analysis of factor importance.
The importance ordering of factors affecting optimal dwell point strategy selection based on RF are shown in Table 3.
As shown in Table 3, the selection of the optimal dwell point strategy is relatively important to time.That is, the access car demand is mainly affected by time, and fluctuations due to multiple environmental factors.Predicting the arrival rate by fitting the long-term time data, and reasonably adjusting of the dwell point strategy, which can also have a certain improve.Traffic density also has a certain effect on the dwell point strategy.The temporary change of traffic density can also temporarily change the access car demand, thus affecting the selection of the optimal dwell point strategy.The next is the effect of storage and retrieval queue, which is probably indicates the trend of access car demand and also effect on the willingness of users.The weather has little effect on the dwell point strategy, indicating that the parking system studied has a relatively fixed demand.The importance ordering of factors is related to the environment of the parking system.The demand of some parking systems may be more random, which is not greatly affected by time, but is greatly affected by other environmental factors, some may be greatly influenced by human factors.By building the operation model of the system researched, and investigating the influencing factors of dynamic demand, the selection model of the optimal dwell point strategy under the dynamic demand can be built based on RF, which can solve the selection problem of the optimal dwell point strategy under various environmental conditions.The method has a wider scope of application and stronger universality.

Contrast experiment
For further exploring the effectiveness of dwell point strategy research under dynamic demand, a contrast experiment will be constructed based on previous studies.T T W =+ .Comparing the single expected time spent and user expected waiting time of the day, and regarding the user expected waiting time as user satisfaction.

Experimental comparison between dynamic and non-dynamic demand.
Without considering the dynamic demand, the parking system mostly operates with a single dwell point strategy, so the experiment compared the hybrid strategy with the single dwell point strategy.Gotten the performance improvement of the hybrid strategy over each single one, which is the time saving rate and the satisfaction improvement rate respectively.The results are shown in Table 4.  4, for the compact intelligent parking system, the hybrid strategy selected has the best performance under dynamic demand, it combines the optimal operation of single dwell point strategy in each time period, and effectively saves the system operation time and user waiting time.

Experimental comparison of different processing methods for dynamic demand.
For selecting the optimal dwell point strategy, in previous research, some are qualitative analysis, and some perform demand forecasting by fitting time series data.Therefore, a comparative experiment is constructed.Experiment 1 selected the optimal dwell point strategy by qualitative analysis.The morning peak is 7:00-10:00, selecting the strategy of return to I/O point, and the evening peak is 17:00-21:00, selecting the strategy of return to the middle, and the rest selecting the in-place reset strategy.Experiment 2 selected the optimal dwell point strategy by demand forecast.Built the dynamic based on fitting the time series data by ARIMA, which without multiple environmental factors.Performance improvement refers to hybrid strategy experiment versus the experiment, the results are shown in Table 5.As shown in Table 5, Selecting the optimal dwell point strategy by qualitative analysis, which is lack of handling of environmental changes.Selecting by the model of optimal dwell point strategy under dynamic demand, it can handle environmental changes lead to changes in demand, make the selection more in line with the actual demand, and the performance improvement is more significant.In terms of selecting optimal dwell point strategy by demand forecast with the time series data only, research that takes into account the dynamic demand under environmental impact effectively improves system performance.And due to some parking systems are less affected by time periodicity, previous research has fewer applicable scenarios, therefore, the model has a wider range of adaptation.The amount of data required for the model is not large, and the model can be continuously updated by the updating data, so the timeliness is stronger.

Conclusion
Based on the compact intelligent parking system with high land utilization rate, the research considers the dynamic demand under environmental factors, and selects the optimal dwell point strategy under dynamic demand.By combining the operation model and the analysis of dynamic demand, the selection model of the optimal dwell point strategy under dynamic demand is built based on random forest, and the influence of various factors effect on the model is analysed.The research result shows that it makes up for the neglect of environmental impact factors in previous studies, and effectively solves the problems of low operation efficiency and long user waiting time in the current system.Although the research only takes a single compact intelligent parking system as an example, the model is suitable for many different scenarios.By building the operation model of the system researched, and analysing the environmental impact factors of dynamic demand, the selection model of the optimal dwell point strategy under the dynamic demand can be built based on RF, which can solve the selection problem of the optimal dwell point strategy under various environmental conditions.The research provides a scientific basis for the operation and management under actual demand, and effectively solve the parking problem to a certain extent.However, the research only studies a single strategy, the next step will be to combine other strategies such as storage strategies, and to collect more data to build a more accurate model.

Figure 1 .
Figure 1.Compact Intelligent Parking SystemFigure2. the working principle of RF Each decision tree in RF is learned by random sampling with replacement, and multi-decision tree combination can get more accurate and stable results.Compared to general mathematical model, RF is not easy to overfit, good at dealing with multi -dimensional data, can mine the nonlinear relationship between features, relatively simple to implement, and has been proved applicable to small data sets.In addition, RF can quantify the relative importance of characteristic variables in the results, which increase the interpretability of the model.Equation (4) is importance score

Figure 3 .
Figure 3. Queuing network of retrieval taskSince the queuing network contains some service devices, which obeying the general distribution, For avoiding excessive computation, the decomposition method[14] will be used to solve the non-product queuing network.Equation (6).is the average waiting time gotten by the decomposition method. And

3. 3 . 2
Model Building.The entire model building flow is shown in Figure 4. Considering the influence of multiple environmental factors on dynamic demand, and the selection model of the optimal dwell point strategy under dynamic demand is built.

Figure 4 .
Figure 4. Model building flow 1) Dataset establishment: The data of each time period is formed by the assignment of dynamic demand influencing factors, and the optimal dwell point strategy, which is gotten by Equation (11), thus forming a data set.That is, the data input is   1 2 3 4 5

Figure 5 .
Figure 5. Selection Result of Dwell Point Strategy under Dynamic Demand after Sorting

Table 1 .
Sample Data Characteristics

Table 2 .
Statistical results of evaluation indicators

Table 3 .
Importance ranking of factors Taken the experiment data from 7 to 22 every 1 hour, a total of a weekday as example, Ran operation model by actual arrival rate of each time period, which can get the storage and retrieval operation time and queuing time

Table 4 .
Performance of each dwell point strategies ( unit: second )

Table 5 .
Comparison of experimental performance (unit: second)