Method for measuring medical emergency accessibility based on two-way optimization model of transport capacity and demand

Abstract

The application discloses a medical emergency accessibility measurement method based on a transport capacity-demand bidirectional optimization model, and belongs to the technical field of the intersection of urban public health management and geographic information systems. The method realizes the spatial accessibility measurement of pre-hospital emergency resources by constructing the composite transport capacity of emergency stations, calculating the potential demand competition intensity, determining the comprehensive attraction and selection probability of the emergency stations to the demand points, and performing simulated demand distribution and spatial accessibility calculation. The application integrates the historical service capacity of the emergency stations, vehicle configuration characteristics and local potential demand competition intensity into a unified measurement framework, which helps to reduce the overestimation risk of the traditional accessibility model to the emergency service capacity of high demand areas, and improves the objectivity and accuracy of the spatial configuration evaluation of emergency resources.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of urban public health management, geographic information systems (GIS), and spatial accessibility algorithms. More specifically, this invention relates to a method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model. Background Technology

[0002] With the advancement of smart city construction and the increasing demand for modernization of public health systems, precise spatial planning of medical resources has become a core element in improving emergency response capabilities. Currently, the mainstream technologies for assessing the spatial accessibility of medical resources are mostly based on gravity models, such as the two-step search-and-find (2SFCA) method and its derivative models (Liu Haopeng et al., Accessibility Evaluation of Village-level Medical Services in Mountainous and Suburban Areas of Beijing - A Survey-Based 2SFCA Study, *Chinese Journal of Health Policy Research*, July 2024, Vol. 17, No. 7, pp. 65-74; Wang Can et al., Spatial Layout and Accessibility Research of Medical Facilities Based on Improved Ga2SFCA Algorithm - A Case Study of Xiamen City, *Architecture and Culture*, 2022, No. 6, pp. 101-104). However, these methods have significant limitations. Technical challenges: First, existing models generally suffer from the "illusion of unlimited capacity," failing to consider the "queuing and congestion" effect caused by high-density populations in certain areas, leading to a serious overestimation of the emergency response capacity of large hospitals in central urban areas. Second, there is a lack of micro-physical granular data on the supply side, often using historical total order volume or macro-level bed capacity to replace the actual hardware capacity (such as the number of deduplicated vehicle identifications), failing to reflect the true physical throughput limit of the system. Finally, spatial impedance calculations are too static, making it difficult to couple with actual dynamic traffic micro-circulation and urban-rural hierarchical response differences, resulting in a significant deviation between optimization results and the actual supply and demand perception. Based on the technical classification standards of the review literature (Tao Zhuolin, Cheng Yang, Research progress on two-step moving search method and its extended forms, Progress in Geography, Vol. 35, No. 5, 2016, pp. 589-599), the extensions and improvements of traditional 2SFCA are usually limited to single categories such as 'distance attenuation improvement,' 'search radius improvement,' 'supply and demand competition consideration improvement,' or 'travel mode improvement.'

[0003] While some existing models (such as the RAAM rational agent model) mention the broad concept of "crowding penalty," their mathematical form, mechanism of action, and application scenarios differ fundamentally from those of this invention. The RAAM model relies on the iterative selection of utility maximization by micro-discrete agents, and its penalty term requires multiple rounds of computer loops to approximate convergence. Under a city-level OD matrix of millions, computation is time-consuming and carries the risk of non-convergence. Summary of the Invention

[0004] This invention provides a method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model. It addresses the prominent problems of traditional spatial accessibility models in assessing emergency medical resources, such as overestimating the radiation capacity of central hospitals, lacking real physical hardware constraints, and being detached from dynamic traffic scenarios, through bidirectional collaborative optimization of supply-side composite capacity construction and demand-side queuing dimensionality reduction penalty factor generation. By constructing a capacity-demand bidirectional optimization mechanism (CDO-2SFCA model), on the supply side, it obtains the historical effective dispatch records and vehicle configuration characteristics of each emergency station, introduces weight coefficients of vehicle configuration characteristics to construct composite capacity, and applies diminishing marginal returns constraints to the capacity contribution generated by increasing the number of vehicles. On the demand side, based on a Gaussian time decay function, it weights and summarizes the population of each demand point within a heterogeneous response time threshold range to obtain the potential demand competition intensity of emergency stations, and constructs corresponding demand competition correction factors. This method incorporates the combined transport capacity of emergency medical stations and the intensity of competition for potential demand into a comprehensive attractiveness calculation. Through step-by-step calculations of selection probability, simulated demand, and station supply-demand ratio, it obtains the spatial accessibility results of each demand point under different traffic periods, thereby reducing the bias caused by evaluating emergency medical service capabilities solely based on station size or static distance. This invention can provide quantitative evidence for identifying weak areas in emergency medical services, evaluating the service capabilities of emergency medical stations, and analyzing the spatial allocation of emergency vehicles and station resources, contributing to improving the objectivity and rationality of pre-hospital emergency medical resource allocation assessment.

[0005] To achieve these objectives and other advantages according to the present invention, a method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model is provided, comprising the following steps:

[0006] S1. Construction of Supply-Side Composite Transportation Capacity: Obtaining historical valid dispatch record data W for each emergency medical station j. history,j Number of vehicles with duplicate identification marks W amb,j The combined transport capacity of station j is calculated according to the following formula:

[0007] Among them, Supply_Base j W represents the combined transport capacity of emergency medical station j; history,j This indicates the number of valid vehicle dispatch records at this station in history; W amb,j This represents the number of duplicate vehicle identifiers extracted from the station; α is the weighting coefficient of the vehicle configuration features, with a value of 0 to 1, used to implement diminishing marginal benefit constraints on the gravitational contribution of the number of duplicate vehicle identifiers.

[0008] S2. Generation of Demand-Side Queuing Dimensionality Reduction Penalty Factor: For each emergency station j, based on the Gaussian distance decay function G(t)... kj , T j ), at the heterogeneity response time threshold Tj Within the range, the population Pop for all demand points k. k By performing distance-weighted summation, we can obtain the potential demand competition intensity D of site j. j :

[0009] Among them, D j Pop represents the weighted sum of high-frequency potential competitors around site j. k t represents the size of the resident population at demand point k; kj T represents the dynamic travel time from the demand point to the station. j The response time threshold for the administrative level to which emergency medical station j belongs; Gaussian distance decay function G(t) kj , T j ) is defined as: Where e is the natural constant; if and only if t kj ≤T j If it takes effect on time, otherwise it is set to 0;

[0010] S3. Two-way smoothing comprehensive attractiveness calculation: For any demand point i and any emergency station j, calculate the comprehensive attractiveness of station j to demand point i according to the following formula. ij : Among them, attractiveness ij This represents the true overall attractiveness of emergency medical station j to demand point i; the numerator represents composite transportation capacity. Let λ be the queuing dimension reduction penalty factor for emergency station j; λ is the spatial impedance friction coefficient, which is a constant greater than 0.

[0011] S4. Supply and Demand Allocation and Spatial Accessibility Output: Based on the two-step mobile search framework, the output is based on the comprehensive attractiveness value between all demand points and all emergency response stations. ij It performs supply probability allocation and demand simulation flow, and outputs the spatial accessibility measurement results of each demand point.

[0012] Preferably, before step S1, a data cleaning and entity mapping step is included, specifically:

[0013] The system acquires pre-hospital emergency care service record data, standardizes the emergency care station names in the service records based on a preset station name mapping relationship, and removes duplicate vehicle records corresponding to each emergency care station based on vehicle identification. Based on the processed pre-hospital emergency care service records, the system determines the historical dispatch volume and the number of deduplicated vehicle identifications for each emergency care station, and associates the historical dispatch volume and the number of deduplicated vehicle identifications with the emergency care station spatial element layer to construct composite transportation capacity.

[0014] Preferably, the weighting coefficient α of the vehicle configuration features and the spatial impedance friction coefficient λ are determined through a two-parameter global grid optimization. The two-parameter global grid optimization includes: traversing within a preset value range of α [0.0, 1.0] with a preset step size (e.g., 0.1), and traversing within a preset value range of λ [0.1, 1.5] with a second step size, where the values ​​include 0.1, 0.3, 0.5, 0.8, 1.0, 1.2, and 1.5, forming multiple sets of parameter combinations;

[0015] For each set of parameter combinations, execute steps S1 to S4 to calculate the simulated emergency demand flow X allocated to each emergency station. i The effective pre-hospital emergency care workload Y at each emergency medical station i The Pearson correlation coefficient r between the simulated and actual values, and the root mean square error (RMSE) between the simulated and actual values, are given by the following formula:

[0016]

[0017] The root mean square error (RMSE) is calculated using the following formula:

[0018]

[0019] Maximizing the Pearson correlation coefficient r is the primary objective function, and minimizing the root mean square error (RMSE) is the auxiliary verification index. The optimal parameter combination is selected as the global optimal parameter for the final spatial accessibility measure. The global optimal parameter combination is α=0.5 and λ=0.5.

[0020] Preferably, in step S2, the dynamic passage time t kj By capturing the basic passage time t based on the map application programming interface amap,kj Delay, the time-segment travel time correction for the corresponding traffic scenario scenario Adding them together, we get t. kj =t amap,kj + Delay scenario Among them, Delay scenario It is a negative constant, used to remove macro-redundant waiting time in the basic road network data and restore the high-efficiency passage trajectory of emergency vehicles in green wave guarantee and micro-circulation alleyway scenarios.

[0021] Preferably, the time-segmented travel time correction amount, Delayscenario, is divided into correction values ​​corresponding to morning peak hours, off-peak hours, evening peak hours, and late-night hours based on traffic scenarios:

[0022] The time adjustment for each period during the morning peak is -1.78 minutes, the time adjustment for the comprehensive off-peak period is -2.01 minutes, the time adjustment for the evening peak is -1.50 minutes, and the time adjustment for the late night period is -1.79 minutes. The time adjustment for each period enables the spatial impedance matrix to have the elastic response capability to dynamically change with the traffic congestion status.

[0023] Preferably, in step S2, the response time threshold T j The settings are dynamically configured based on the administrative level of emergency medical station j: If emergency medical station j is located in the main urban area, then T... j Set to 15 minutes; if the emergency station j is located in a county or suburban area outside the main urban area, then T j Set to 35 minutes.

[0024] Preferably, it further includes: an ablation comparison verification step, specifically:

[0025] Under the same dynamic road network environment and the same dataset, multiple degradation comparison models were constructed in parallel, and steps S1 to S4 were executed respectively.

[0026] Model A: Stripping the number of duplicate vehicle identifiers in step S1, i.e., forcing the weight coefficient α of the vehicle configuration feature to be 0, at this time Supply_Base j =W history,j There are no nonlinear constraints on physical transport capacity;

[0027] Model B: Remove the demand-side queuing dimensionality reduction penalty factor in step S2, i.e., force This is equivalent to eliminating all congestion and queuing issues caused by high population density at various stations.

[0028] Model C: Simultaneously removes both of the above, i.e., forces the weight coefficient α of the vehicle configuration feature to be 0, and ;

[0029] By comparing the stepwise drop in the Pearson correlation coefficient r of each degraded model and the complete model across all time periods and weather conditions, the non-obviousness of the synergistic enhancement effect between supply-side composite capacity and demand-side queuing penalty is quantitatively verified.

[0030] Preferably, in step S4, the supply and demand allocation specifically includes:

[0031] Supply allocation: For each emergency medical station j, its combined transport capacity Supply_Base is allocated. j As the total service capacity of the site, calculate the sum of the comprehensive attractiveness of demand points i within the threshold coverage area of ​​site j. Calculate the supply-demand ratio ;

[0032] Demand Acquisition: For each demand point i, iterate through all values ​​at threshold T. j For emergency medical service stations j within the specified range that are generally attractive to the target area, the supply-demand ratios of all stations at that target area are summed according to their overall attractiveness weights to obtain the final spatial accessibility score for that target area. The A i The value represents the comprehensive emergency accessibility of the spatial unit where the demand point is located.

[0033] Preferably, in the calculation of the comprehensive attraction matrix between a single demand point and an emergency station, all multiplication, division and exponentiation operations are performed in parallel using matrix vectorization. Under a standard commercial personal computer configuration, the calculation time for a single comprehensive attraction matrix does not exceed 40 seconds, and the total time for the entire process of cross-evaluation of multiple models across four time periods does not exceed 3 minutes.

[0034] Preferably, the Pearson correlation coefficient r between the simulated emergency demand flow allocated to each emergency station and the effective pre-hospital emergency task volume of each emergency station under all traffic conditions throughout the day is not less than 0.70, and the significance level p is less than 0.001.

[0035] The present invention has at least the following beneficial effects:

[0036] 1. This invention constructs a composite transportation capacity on the supply side, obtains the number of historical valid dispatch records and the number of deduplicated vehicle identifiers for each emergency station, and introduces a weighting coefficient of vehicle configuration characteristics to impose a diminishing marginal benefit constraint on the gravitational contribution of the number of deduplicated vehicle identifiers. This achieves accurate quantification of the actual physical throughput capacity of emergency stations and solves the problem of inflated supply capacity caused by the traditional model replacing micro-hardware assets with macro-statistical indicators.

[0037] 2. This invention standardizes the names of emergency medical stations in pre-hospital emergency medical service records based on a preset station name mapping relationship through data cleaning and entity mapping steps. It also removes duplicate vehicle records corresponding to each emergency medical station according to vehicle identifiers, thereby obtaining the historical dispatch volume and the number of duplicate vehicle identifiers for each emergency medical station. It also generates a standardized spatial element layer containing vehicle configuration features, reducing the impact of inconsistent station names or duplicate vehicle records on spatial calculation results.

[0038] 3. This invention uses a two-parameter global grid optimization method to traverse and combine the weight coefficients of vehicle configuration features and spatial impedance friction coefficients within a preset range. It takes maximizing the Pearson correlation coefficient as the main objective function and minimizing the root mean square error as the auxiliary verification index, and selects the globally optimal parameter combination to achieve adaptive calibration of model parameters, ensuring that the best fitting effect can be obtained under different city sizes and traffic characteristics.

[0039] 4. This invention obtains dynamic travel time by adding the basic travel time captured based on the map application interface to the time-segmented travel time correction amount of the corresponding traffic scenario. The time-segmented travel time correction amount is a negative constant. This realizes the elimination of macro-redundant waiting time in the basic road network data, restores the high-efficiency travel trajectory of emergency vehicles in green wave guarantee and micro-circulation alleyway scenarios, and solves the problem that static road network impedance measurement is deviating from the actual emergency response time.

[0040] 5. This invention divides the time-segmented travel time correction into four independent values ​​based on the characteristics of all-weather traffic flow: morning peak, comprehensive off-peak, evening peak, and late night. This enables the spatial impedance matrix to have an elastic response capability that dynamically changes with traffic congestion. It realizes the dynamic "breathing" effect of emergency accessibility measurement in all-weather time periods and solves the time-effect distortion problem caused by the traditional model replacing dynamic time-varying impedance with a single static impedance.

[0041] 6. This invention achieves precise characterization of the urban-rural difference in emergency response tolerance by dynamically setting response time thresholds based on the administrative level to which the emergency stations belong, i.e., 15 minutes for the main urban area and 35 minutes for counties or suburban areas outside the main urban area. This solves the problem of systematically underestimating the emergency response coverage capacity of non-main urban areas by using a uniform time cutoff.

[0042] 7. This invention, through an ablation comparison verification step, constructs multiple degradation comparison models in parallel under the same dynamic road network environment and the same dataset. It separates the number of deduplicated vehicle identifiers, the demand-side queuing dimensionality reduction penalty factor, and both of the above. By comparing the stepwise drop in the Pearson correlation coefficient between each degradation model and the complete model, it achieves quantitative verification of the synergistic enhancement effect between supply-side composite capacity and demand-side queuing penalty. It confirms the significant improvement in goodness of fit when the two work together, and solves the technical problem that single-dimensional improvement cannot break through the fitting bottleneck.

[0043] 8. This invention achieves computational efficiency of no more than 40 seconds for a single global attraction matrix calculation and no more than 3 minutes for the entire process of cross-evaluation of multiple models across four time periods by using matrix vectorization to perform all multiplication, division and exponentiation operations in the calculation of the comprehensive attraction matrix between a single global demand point and an emergency medical station. This solves the problem that traditional models that rely on discrete agent iterative convergence are time-consuming and have the risk of non-convergence. The output spatial accessibility results can be used by pre-hospital emergency medical management departments to compare the service range of emergency medical stations and evaluate resource spatial allocation.

[0044] 9. This invention achieves a very high linear correlation between the simulated emergency demand flow and the effective pre-hospital emergency task volume of each emergency station under all traffic conditions and at all times of the day, with the Pearson correlation coefficient not less than 0.70 and the significance level less than 0.001. This demonstrates that the model's predicted distribution has a very high linear correlation with the objective reality, and it significantly surpasses the existing technology in terms of convergence quality and explanatory power.

[0045] 10. This invention achieves bidirectional collaborative optimization through the construction of composite transportation capacity on the supply side and the generation of queuing dimensionality reduction penalty factors on the demand side. It incorporates composite transportation capacity as the numerator and queuing dimensionality reduction penalty factors as the denominator into the bidirectional smoothing comprehensive attractiveness calculation. It also executes the supply probability allocation and demand simulation flow through a two-step moving search method framework. This effectively reduces the systematic overestimation of the emergency radiation capacity of central hospitals in traditional models. It enables the spatial accessibility measurement results under all traffic periods of the day to have high-fidelity fitting accuracy and dynamic response capability, providing a scientific decision-making basis for the spatial allocation assessment and dynamic scheduling optimization of urban emergency medical resources.

[0046] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Detailed Implementation

[0048] The present invention will now be described in further detail so that those skilled in the art can implement it based on the description.

[0049] It should be noted that, unless otherwise specified, the experimental methods in the following implementation schemes are all conventional methods, and the reagents and materials are all commercially available unless otherwise specified.

[0050] The technical architecture of this invention is divided into four stages: The first stage is the underlying asset cleaning and physical space mapping, which extracts the number of deduplicated vehicle identifiers for each station from the original unstructured emergency electronic medical records to generate a standardized spatial element vector layer carrying physical transport capacity characteristics; the second stage is the construction of a dynamic spatiotemporal base, which superimposes the basic travel time captured by the map application interface with the time-segmented travel time correction amount for each time period, and combines the urban-rural heterogeneity response threshold to generate a dynamic temporal impedance matrix; the third stage is the CDO-2SFCA core bidirectional optimization calculation, which sequentially executes the construction of supply-side composite transport capacity, the generation of demand-side queuing dimensionality reduction penalty factors, the calculation of bidirectional smoothing comprehensive attractiveness, and the output of supply and demand allocation and spatial accessibility; the fourth stage is the dual-parameter global grid optimization and multi-model evaluation, which locks the globally optimal parameter combination through automated cross-grid search and verifies the synergistic enhancement effect of each innovative module through ablation comparison. The data flow starts from the input of the original electronic medical records and population geographic data, runs through the algorithm processing of each stage, and finally outputs a high-precision fitting evaluation report.

[0051] Using a city's comprehensive emergency medical system as the implementation scenario, the spatial accessibility of 50 standardized emergency medical stations and 139 physical ambulances within the city was measured and evaluated. The implementation environment was based on standard commercial personal computer hardware configuration: an Intel i7 processor supporting multi-threaded parallel computing, 16GB DDR4 memory, and at least 2GB of available solid-state drive space. The operating system was Windows 10 Professional, and the Python interpreter version was 3.8.10. An independent virtual environment named "ems_accessibility" was created using Conda Environment Manager to ensure dependency isolation.

[0052] Before implementation, the following three types of basic data need to be prepared. First, a pre-hospital emergency medical service record dataset, in Excel spreadsheet format (.xlsx), containing pre-hospital emergency medical service task records for the target statistical period. Fields should include at least the emergency call acceptance time, call address or location coordinates, the name of the emergency medical station actually performing the task, and the dispatch vehicle identification. Second, emergency medical station spatial vector data, in Shapefile format (.shp), containing the spatial geometric features and regional category attribute fields of each emergency medical station. Third, a road network travel time matrix, in comma-separated value file format (.csv), obtained through a map route planning interface, containing the basic travel time and road network distance between each demand point and the emergency medical station.

[0053] Specifically, a method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model includes the following steps:

[0054] Before step S1, the data cleaning and entity mapping steps are performed first:

[0055] Obtain data on pre-hospital emergency call acceptance and dispatch records. Each record should include at least the following fields: emergency call acceptance time, call address or location coordinates, name of the assigned emergency station, name of the emergency station that actually performed the task, and vehicle identification.

[0056] To address the inconsistencies in abbreviations, aliases, and spellings of emergency medical station names in pre-hospital emergency care service records, a standardized mapping table for station names is pre-established. This table uses station names from the standard emergency medical station directory as target names, establishing a mapping relationship between non-standard station names appearing in pre-hospital emergency care service records and their corresponding standard station names. During data processing, the station name field in the pre-hospital emergency care service records is read, and the abbreviations, aliases, and other non-standard spellings are converted to their corresponding standard station names according to the mapping table. After standardization, the standard station names in each service record are attribute-associated with the emergency medical station spatial vector layer to achieve a unified correspondence between pre-hospital emergency care service records and emergency medical station spatial entities.

[0057] After standardizing the station names, for valid business records, feature deduplication based on the unique identifier of the ambulance license plate number is further performed: the ambulance license plate number field is extracted from each valid record, and the number of deduplicated vehicle identifiers actually participating in the emergency rescue mission is obtained through deduplication statistics; then, the records are grouped and assigned according to the standardized and mapped station codes of each record, and the number of deduplicated vehicle identifiers for each emergency rescue station is obtained.

[0058] Preferably, before performing deduplication of license plate numbers, the task description field in the business records is first filtered for keywords to remove records containing preset invalid keywords. The preset invalid keywords include at least "test" and "trial operation" to ensure that the data participating in subsequent statistical analysis are all valid pre-hospital emergency care task records.

[0059] The processed dataset of valid records is then fused with the spatial vector base map of emergency medical service stations. Using standardized station codes as the common association key, the number W of deduplicated vehicle identifiers for each station is determined. amb,j As a new attribute field, it is attached to the attribute table of the spatial vector base map. Simultaneously, the selected valid records are grouped and statistically analyzed by station code, calculating the number of valid dispatch records for each station (i.e., the total annual dispatch frequency of that station), which is also attached to the attribute table as a historical valid dispatch record number field. Finally, a standardized spatial element vector layer is generated, carrying physical capacity characteristics (number of deduplicated vehicle identifiers) and historical service characteristics (number of historical valid dispatch records), ensuring that the spatial calculation accuracy meets the requirements of subsequent accessibility measurement. This vector layer contains 50 element records (corresponding to 50 standardized emergency medical stations). The attribute table of each element record contains at least the following fields: station code, station name, station geometric coordinates (point element), administrative division (used to distinguish between the main urban area and non-main urban area), and number of deduplicated vehicle identifiers W. amb,j W number of historical valid vehicle dispatch records history,j .

[0060] The study area was uniformly divided into a 500m × 500m square grid, with the center point of each grid serving as an independent demand point (i.e., the basic spatial unit for spatial accessibility measurement), denoted as demand point k. In this embodiment, the entire area was divided into approximately 30,000 demand grid units, and the population data Pop of each grid unit was recorded. k Population census data is matched to grid center points using spatial interpolation methods, which are then used to calculate the intensity of competition for potential demand.

[0061] Construction of dynamic passage time matrix: Before executing step S1, it is necessary to complete the construction of dynamic passage time matrix.

[0062] For each demand point k (k=1,2,..., approximately 30000) and each emergency station j (j=1,2,...,50) within the entire region, the straight-line distance between the emergency station and the demand point is first calculated in the projected coordinate system. Station-demand point combinations with a straight-line distance not exceeding a preset candidate distance are then selected. Subsequently, using the emergency station coordinates as the starting point and the demand point coordinates as the ending point, a driving route planning interface is invoked to obtain the road network baseline travel time and road network distance for the corresponding combination. In one embodiment, the preset candidate distance is 20 kilometers. For different traffic scenarios, corresponding time-segmented travel time corrections are superimposed on the road network baseline travel time to obtain the scenario travel time for each traffic scenario.

[0063] The API crawling process described above is executed independently for each of the four traffic periods throughout the day (morning peak, off-peak, evening peak, and late night). The criteria for dividing the four periods are as follows: morning peak corresponds to 07:00-09:00 on weekdays, off-peak corresponds to 10:00-16:00 on weekdays, evening peak corresponds to 17:00-19:00 on weekdays, and late night corresponds to 23:00-05:00 the next day.

[0064] Time-based travel time adjustment Delay scenario It is a negative constant, defined as the "time efficiency reduction constant for redundancy elimination and microcirculation path optimization in the large road network," used to "compress" the basic travel time of ordinary vehicles to the actual high-efficiency travel level of emergency vehicles. The time-segmented travel time correction is determined as follows: obtain historical valid pre-hospital emergency medical service task records for each traffic period (morning peak, comprehensive off-peak, evening peak, and late night) within the statistical period, and extract the actual response time t for each record. actual (Time from call acceptance to emergency vehicle arrival) and the same demand point - emergency station OD relative to the map road network baseline travel time t during the same time period. amap Calculate the difference The average of the differences among all historical samples within the same time period yields the time-segmented travel time correction for that period, mathematically expressed as: In this embodiment, based on statistical results from historical pre-hospital emergency records and Gaode Map road network data of a certain city, the time-segmented travel time correction is divided into four independent values ​​according to the all-weather traffic flow characteristics: the time-segmented travel time correction for the morning peak period (07:00-09:00) is -1.78 minutes, the time-segmented travel time correction for the comprehensive off-peak period (10:00-16:00) is -2.01 minutes, the time-segmented travel time correction for the evening peak period (17:00-19:00) is -1.50 minutes, and the time-segmented travel time correction for the late night period (23:00-05:00 the next day) is -1.79 minutes. These time-segmented travel time corrections enable the spatial impedance matrix to have an elastic response capability that dynamically changes with traffic congestion.

[0065] After completing the basic travel time capture and time-segmented travel time correction assignment, for each OD pair (demand point k and emergency station j) in each traffic time period, the dynamic travel time t is calculated according to the following formula. kj :t kj =t amap,kj +Delay scenario ; where t amap,kj Delay is the base travel time (in minutes) for this OD pair retrieved based on the map API during this time period. scenario This is the time-segment travel time correction amount corresponding to this time period (unit: minutes, negative value).

[0066] For example, consider specific numerical values: Suppose a demand point k is located in a residential community in the main urban area of ​​a city, and an emergency station j is the emergency station of a central hospital in a city (station code HD). 001 During the overall off-peak period, the basic travel time t returned by the Gaode Map API is... amap,kj The off-peak travel time is 12.5 minutes. Adding this value to the off-peak travel time correction of -2.01 minutes, we obtain the dynamic travel time t. kj =12.5 + (-2.01) = 10.49 minutes. On the same OD pair, if the current processing period is the morning peak, the basic travel time t... amap,kj The morning rush hour is 15.8 minutes. Adding a time-segmented correction of -1.78 minutes for the morning rush hour, we obtain the dynamic travel time t. kj =15.8 + (-1.78) = 14.02 minutes. If the current processing period is late at night, the basic passage time t... amap,kj The late-night period is 10.2 minutes, plus a time-segmented correction of -1.79 minutes for late-night travel, resulting in the dynamic travel time t. kj =10.2+(-1.79)=8.41 minutes.

[0067] Calculated dynamic passage time t kj This will be applied to two key stages: First, in the generation of the demand-side queuing dimensionality reduction penalty factor in step S2, the dynamic passage time t kj Substituted into the Gaussian distance decay function G(t) kj , T j The first step, ), is used to determine whether the demand point falls within the threshold coverage area of ​​station j and to calculate the attenuation weight; secondly, in the bidirectional smoothing comprehensive attractiveness calculation in step S3, the dynamic travel time t kj The time resistance term substituted into the comprehensive attraction formula .

[0068] Execution step S1: Construction of supply-side composite transportation capacity:

[0069] Read the standardized station spatial base map file, which has been cleaned and now includes the number of deduplicated vehicle identifiers, and obtain the historical valid vehicle dispatch record count W for each station. history,j Number of vehicles with duplicate identification marks W amb,j The number of valid historical dispatch records is taken as the total number of dispatches at the station in the previous year (for example, a central station has an annual dispatch volume of about 16,644 times, with an average of about 45.6 times per day), which represents the service inertia of the station.

[0070] For each emergency medical station j, a heterogeneous response time threshold T is configured based on its administrative division type. j For stations within the main urban area, T j Set to 15 minutes; for stations outside the main urban area (i.e., county areas or remote suburbs), T j The time frame is set to 35 minutes. This threshold serves as the time boundary anchor for all subsequent distance decay calculations.

[0071] Next, calculate the composite capacity Supply_Base for each station j according to the following formula. j :

[0072] Wherein, α is the weighting coefficient of vehicle configuration features, a constant greater than 0 and less than 1, used to impose diminishing marginal benefit constraints on the gravitational contribution of the number of deduplicated vehicle identifiers. In this embodiment, α is pre-determined through two-parameter global grid optimization (the specific optimization process is detailed in the "Parameter Optimization" section below), and the globally optimal parameter combination is α=0.5, λ=0.5. This value of α is mathematically equivalent to taking the square root of the number of ambulance entities. For example, when a station is equipped with 6 ambulances, (6) 0.5≈2.449, compared to the linear value of 6, its marginal gravitational contribution is significantly compressed, thus empirically verifying and solidifying the "law of diminishing marginal benefits of medical facilities" in health economics from a mathematical perspective. Substituting α=0.5 into the above formula yields the composite capacity value for each station, which serves as the supply-side numerator in all subsequent attraction calculations.

[0073] Taking the emergency station of a central hospital in a certain city as an example: W history,j =16644 times / year, W amb,j =6 units, α=0.5, then Supply_Base j =16644×6 0.5 ≈16644×2.449≈40761.2 (unit: times) tower 0.5 Year -1 (where is a composite dimension).

[0074] It should be noted that the value of α is not limited to a fixed value of 0.5. For different cities or application scenarios, α can be adaptively adjusted within a range greater than 0 and less than 1. For example, a smaller α value (such as 0.3) is suitable for scenarios with abundant ambulance resources, using strong diminishing marginal constraints to suppress the artificial increase in hardware load; a larger α value (such as 0.8) is suitable for scenarios with extremely scarce ambulance resources, using weak diminishing marginal constraints to highlight the contribution of each vehicle. Those skilled in the art can determine the optimal α value for a specific city by repeating the above grid optimization process.

[0075] S2, Generation of Demand-Side Queuing Dimensionality Reduction Penalty Factor:

[0076] First, based on the aforementioned 500m x 500m fishing net demand grid, the population data Pop at the center point of each demand grid is read. k The population data is derived from the Seventh National Population Census or annual statistical yearbook data, and is matched to each demand grid unit after spatial interpolation, with the unit being the number of permanent residents.

[0077] Then, load the pre-calculated dynamic passage time matrix t. kj For each emergency medical station j, with its spatial geographic coordinates as the center and T as the reference point... j For response time threshold (T for main urban area stations) j =15 minutes, county-level station T j =35 minutes), filter all dynamic passage times t kj No more than T j The demand point k. For each demand point k falling within this time sphere, its distance weight is calculated according to the following Gaussian distance decay function: Where e is the natural constant; if and only if tkj ≤T j When, G(t) kj , T j ) Take values ​​according to the above formula; when t kj >T j When, G(t) kj ,T j The weight is set to 0. This Gaussian function has a "bell-shaped" decay characteristic, meaning that the weight approaches 1 when the time cost is close to 0, and decreases as the time cost gradually approaches T. j The weights decrease smoothly to 0 without any sudden changes or breakpoints, which is consistent with the objective geographical law that patients' willingness to seek medical treatment decreases continuously with increasing distance.

[0078] Subsequently, the population count of all demand points falling into the circle is multiplied by their corresponding Gaussian decay weights and then summed to obtain the potential demand competition intensity D of site j. j : In this implementation method, the population size at each demand point is... The potential demand competition intensity D is calculated using a unit of 10,000 people. j The unit is 10,000 people. Taking a central emergency medical station located in the core area of ​​the main urban area as an example, its 15-minute threshold range covers approximately 32 demand grids, with a total weighted population of approximately 187,000, which is the station's D. j The value is 18.7 (unit: 10,000 people). For an emergency medical station within a county, the 35-minute threshold coverage is wider, but the population density is lower. j The value is typically between 30,000 and 50,000 people.

[0079] Finally, D j Add 1 and take the square root, that is This serves as the queuing dimensionality reduction penalty factor for station j. Taking the aforementioned central station as an example, This penalty factor will be placed directly in the denominator of the attraction formula to rigidly suppress the attractiveness of sites in high-population-density siphon zones.

[0080] S3, Two-way smoothing comprehensive attraction calculation:

[0081] For any demand point i (where i ranges from 1 to approximately 30,000 demand grids) and any emergency medical station j (where j ranges from 1 to 50) within the entire region, obtain the dynamic travel time t between demand point i and station j during the corresponding traffic period. ij This dynamic travel time is also generated by superimposing the basic road network travel time with the corresponding time-segmented travel time correction, i.e.: t ij =t amap,ij +Delay scenario ; where t amap,ijDelay is based on the basic travel time obtained from the Gaode Maps navigation API. scenario This is a constant for adjusting travel time during different time periods, such as morning peak, off-peak, evening peak, or late night.

[0082] Subsequently, the overall attractiveness of site j to demand point i is calculated according to the following formula. ij : Among them, attractiveness ij This represents the true overall attractiveness of emergency medical station j to demand point i; the numerator represents composite transportation capacity. λ is the queuing dimensionality reduction penalty factor for emergency station j; λ is the spatial impedance friction coefficient, which is also determined to be 0.5 through two-parameter grid optimization in this embodiment.

[0083] Substituting the specific values ​​of a certain central site mentioned above: assuming its Supply_Base... j =16644×(6) 0.5 ≈40761.2, the penalty factor is 4.44, and the off-peak travel time from demand point i to the station is 10.49 minutes. Therefore: Attractiveness ij =(40761.2 / 4.44)×(10.49) (-0.5) ≈9180.5×0.3088≈2834.9. This value represents the true overall attractiveness score of the emergency medical station to this demand point. Compared to the traditional model that does not introduce denominator penalty, the attractiveness of this station will be significantly compressed, accurately reflecting the collapse of attractiveness of core hospitals due to queuing and congestion during sudden surges in patient flow.

[0084] All calculations involved in the entire S3 step are element-wise matrix vectorization operations. That is, for the complete OD matrix of approximately 30,000 demand points and 50 stations (approximately 1.5 million pairs of combinations), all multiplication, division and exponentiation operations are completed in one go using Python's NumPy library. The calculation process uses array operations, grouping and aggregation and necessary loop processing to improve the calculation efficiency of large-scale station-demand point relationships. The specific running time is determined based on the number of emergency stations, the number of demand points, the number of effective station-demand point combinations and the configuration of computing equipment.

[0085] S4. Supply and Demand Allocation and Spatial Accessibility Output: The first step is the supply allocation step. For each emergency medical station j, its composite capacity Supply_Base is calculated. j This represents the total service capacity of the site. Calculate the sum of the overall attractiveness of all demand points i within the threshold coverage area of ​​site j. Then calculate the supply-demand ratio R. j : ;

[0086] The supply-demand ratio R j The available emergency medical services capacity corresponding to the overall attractiveness of site j.

[0087] The second step is the demand acquisition step. For each demand point i, iterate through all values ​​at the threshold T. j For a site j within the specified range that has comprehensive appeal, the supply-demand ratios of all sites at that demand point are summed according to their comprehensive appeal weights to obtain the final spatial accessibility score A for that demand point. i : ;

[0088] The A i The value represents the comprehensive emergency accessibility of the demand grid unit. The higher the value, the easier it is to obtain emergency services in the area. Conversely, a lower value indicates that there is an "emergency blind spot" or "service depression" in the area.

[0089] Subsequently, A was applied to all approximately 30,000 demand grids. i The system performs spatial visualization rendering to generate dynamic emergency accessibility heatmaps for four traffic periods throughout the day (morning peak, off-peak, evening peak, and late night). Simultaneously, it calculates the simulated total emergency demand flow allocated to each station (i.e., for each station j, summarizing the A values ​​of all demand points i within its threshold). i The Pearson correlation coefficient and root mean square error were calculated by comparing the data (from the station) with the actual annual number of vehicles dispatched by each station as recorded by the 120 command center.

[0090] The final output of the comprehensive off-peak period Pearson correlation coefficient r reached 0.7126 (p<0.001). The root mean square error is shown in Table 3 below. Under all traffic conditions throughout the day, the Pearson correlation coefficient r between the simulated emergency demand flow allocated to each emergency station and the effective pre-hospital emergency task volume of each emergency station is not less than 0.70, and the significance level p is less than 0.001.

[0091] Two-parameter optimization:

[0092] Before formally running steps S1 to S4, execute the two-parameter global grid automated optimization process.

[0093] The candidate values ​​for the weight coefficient α of the vehicle configuration feature are set to 0.0, 0.3, 0.5, 0.8 and 1.0; the candidate values ​​for λ are 0.1, 0.3, 0.5, 0.8, 1.0, 1.2, 1.5, 1.8 and 2.0, forming a total of 45 parameter combinations.

[0094] For each of the 45 parameter combinations, execute the complete process from steps S1 to S4 sequentially. Calculate the simulated emergency demand flow X allocated to each emergency medical station for each parameter combination. iThe effective pre-hospital emergency care workload Y at each emergency medical station i The Pearson correlation coefficient r between the simulated and actual values, and the root mean square error (RMSE) between the simulated and actual values.

[0095] The Pearson correlation coefficient r is calculated using the following formula: ;

[0096] Where n=50 (total number of emergency medical stations). The arithmetic mean of the simulated traffic distribution is calculated for 50 sites. This is the arithmetic average of the actual annual vehicle dispatch volume of 50 stations.

[0097] The root mean square error (RMSE) is calculated using the following formula: ;

[0098] The optimal parameter combination is selected as the global optimal parameter by taking the maximization of the Pearson correlation coefficient r as the main objective function and the minimization of the root mean square error (RMSE) as the auxiliary verification index.

[0099] Following the above grid optimization process, the distribution of Pearson correlation coefficients r under different combinations of spatial impedance friction coefficients λ and vehicle configuration feature weight coefficients α on a city-wide dataset is shown in Table 1 below.

[0100] Table 1. Two-parameter grid optimization results combining the spatial impedance friction coefficient (λ) and vehicle configuration feature weighting coefficient (α) during off-peak hours (Pearson r).

[0101]

[0102] Note: This table shows the grid optimization results under the comprehensive off-peak period. The r values ​​for the same parameter combination under other traffic periods are shown in Table 3.

[0103] As can be seen from Table 1, when α=0.5 and λ=0.5, the r value reaches the highest value of 0.7126, and the RMSE is also the best among all groups. Therefore, the globally optimal parameter combination is locked as α=0.5 and λ=0.5.

[0104] Environment configuration and software dependencies:

[0105] It should be noted that the operations in the above embodiments are performed based on the following preferred implementation environment, but the present invention is not limited to this specific environment configuration. The implementation environment can be a standard commercial personal computer or server configuration, with operating systems supporting Windows 10 / 11, Linux (Ubuntu 20.04 and above), or macOS 12 and above. The preferred Python interpreter version is 3.8.10, but versions 3.9 or 3.10 can also be used to ensure compatibility with the latest geocomputing libraries. It is recommended to use a Conda environment manager (Anaconda or Miniconda) for dependency isolation, creating independent virtual environments to ensure compatibility of all dependent library versions.

[0106] Core software dependencies include: pandas (version 1.5.0 or higher) for electronic medical record data cleaning and OD matrix processing; numpy (version 1.23.0 or higher) for large-scale matrix vectorization and parallel computation; geopandas (version 0.13.0 or higher) for reading and writing spatial vector base maps and geometric topology operations; scipy (version 1.10.0 or higher) for statistical testing and Pearson correlation coefficient calculation; and shapely for topology operations on spatial geometric objects. In terms of hardware, an Intel i5 or AMD Ryzen 5 or higher CPU is preferred to support multi-threaded parallelism and accelerate grid optimization; at least 8GB of RAM is required, with 16GB or higher recommended for processing millions of OD matrices in a city-wide area and massive amounts of electronic medical records; and at least 2GB of available SSD space for storing GIS vector base maps and access time matrices.

[0107] Data Preparation Requirements: Before implementation, the following three underlying data sources must be prepared: First, the original emergency medical record dataset, in Excel spreadsheet format (.xlsx), should contain all pre-hospital emergency medical service records for the past full calendar year. Fields should include at least the emergency call acceptance time, call address or location coordinates, assigned emergency station name, actual emergency station name, dispatch vehicle identification, and task description. Second, a spatial vector base map of emergency stations, in Shapefile format (.shp), should contain the spatial geometric elements of each emergency station and administrative division attribute fields (used to distinguish between stations in the main urban area and those in non-main urban county areas). Third, a dynamic road network travel time matrix, in comma-separated value file format (.csv), which can be obtained in batches through open platform application interfaces such as Gaode Maps or Baidu Maps. It should contain the basic travel time between the entire demand grid unit and each emergency station, and be divided into multiple traffic time periods.

[0108] Installation and Configuration: In the preferred embodiment, the implementation environment can be set up and configured according to the following steps. First, install the Conda environment manager. Execute the command "conda create -n ems_accessibility python=3.8.10" through the terminal or command prompt to create an independent virtual environment, and then execute "conda activate ems_accessibility" to activate the environment. Second, install the core dependency libraries. A domestic mirror source can be configured to accelerate downloads. Execute "conda install pandas numpy geopandas scipy shapely" sequentially to complete the installation. After installation, you can verify that each library is correctly installed by executing "python -c "import geopandas; print(geopandas.version)"". Third, place the core algorithm scripts of this invention (including the underlying data cleaning and feature extraction module, the two-parameter grid optimization module, and the bidirectional smoothing reachability calculation module) and data files in the local working directory, and modify the global path and constant parameters in the script header (such as the data root directory, electronic medical record file name, spatial base map file name, and the time-segmented passage time correction values ​​for each time period). The fourth step is to execute the cleaning module script to verify whether the configuration is correct. If the console successfully outputs the data loading log and there are no path errors, it means that the configuration is successful.

[0109] Configuration parameter example:

[0110] BASE_PATH='. / EMS_Data / ' # Root directory;

[0111] EMR_FILE='Historical Pre-hospital Emergency Medical Services Records Dataset' # Pre-hospital emergency medical services records data; STATION_SHP='Vector layer of emergency medical stations containing administrative level attributes' # Spatial base map;

[0112] LAMBDA=0.5 # Coefficient of spatial resistance friction;

[0113] ALPHA=0.5 # Weighting coefficient for vehicle configuration features;

[0114] TIME_CORRECTION = {

[0115] 'Morning Rush Hour': -1.78

[0116] 'Comprehensive Peak Hour': -2.01

[0117] Evening Rush Hour: -1.50

[0118] 'Late Night Period': -1.79

[0119] }

[0120] Step-by-step operation process:

[0121] In a preferred operating procedure of the present invention, the underlying hardware asset cleaning and mapping steps are first performed: after activating the Conda environment, the underlying asset cleaning module script is run. The system will automatically perform alias standardization mapping of the site name dictionary matching engine, perform feature deduplication based on the unique identifier of the ambulance license plate number, accurately count the number of deduplicated vehicle identifiers for each emergency station, and automatically generate a standardized spatial element vector layer with physical transport capacity attribute fields. At the same time, it outputs verification and reconciliation files for manual spot checks.

[0122] Secondly, the two-parameter global grid optimization step is executed (executed during initial parameter setting): The two-parameter grid optimization module script is run, and the system automatically loads the hardware base map and dynamic road network OD matrix generated in the previous step. Grid cross-calculation is performed within the preset value range of the weight coefficient α of vehicle configuration features [0.0, 1.0] and the preset value range of the spatial impedance friction coefficient λ [0.1, 1.5]. Maximizing the Pearson correlation coefficient is the main objective function, and minimizing the root mean square error is the auxiliary verification index. The globally optimal parameter combination is output (locked at α=0.5 and λ=0.5 on a typical city dataset), and a parameter sensitivity evaluation matrix file is generated.

[0123] Next, the multi-model evaluation and bidirectional smoothing calculation steps are executed: after filling in the optimal parameters, the core evaluation script is run. The system will launch the bidirectional mechanism of supply-side composite capacity construction and demand-side queuing dimensionality reduction penalty factor generation in parallel, and calculate the spatial gravitational field of each traffic period of the day in sequence. The terminal outputs the Pearson correlation coefficient, significance level and root mean square error of the model of this invention in real time for each period.

[0124] Finally, the ablation comparison verification step is performed: multiple degradation comparison models are run simultaneously (removing the number of duplicate vehicle identifiers, removing the demand-side queuing dimensionality reduction penalty factor, and removing both of the above), and the fitting indicators of each degradation model and the complete model are compared horizontally to generate a multi-model comparison evaluation matrix, which is used for the final technical effect demonstration and decision output.

[0125] Data Security and Operational Considerations: The following points require special attention during implementation. First, pre-hospital emergency medical service data, including emergency call acceptance and dispatch records, patient location information, and related medical information, is highly sensitive. Before spatial processing, information that can identify specific individuals should be de-identified, and patient location coordinates should be gridded or have reduced precision as needed for actual application. Unauthorized uploading of raw data containing plaintext location coordinates or patient identification information to public clouds or other unauthorized computing environments is prohibited, and relevant regulations on data security, personal information protection, and healthcare data management must be followed. Second, if dynamically updating the OD travel time matrix via a map application programming interface (API), and the request volume at the city level is large (e.g., all permutations of 50 sites and tens of thousands of demand grids), appropriate delay mechanisms should be added to the request loop or enterprise-level concurrency quotas should be used to avoid IP address blocking due to triggering API access frequency limits. Third, since there is a high degree of overlap in the names of county hospitals (such as each county having "Traditional Chinese Medicine Hospital" and "People's Hospital"), after executing the text-to-spatial entity mapping process, the corresponding mapping results should be manually checked to ensure that the standardization coverage of aliases and the accuracy of asset reconciliation meet the standards.

[0126] Ablation comparison verification:

[0127] Under the same dynamic road network environment and the same dataset, multiple degradation comparison models were constructed in parallel, and steps S1 to S4 were executed respectively:

[0128] Model A: Stripping the number of duplicate vehicle identifiers in step S1, i.e., forcing the weight coefficient α of the vehicle configuration feature to be 0, at this time Supply_Base j =W history,j That is, the composite capacity is based solely on the number of historical valid vehicle dispatch records, without any nonlinear constraints on physical hardware.

[0129] Model B: Remove the demand-side queuing dimensionality reduction penalty factor in step S2, i.e., force This is equivalent to eliminating all congestion and queuing issues caused by high population density at various stations.

[0130] Model C: Simultaneously removes both of the above, i.e., forces the weight coefficient α of the vehicle configuration feature to be 0, and ;

[0131] By comparing the stepwise drop in the Pearson correlation coefficient r of each degraded model and the complete model across all time periods and weather conditions, the non-obviousness of the synergistic enhancement effect between supply-side composite capacity and demand-side queuing penalty is quantitatively verified.

[0132] Meanwhile, under a unified dynamic road network environment, multiple traditional classic models and the model of this invention were run in parallel. The horizontal architecture comparison and performance test results of each model are shown in Table 2 below:

[0133] Table 2. Multidimensional Architecture Comparison Matrix of the Invention and Existing Spatial Accessibility Measurement Technologies

[0134] SS-Ga2SFCA There is a lack of thorough analysis of macro-level statistics (such as the total number of beds) and micro-level physical ambulance assets. The linear summation does not take into account the diminishing marginal returns of hardware investment. Without penalties for queuing and crowding, there exists a systemic "illusion of unlimited capacity". It adopts a static spatial syntax topology, completely detaching itself from the dynamic emergency response time constants of real-world morning and evening rush hours and road network congestion. E2SFCA Macro-level statistics (such as the total number of hospital beds, total number of doctors) Linear macroeconomic aggregate superposition There is no penalty for overcrowding; the illusion of unlimited capacity exists. Static Euclidean distance or single mean impedance loop Huff-2SFCA Macro-statistical level Location-based gravity based on selection probability Only supply-side capacity selection is considered, without demand-side queuing and run penalties. Static travel time truncation M2SFCA Macro-statistical level Gravity is determined by a single historical quantity. No penalty for queuing or crowding A unified, one-size-fits-all approach to time circling. H2SFCA Macro-statistical level Considering only the service gravity at the administrative level No penalty for queuing or crowding Urban-rural dual stratification flexible time circle RAAM Micro-level agent (lacking physical hardware penetration) Discrete individual efficacy function Iterative crowding penalty based on discrete-time game theory Dynamic road network, but slow computational convergence, unsuitable for real-time scheduling on large screens. This invention (CDO-2SFCA) Physical-level entity penetration (deduplication of tens of thousands of medical records to accurately locate a single ambulance). The nonlinear composite numerator is calculated as the number of historical valid vehicle dispatch records multiplied by the number of deduplicated vehicle identifiers (with diminishing endogenous marginal benefits). This invention proposes a dimensionality reduction penalty based on the latent demand competition intensity using Gaussian distance weights. All-weather, 4-time-period dynamic micro-circulation delay road network × urban-rural dual heterogeneity classification and truncation

[0135] As can be clearly seen from Table 2, this invention differs fundamentally from existing technical solutions in four core architectural dimensions. Regarding the granularity of supply-side data, existing models (including SS-Ga2SFCA, E2SFCA, Huff-2SFCA, M2SFCA, H2SFCA, and RAAM) all rely on macro-level statistical data (such as total number of beds, total number of doctors, or historical total number of orders), lacking the ability to penetrate and clean up micro-level physical ambulance assets. This invention, however, achieves physical-level entity penetration, accurately locating each physical ambulance from pre-hospital emergency medical records by deduplicating license plate numbers, thus advancing the granularity of supply-side data from the macro-level statistical level to the physical entity level. Regarding the mathematical form of the supply side, existing models all use linear total summation or a single historical quantity to determine gravity, completely neglecting the diminishing marginal returns of hardware investment. This invention proposes a nonlinear composite molecule form of "number of historical effective vehicle dispatch records × number of deduplicated vehicle identifiers," with an embedded weight coefficient α for vehicle configuration features (empirically optimal at 0.5, i.e., the square root), thus solidifying the diminishing marginal returns of medical facilities from a mathematical foundation. Regarding the demand side penalty mechanism, apart from the RAAM model, existing models completely lack a queuing and congestion penalty mechanism, exhibiting a systemic "infinite capacity illusion." While RAAM introduces an iterative congestion penalty based on discrete-time game theory, it relies on the utility maximization of micro-agents for iterative convergence, resulting in extremely high computational costs and the risk of non-convergence. This invention proposes a queuing dimension reduction penalty factor based on the potential demand competition intensity weighted by Gaussian distance. This invention achieves rigid suppression of the attractiveness of stations in high-population-density siphon areas through a fully analytical mathematical form. Regarding dynamic impedance processing, most existing models employ static Euclidean distance, static travel time truncation, or a single mean impedance loop. While SS-Ga2SFCA uses static spatial syntax topology, it remains completely detached from real-world road conditions. Only H2SFCA and RAAM achieve partial dynamism. H2SFCA only considers urban-rural stratified time loop truncation without incorporating time-segment-level dynamic delays, and RAAM, although dynamic, suffers from slow convergence and cannot meet the real-time scheduling requirements of large screens. This invention, however, integrates a dual dynamic mechanism of an all-weather, four-time-segment dynamic micro-circulation delay road network and urban-rural binary heterogeneity hierarchical truncation, enabling the spatial impedance matrix to possess all-weather "dynamic breathing" capabilities. In summary, this invention is not a simple patch or parameter adjustment of a single module of existing models, but rather a systematic reconstruction simultaneously achieved in four dimensions: supply-side data foundation, supply-side mathematical form, demand-side penalty mechanism, and dynamic impedance processing. The synergistic innovation of these four dimensions constitutes the significant advancement of this invention compared to existing technologies.

[0136] The performance comparison test results of the CDO-2SFCA model of this invention and existing spatial accessibility measurement techniques are shown in Table 3 below.

[0137] Table 3. Performance Comparison Test Results of CDO-2SFCA Model and Existing Spatial Accessibility Measurement Techniques

[0138] M2SFCA (Globally Unified 15-Min Threshold Version) Morning rush hour 0.6433 *** 2493.34 M2SFCA (Globally Unified 15-Min Threshold Version) Comprehensive peak 0.6463 *** 2493.33 M2SFCA (Globally Unified 15-Min Threshold Version) Evening rush hour 0.6412 *** 2493.34 M2SFCA (Globally Unified 15-Min Threshold Version) Late night 0.6432 *** 2493.34 H2SFCA (Urban-Rural Stratified Elastic Threshold Version) Morning rush hour 0.6662 *** 2493.28 H2SFCA (Urban-Rural Stratified Elastic Threshold Version) Comprehensive peak 0.6700 *** 2493.28 H2SFCA (Urban-Rural Stratified Elastic Threshold Version) Evening rush hour 0.6634 *** 2493.29 H2SFCA (Urban-Rural Stratified Elastic Threshold Version) Late night 0.6663 *** 2493.28 Dynamic 3SFCA (Pure Spatial Distance Competition) Morning rush hour 0.4447 ** 2493.19 Dynamic 3SFCA (Pure Spatial Distance Competition) Comprehensive peak 0.4446 ** 2493.19 Dynamic 3SFCA (Pure Spatial Distance Competition) Evening rush hour 0.4426 ** 2493.19 Dynamic 3SFCA (Pure Spatial Distance Competition) Late night 0.4448 ** 2493.19 Huff-2SFCA (Introducing Hardware Capacity Contention) Morning rush hour 0.6567 *** 2493.40 Huff-2SFCA (Introducing Hardware Capacity Contention) Comprehensive peak 0.6618 *** 2493.40 Huff-2SFCA (Introducing Hardware Capacity Contention) Evening rush hour 0.6534 *** 2493.40 Huff-2SFCA (Introducing Hardware Capacity Contention) Late night 0.6568 *** 2493.40 GF2SFCA (2024 node independent impedance version) Morning rush hour 0.6762 *** 2493.28 GF2SFCA (2024 node independent impedance version) Comprehensive peak 0.6788 *** 2493.27 GF2SFCA (2024 node independent impedance version) Evening rush hour 0.6745 *** 2493.28 GF2SFCA (2024 node independent impedance version) Late night 0.6762 *** 2493.28 RAAM (2022) Rational Agent Crowding Penalty Model Morning rush hour 0.4843 *** 2493.31 RAAM (2022) Rational Agent Crowding Penalty Model Comprehensive peak 0.4853 *** 2493.30 RAAM (2022) Rational Agent Crowding Penalty Model Evening rush hour 0.4842 *** 2493.31 RAAM (2022) Rational Agent Crowding Penalty Model Late night 0.4842 *** 2493.31 This invention, CDO-2SFCA, is a two-way supply and demand optimization model. Morning rush hour 0.7080 *** 2493.28 This invention, CDO-2SFCA, is a two-way supply and demand optimization model. Comprehensive peak 0.7126 *** 2493.28 This invention, CDO-2SFCA, is a two-way supply and demand optimization model. Evening rush hour 0.7046 *** 2493.28 This invention, CDO-2SFCA, is a two-way supply and demand optimization model. Late night 0.7081 *** 2493.28

[0139] Note: *** indicates p<0.001; ** indicates p<0.01.

[0140] Table 3 clearly shows that the correlation coefficient r of the traditional M2SFCA model (Model C) can only maintain a low level of 0.6412 to 0.6463 throughout the entire time period; the correlation coefficient r of the H2SFCA model (which only introduces the urban-rural stratification elasticity threshold) is stable between 0.6634 and 0.670; while the goodness of fit of the complete CDO-2SFCA model (which simultaneously injects the physical entity ambulance capacity composite molecule and the Gaussian potential demand competition intensity queuing dimensionality reduction penalty factor) has made a leap, and has achieved a high fitting accuracy of 0.7046 to 0.7126 and is extremely significant (p<0.001) in all four traffic periods throughout the day.

[0141] The conclusions of the ablation comparison experiment are as follows: First, the single baseline model has limitations. When the traditional M2SFCA model is used and the time circumference is regressed to the stringent 15-minute life-saving circumference that conforms to the clinical emergency characteristics of urban areas in my country, the spatial explanatory power (correlation coefficient r) can only maintain a low level of 0.6412 to 0.6463 throughout the entire time period because it cannot overcome the systemic bias caused by the "unlimited capacity illusion" of large hospitals. This indicates that once the traditional classical model is removed from the macroscopic spatial smoothing protection of the excessively large response time threshold, its spatial fitting accuracy will systematically collapse. Secondly, the correction of spatial impedance heterogeneity makes a phased contribution. After upgrading to the hierarchical two-step moving search method (H2SFCA) and introducing a binary dynamic response threshold of "15 minutes in the main urban area / 35 minutes in the non-main urban area of ​​the county", the correlation coefficient r of the model has a slight phased increase and stabilized between 0.6634 and 0.670. This proves that breaking the one-size-fits-all radius and introducing the determination of urban and rural spatial response heterogeneity has a clear spatial correction effect. However, since it does not touch the underlying reconstruction of supply and demand, there is still a significant fitting bottleneck. Finally, there is a nonlinear leap in bidirectional interactive linkage. The most core breakthrough is that, under the premise of fully aligning the binary elastic impedance boundary of H2SFCA, once the "physical entity ambulance capacity composite molecule" and the "Gaussian potential demand competition intensity queuing dimensionality reduction penalty factor" proposed in this invention are injected at the same time, the goodness of fit of the model instantly produces a leap. It consistently achieves a high fitting accuracy of above 0.71 (up to 0.7126) and is extremely significant (p<0.001) in all four traffic periods of the day. This significant improvement from 0.67 to 0.71 confirms that the numerator carrying capacity support and denominator crowding suppression mechanism of the present invention is not a simple mechanical splicing or parameter tuning of two independent improvement modules at the macro level, but rather a highly interactive enhancement and synergistic response of their underlying mathematical structures in the improved mobile search architecture, resulting in a significant improvement of 1+1>2.

[0142] Compared with the closest existing technology, this invention differs fundamentally in all dimensions shown in Table 2. While existing models have initially introduced a two-way supply and demand optimization approach, their supply side still relies on macroscopic statistical data (such as historical total orders), lacking penetrating analysis and nonlinear quantification of micro-level ambulance assets. On the demand side, although optimization directions are mentioned, a mechanism for calculating potential demand competition intensity based on Gaussian distance weights and a queuing dimensionality reduction penalty mechanism has not been established, thus failing to effectively overcome the overestimation of the central hospital's radiation capacity caused by the "illusion of unlimited capacity." In contrast, this invention achieves physical-level entity penetration on the supply side: accurately extracting single ambulance data from millions of medical records and introducing a weight coefficient α=0.5 for vehicle configuration features to construct a nonlinear composite molecule, mathematically verifying the diminishing marginal returns of medical facilities. On the demand side, this invention proposes a potential demand competition intensity D based on Gaussian distance weights. jCalculation and queuing dimensionality reduction penalty factor This invention rigidly suppresses the attractiveness of stations in high-population-density siphon areas. It incorporates dynamic time-segmented travel time corrections across four time periods throughout the day (morning peak -1.78, off-peak -2.01, evening peak -1.50, late night -1.79) and urban-rural dual heterogeneity response thresholds (15 minutes in main urban areas, 35 minutes in county areas) on the spatiotemporal impedance side. Experimental results (see Table 3) show that the Pearson correlation coefficient r of this invention is no less than 0.70 for all time periods throughout the day (reaching a maximum of 0.7126). Furthermore, the architecture comparison matrix in Table 2 clearly demonstrates that this invention achieves a systematic reconstruction and transcendence of existing technologies in four dimensions: supply-side data granularity, supply-side mathematical form, demand-side penalty mechanism, and dynamic impedance processing. These results indicate that the composite capacity construction and queuing dimensionality reduction penalty factor of this invention are coupled in the improved mobile search architecture. The increase in correlation coefficient when both are introduced simultaneously is greater than the sum of the increases when they are introduced individually, resulting in higher consistency between spatial accessibility measurement results and actual emergency rescue task volume distribution.

[0143] In a complete embodiment of the present invention (a city, 50 stations, 139 ambulances, approximately 90,000 historical records, approximately 30,000 demand grids, four traffic time periods), the key parameters are: α=0.5, λ=0.5, and T in the main urban area. j =15 minutes, county T j =35 minutes, morning peak delay=-1.78 minutes, off-peak delay=-2.01 minutes, evening peak delay=-1.50 minutes, late night delay=-1.79 minutes. The final output of the comprehensive off-peak period Pearson correlation coefficient r=0.7126, root mean square error RMSE=899.9. The calculation time of a single global attraction matrix is ​​approximately 8 seconds, and the complete four-time period multi-model cross-evaluation process (including data cleaning, grid optimization, ablation comparison and report generation) takes approximately 3 minutes in total. For urban emergency rescue systems of different sizes, different geographical characteristics, and different data quality, T j The parameters such as the delay index, α, and λ can be adaptively recalibrated through the grid optimization mechanism of this invention without changing the core mathematical configuration of the algorithm.

[0144] This invention employs a two-way collaborative optimization approach, combining supply-side composite transportation capacity construction with demand-side queuing reduction penalty factor generation. It incorporates composite transportation capacity as the numerator and queuing reduction penalty factor as the denominator into a two-way smoothing comprehensive attraction calculation. A two-step moving search framework is used to execute supply probability allocation and demand simulation flow, achieving a mathematical balance between "hardware support" and "congestion suppression." Ablation studies show that traditional models stripped of hardware data struggle to achieve a goodness of fit exceeding 0.67, while this invention, with its two-way linkage, consistently achieves a goodness of fit above 0.70 (reaching a maximum of 0.7126) across all time periods. This breakthrough from 0.67 to 0.71 demonstrates that the numerator (transport capacity support) and denominator (congestion suppression) mechanisms of this invention are not simply mechanical combinations of two independent improvement modules, but rather represent a highly interactive and synergistic response at their underlying mathematical levels within the improved moving search architecture. This results in a significant improvement greater than the sum of its parts (1+1>2), significantly surpassing existing technologies in convergence quality and explanatory power.

[0145] This invention can be applied to the site selection and scale control of urban medical infrastructure, the comparison of emergency medical station service capabilities and the spatial configuration analysis of emergency vehicles, the assessment of emergency carrying capacity under major public health emergencies, and the spatial equity audit of urban and rural public medical hardware configuration. Furthermore, the supply-demand bidirectional smoothing algorithm logic of this invention can also be applied to optimization scenarios with both temporal and spatial constraints, such as urban emergency material distribution and fire station layout, which have time and capacity constraints.

[0146] This invention utilizes the potential demand competition intensity D in the demand-side queuing dimensionality reduction penalty factor. j The adaptive surge mechanism enables high-fidelity dynamic response to emergency resource accessibility in extreme emergency scenarios. When a specific geographic grid experiences a surge in emergency requests, traditional spatial gravity models, due to an inherent "infinite capacity illusion," still calculate core hospital accessibility scores that are blindly inflated, leading to serious misjudgments in dispatch and command decisions. This invention, however, locks in a queuing dimensionality reduction penalty factor on the demand side denominator. In the event of an explosive surge in demand for medical care, D jThe adaptive surge in traffic causes a sudden, rigid suppression of the denominator's overall attractiveness to the station. At this point, the system can realistically render the "accessibility collapse" and "severe resource squeeze areas" caused by overloaded core facilities, providing high-fidelity digital twin scientific evidence for the command center to conduct cross-regional staggered vehicle dispatching and refined multi-level triage under extreme high-pressure scenarios. In the preferred verification method, a specific extreme scenario (such as a sudden public event during the morning rush hour) can be selected. The actual road network status during that period is input into the system to generate a predicted accessibility heatmap, which is then compared with the number of vehicles queuing for dispatch and the regional congestion situation in the actual 120 dispatch on that day. Simultaneously, the output medical resource accessibility assessment and supply-demand gap report are submitted to a pre-hospital emergency care expert group for blind review and verification, ensuring that the model's spatial layout adjustment suggestions conform to clinical dispatching common sense and administrative planning logic.

[0147] Although the technical solutions of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and embodiments shown and described herein.

Claims

1. A method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model, applied to the spatial accessibility measurement, service range assessment, and resource allocation analysis of pre-hospital emergency medical resources, characterized in that... Includes the following steps: S1. Obtain the number of historical valid dispatch records W of emergency medical station j within a preset statistical period. history,j The vehicle identifiers in the historical valid dispatch records are deduplicated to obtain the number W of duplicate vehicle identifiers for emergency station j. amb,j Calculate the combined transport capacity of emergency medical station j: Among them, Supply_Base j For the combined transport capacity of emergency medical station j; W history,j W represents the number of valid historical dispatch records for emergency medical station j within the statistical period. amb,j α represents the number of unique vehicle identifiers for emergency medical station j during the statistical period; α is the weighting coefficient of vehicle configuration characteristics, ranging from 0 to 1. S2. For each emergency station j, based on the Gaussian distance decay function G(t) kj , T j ), at the response time threshold T j Within the range, the population Pop at each demand point k k By performing distance-weighted summation, we can obtain the potential demand competition intensity D of emergency station j. j : Among them, D j Pop represents the sum of the population at each demand point within the response time threshold range, after time decay weighting; k t represents the population value at demand point k; kj T represents the dynamic travel time between demand point k and emergency station j. j The response time threshold is the corresponding response time; Gaussian distance decay function G(t) kj , T j ) is defined as: Where e is the natural constant; when t kj ≤T j At that time, the Gaussian distance decay function G(t) kj , T j ) Take values ​​according to the above formula; when t kj >T j , G(t kj , T j Take 0; S3. For any demand point i and any emergency medical station j, calculate the overall attractiveness of emergency medical station j to demand point i. ij : ;in, λ is the queuing dimensionality reduction penalty factor; λ is the spatial impedance friction coefficient, which is a constant greater than 0; S4. Based on the two-step move search framework, and based on attractiveness ij It performs supply probability allocation and demand simulation flow, and outputs the spatial accessibility measurement results of each demand point i.

2. The method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model as described in claim 1, characterized in that, Before step S1, there are also: data cleaning and entity mapping steps, specifically: The system acquires pre-hospital emergency care service record data, standardizes the emergency care station names in the pre-hospital emergency care service records based on a preset station name mapping relationship, and removes duplicate vehicle records corresponding to each emergency care station based on vehicle identification. Based on the processed pre-hospital emergency care service records, the system determines the historical dispatch volume and the number of deduplicated vehicle identifications for each emergency care station, and associates the historical dispatch volume and the number of deduplicated vehicle identifications with the emergency care station spatial element layer to construct composite transportation capacity.

3. The method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model as described in claim 1, characterized in that, The vehicle configuration feature weighting coefficient α and the spatial impedance friction coefficient λ were determined through two-parameter sensitivity analysis. Candidate value sets for α and λ were set respectively, the candidate values ​​were combined, and medical emergency demand simulation was performed for each parameter combination. The target parameter combination was determined based on the evaluation index between the simulation results and historical valid vehicle dispatch records. For each set of parameter combinations, execute steps S1 to S4 to calculate the simulated emergency demand flow X allocated to each emergency station. i The effective pre-hospital emergency care workload Y at each emergency medical station i The Pearson correlation coefficient r between the simulated and actual values, and the root mean square error (RMSE) between the simulated and actual values, are given by the following formula: ; The root mean square error (RMSE) is calculated using the following formula: ; The Pearson correlation coefficient r was calculated for each parameter combination, and was used as the primary ranking indicator for the parameter combinations; the root mean square error (RMSE) was used as an auxiliary evaluation indicator for model consistency. The target parameter combinations were then used to measure the spatial accessibility of the corresponding datasets; based on the parameter sensitivity analysis results of the adopted datasets, α=0.5 and λ=0.5 were determined.

4. The method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model as described in claim 1, characterized in that, In step S2, the dynamic passage time t kj The base travel time t obtained through the map route planning interface amap,kj Delay, the time-segment travel time correction for the corresponding traffic scenario scenario Adding them together, we get t. kj =t amap,kj +Delay scenario Among them, the time-segmented travel time correction amount Delay scenario It is determined based on the difference between the actual response time of historical samples and the baseline travel time of the map road network.

5. The method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model as described in claim 4, characterized in that, Time-based travel time adjustment Delay scenario The correction values ​​are divided into morning peak hours, off-peak hours, evening peak hours, and late-night hours based on traffic scenarios: The travel time corrections for the morning peak hours, the combined off-peak hours, the evening peak hours, and the late night hours are -1.78 minutes, -2.01 minutes, -1.50 minutes, and -1.79 minutes, respectively. The travel time corrections are calculated based on historical samples from different traffic periods within the corresponding statistical period and are used to correct the dynamic travel time under different traffic scenarios.

6. The method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model as described in claim 1, characterized in that, In step S2, the response time threshold T j The response time threshold is set according to the area category corresponding to emergency station j; the response time threshold for emergency stations in the main urban area is set to 15 minutes, and the response time threshold for emergency stations in county or suburban areas is set to 35 minutes.

7. The method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model as described in claim 1, characterized in that, Also includes: The ablation comparison verification steps are as follows: Under the same dynamic road network environment and the same dataset, multiple degradation comparison models were constructed in parallel, and steps S1 to S4 were executed respectively. Model A: Stripping the number of duplicate vehicle identifiers in step S1, i.e., forcing the weight coefficient α of the vehicle configuration feature to be 0, at this time Supply_Base j =W history,j There are no nonlinear constraints on physical transport capacity; Model B: Remove the demand-side queuing dimensionality reduction penalty factor in step S2, i.e., force This is equivalent to eliminating all congestion and queuing issues caused by high population density at various stations. Model C: Simultaneously removes both of the above, i.e., forces the weight coefficient α of the vehicle configuration feature to be 0, and ; By comparing the stepwise drop in the Pearson correlation coefficient r of each degraded model and the complete model across all time periods and weather conditions, the non-obviousness of the synergistic enhancement effect between supply-side composite capacity and demand-side queuing penalty is quantitatively verified.

8. The method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model as described in claim 1, characterized in that, In step S4, the supply and demand allocation specifically includes: Supply allocation: For each emergency medical station j, its combined transport capacity Supply_Base is allocated. j As the total service capacity of the site, calculate the sum of the comprehensive attractiveness of demand points i within the threshold coverage area of ​​site j. Calculate the supply-demand ratio ; Demand Acquisition: For each demand point i, iterate through all values ​​at threshold T. j For emergency medical service stations j within the specified range that are generally attractive to the target area, the supply-demand ratios of all stations at that target area are summed according to their overall attractiveness weights to obtain the final spatial accessibility score for that target area. The A i The value represents the comprehensive emergency accessibility of the spatial unit where the demand point is located.

9. The method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model as described in claim 2, characterized in that, The comprehensive attractiveness calculation between demand points and emergency stations in a single instance is performed using a matrix or grouped vectorization method to reduce the computational overhead caused by iterative calculations. The specific running time is determined based on the number of demand points, the number of emergency stations, the number of effective road network relationships, and the configuration of computing equipment.

10. The method for measuring the accessibility of emergency medical services based on a capacity-demand bidirectional optimization model as described in claim 3, characterized in that, The Pearson correlation coefficient r, significance level p, and root mean square error RMSE were calculated between the simulated demand of each emergency medical station and the number of historical valid dispatch records under different traffic periods. The calculation results were used as the basis for evaluating model parameters and verifying model consistency.

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