Method and device for evaluating the system reliability of stochastic ambulance allocation rescue network

Abstract

The present invention discloses a method for evaluating the system reliability of a stochastic ambulance allocation rescue network, a processor is utilized to process the following steps including constructing a network topology having network nodes accessible to ambulances, multiple rescue paths connecting various network nodes, and the travel time of each rescue path, listing all rescue paths and patient information of the network topology, constructing a multi-level probability table of the number of ambulances in each fire station, and multi-level travel time and corresponding probability table of individual rescue routes, and calculating the combined upper bound vector of the network topology that successfully rescued all injured patients within the rescue time limit. The combined upper bound vector is used to calculate the system reliability.

Description

[Technical Field]

[0001] This invention relates to system reliability assessment, and in particular to a method and apparatus for ambulance dispatch. [Previous Technology]

[0002] In recent years, due to the increasing development, utilization, and destruction of land and Earth resources by humankind, extreme weather phenomena have intensified, leading to a significant increase in the frequency of natural disasters worldwide and causing more severe damage. These disasters include earthquakes, floods, droughts, and forest fires, and their impact is expanding. According to statistics from the U.S. National Oceanic and Atmospheric Administration (NOAA) in 2023, the average frequency of disaster events in the United States over the past five years has increased by 225% compared to the average of the past 40 years, with more than 100 disasters occurring annually. These disasters cause enormous losses to people's lives and property and bring high post-disaster reconstruction costs. Because natural disasters are often difficult to predict, how to quickly formulate effective rescue operations after a disaster to reduce casualties has become an important issue. However, in the past, the evaluation of rescue operation performance lacked comprehensive quantitative indicators, making it difficult for rescue commanders to make consistent and appropriate decisions based on standardized decision-making indicators.

[0003] Taiwan is located in the Circum-Pacific Seismic Belt and lies along the main path of typhoons in the western Pacific, making it prone to frequent natural disasters. Furthermore, Taiwan's distinctive topography—small land area, dense population, high mountains, and swift-flowing rivers—coupled with intensive land development, makes it more susceptible to severe disasters. For example, the Chi-Chi earthquake that struck Taiwan on September 21, 1999, caused widespread building collapses, bridge collapses, and road deformation, ultimately resulting in 2,455 deaths and over 8,000 injuries. In addition, the strong earthquake that struck Hualien on April 3, 2024, although its epicenter was near the coast, reached a magnitude of 7, causing damage to numerous buildings in Hualien City and resulting in 18 deaths and 1,155 injuries. Traffic disruptions and localized power outages further hampered rescue efforts, highlighting once again Taiwan's vulnerability to natural disasters. In these disaster relief operations, due to the need to consider the condition of the injured, the extent of road damage, and limited medical resources, fire stations in the area are often unable to complete the rescue of all the injured within the set limits, which may lead to the death of the injured due to the inability to receive timely medical treatment.

[0004] Since the systems and methods provided by the prior art do not take into account the difficulties that ambulances may encounter when traveling on roads due to road damage or other factors during disaster relief, as well as uncertainties such as the survival rate of the injured, the present invention was developed. [Summary of the Invention]

[0005] To improve upon the shortcomings of prior art, according to one aspect of the present invention, the present invention discloses a method for evaluating the system reliability of a random ambulance dispatch and rescue network as follows: constructing a network topology, including network nodes accessible to ambulances, multiple rescue paths connecting individual network nodes, and the travel time of each rescue path; listing all rescue paths and patient information of the network topology, constructing a multi-order probability table of the number of ambulances in each fire station, and a multi-order travel time and corresponding probability table for individual rescue paths; calculating the combined upper bound vector of the network topology for successfully rescuing all patients within the rescue time limit; and calculating the system reliability using the combined upper bound vector.

[0006] In one embodiment, the above-described method for evaluating a random ambulance dispatch and rescue network further includes evaluating the performance of the random ambulance dispatch and rescue network based on the results of system reliability, and making corresponding rescue decisions based on changes in system reliability. The network nodes include at least a plurality of nodes consisting of a plurality of fire stations, a plurality of affected areas, and triage stations.

[0007] In one embodiment, the combined upper bound vector is obtained through the following steps: calculating the rescue time based on a given patient survival rate; enumerating all candidate solutions for patient configuration based on the number of minor and severe injuries at each patient point in a complex affected area; obtaining feasible ambulance configurations and corresponding patient configurations under different ambulance number scenarios; calculating candidate solutions for the upper bound vector based on the ambulance configuration and the patient configuration, and thereby deriving the aforementioned combined upper bound vector. The steps of obtaining feasible ambulance configurations and corresponding patient configurations include: enumerating possible candidate solutions for ambulance configurations; obtaining feasible ambulance configuration solutions and corresponding patient configuration solutions through a screening process. The screening process can remove infeasible ambulance configurations when the ratio of the number of patients to the number of ambulances is greater than the constraint of the number of trips required for ambulances to travel without road damage.

[0008] In one embodiment, the steps of calculating candidate solutions for the upper bound vector and obtaining the combined upper bound vector include: using the number of minor and severe injuries and the number of ambulances to calculate the number of round trips required for each ambulance on individual complex rescue routes; generating pseudo-time vectors on individual complex rescue routes within a time limit; converting the generated pseudo-time vectors into time vectors according to a time probability table; and combining the time vectors of different complex affected areas into the combined upper bound vector.

[0009] In one embodiment, the steps of calculating the reliability of the system include: removing duplicate terms and non-maximum terms from the combined upper bound vector to obtain a complex number of upper bound vectors; calculating the success probability under different ambulance configuration scenarios using the obtained complex upper bound vectors and the recursive disjoint sum method (RSDP); and summing all possible scenarios using conditional probability to calculate the reliability of the system.

[0010] Another objective of this invention is to disclose a device for evaluating the system reliability of a random ambulance dispatch and rescue network, including a memory electrically connected processor for storing the random ambulance dispatch and rescue network and an algorithm. The processor executes the algorithm to obtain the system reliability of the random ambulance dispatch and rescue network. The algorithm performs the following steps through the processor: defining a network topology of the random ambulance dispatch and rescue network, wherein the network topology includes network nodes that ambulances can access, a plurality of rescue paths connecting each individual network node, and the travel time of each plurality of rescue paths; listing all rescue paths of the network topology, patient information, constructing a multi-order probability table of the number of ambulances in each fire station, and a multi-order travel time and corresponding probability table for each plurality of rescue paths; calculating the combined upper bound vector of the network topology for successfully rescuing all patients within the rescue time limit; and calculating the system reliability using the combined upper bound vector.

[0011] In one embodiment, the network nodes mentioned above include at least a plurality of nodes consisting of a plurality of fire stations, a plurality of affected areas and triage stations.

Implementation Method

[0012] This invention will be described in detail here with reference to specific embodiments and their viewpoints. Such descriptions are for illustrative purposes only and are not intended to limit the scope of the invention. Therefore, in addition to the specific and preferred embodiments described in the specification, the invention can also be widely implemented in other different embodiments. The following describes the implementation of the invention through specific embodiments. Those skilled in the art can easily understand the effectiveness and advantages of the invention from the content disclosed in this specification. Furthermore, the invention can also be used and implemented through other specific embodiments, and the various details set forth in this specification can be applied based on different needs, and various modifications or changes can be made without departing from the spirit of the invention.

[0013] This invention discloses a stochastic ambulance allocation rescue network (SAARN), which constructs the stochastic ambulance allocation network as a network topology and stores it in a readable medium. The method for constructing the network topology includes inputting nodes that ambulances can access, rescue routes connecting each node, and travel time for each rescue route. A quantitative indicator is proposed to assist rescue commanders in evaluating the effectiveness of the SAARN in real time after a disaster, serving as a basis for decision-making in rescue operations. In the SAARN, ambulance routes and connecting points are considered as transmission edges and nodes. Roads may be affected by building collapses, bridge damage, and road deformation, causing the travel time required for ambulances to traverse these roads to exhibit multi-level characteristics. Furthermore, at the time of a disaster, the number of available ambulances at fire stations may be uncertain due to dispatch or maintenance, also exhibiting a multi-level state.

[0014] In the face of uncertain disaster situations, rescue commanders often find it difficult to effectively measure the effectiveness of rescue operations and establish unified rescue standards. Over-reliance on the commander's personal experience in decision-making may lead to inconsistent or overly subjective judgment criteria. Therefore, this invention proposes to construct a SAARN using network analysis techniques and store it in a readable medium. The device includes a processor, memory connected to the processor for storing the SAARN, and an algorithm. The processor executes the algorithm to calculate the system reliability of the SAARN, i.e., the probability that the SAARN can successfully rescue all injured persons while meeting a given patient survival rate. This quantitative indicator helps rescue commanders allocate and configure fire station resources based on a grasp of the risks. Simultaneously, by setting a system reliability threshold as a standard for measuring rescue operations, rescue commanders can adjust rescue operations in a timely manner based on changes in system reliability under different rescue timeframes and patient numbers to ensure the feasibility of rescue operations. This ultimately aims to improve the responsiveness and efficiency of rescue operations, making the rescue process more scientific, quantitative, and standardized.

[0015] The system reliability method and apparatus provided by this invention can be used to assess the status of a post-disaster emergency rescue system, evaluate the current performance of the system in a data-driven manner, and provide rescue commanders with the ability to consolidate the system status and manage system risks. Furthermore, rescue commanders can use this method and apparatus to convert all calculated ambulance configuration plans into a set of data vectors, and then generate configuration plans tailored to different rescue needs based on the algorithms stored in the apparatus. In emergency rescue systems, the travel time required for ambulances along various roads is uncertain due to disaster damage; similarly, because the time and location of a disaster cannot be accurately predicted, the ambulance resources within fire stations will also have multiple possibilities (i.e., multiple states). Furthermore, the extent of post-disaster damage and the urgency of emergency rescue will fluctuate significantly depending on various external factors such as disaster intensity, road damage, and pre-disaster preparedness. Therefore, to immediately establish a comprehensive emergency rescue system after a disaster, the system reliability proposed in this invention can be used as a data indicator to evaluate the effectiveness of the rescue system, enabling effective allocation of rescue resources and the formulation of relevant rescue decisions, ultimately achieving the goal of successfully rescuing all the injured under acceptable risk. The method and apparatus of this invention can provide rescue commanders with a quantifiable performance indicator to measure the overall efficiency of rescue operations with limited ambulance resources, providing a basis for decision-making regarding rescue route selection, ambulance dispatch, and rescue timeline planning. If acceptable standards cannot be met, the rescue commander can request support from nearby fire stations to plan rescue operations and improve rescue efficiency, achieving effective understanding of the rescue situation and risk management.

[0016] Multistate networks are real-world systems such as transportation systems, communication systems, supply chain systems, and emergency rescue systems. In emergency rescue systems established in response to disasters, this invention constructs a network topology for the nodes and paths involved in the emergency rescue system, including nodes accessible to ambulances, multiple rescue paths connecting the nodes, and the travel time for each rescue path. Through the construction of the above network topology, the emergency rescue system can quickly analyze and calculate the travel efficiency of each rescue path, thereby more accurately assessing the expected time for the ambulance to reach the patient.

[0017] This invention will consider different degrees of road damage, assess the travel time required for each road under normal conditions, minor damage and severe damage, construct a post-disaster emergency rescue system as a multi-level rescue network, calculate the upper bound vector of the network to successfully transport all the injured to the hospital within the rescue time limit, and calculate the system reliability through the upper bound vector, that is, the probability that the emergency rescue system will successfully rescue all the injured within the rescue time limit. The system reliability can be further used as the decision basis for rescue route selection, ambulance dispatch and rescue time limit planning.

[0018] This invention discloses an algorithm for evaluating the system reliability of a Random Ambulance Dispatch and Rescue Network (SAARN). System reliability is defined as the probability that the SAARN successfully rescues all injured persons under a given patient survival rate constraint. A typical rescue operation involves dispatching ambulances from the fire station to various affected areas, then transporting all injured persons to triage stations (e.g., hospitals) for initial treatment. To evaluate the performance of the rescue operation, the SAARN is constructed using a network topology to represent transportation. Then, the system reliability is evaluated using the concept of an upper bound vector, which represents the maximum travel time of each transmission edge to achieve a survival rate s while satisfying the number of injured persons D to be rescued.

[0019] The following lists the symbols and related descriptions used in the network model construction and algorithm of the Random Ambulance Dispatch and Rescue Network (SAARN) mentioned in this invention: n Number of roads (transmission edges (arcs)). ai The i-th transmission edge, i = 1, 2, …, n. A The set of transmission edges, denoted by {ai | i = 1, 2, …, n}. ti,, ti The travel time of ai corresponding to the initial state, minor injury, and severe injury, i = 1, 2, …, n. pi,, p iai The probability of ai under the initial state, minor injury, and severe injury, i = 1, 2, …, n. s Expected survival rate in the rescue operation. T The rescue time limit in the rescue operation. m Number of affected areas. Dd j is the number of injured in the j-th affected area, denoted by (dj | j = 1, 2, …, n). ε The number of all possible scenarios for the number of ambulances that can be called. B represents the number of ambulances that can be called in scenario l, where l = 1, 2, …, n. C represents the set of ambulances that can be called in all possible scenarios, denoted by {bl|l = 1, 2, …, ε}. D represents the probability of the number of ambulances that can be called in scenario l. E represents the set of probabilities corresponding to the state of bl, denoted by {ρl|l = 1, 2, …, ε}. F represents the number of pseudo-ambulances cj assigned to the j-th affected area, where j = 1, 2, …, n. G represents the pseudo-allocation candidates, denoted by (cj|j = 1, 2, …, n). Ω represents the set of pseudo-allocation candidates l with bl ambulances, where l = 1, 2, …, ε. M represents the set of transport edges on the rescue path from the fire station (FS) to the j-th affected area, where j = 1, 2, …, m. The set of transport edges along the rescue path from the j-th affected area to the Casualty Collection Point (CCP), where j = 1, 2, …, m. γj represents the number of journeys required to reach the j-th affected area. Γ represents the vector of journeys required to reach all affected areas, denoted by Γ = (γj|j = 1, 2, …, m). Zj represents the pseudo-travel time vector required to reach the j-th affected area, denoted by (zj|ai), where j = 1, 2, …, m. The set of pseudo-travel time vectors required for Zj to reach the j-th affected area is denoted by {Zj|j = 1, 2, …, m}.Xj is the travel time vector required to reach the j-th affected area, j = 1, 2, …, m. Xj is the set of travel time vectors required to reach the j-th affected area, denoted by {Xj|j = 1, 2, …, m}. X is the set of combined vectors of all affected areas. Ψl is the set of maximum travel time vectors, including the travel time of the transport edge with bl ambulances capable of transporting all the injured. f is the number of fire stations. cq,j is the number of ambulances allocated from the q-th fire station (FS) to the j-th affected area, q = 1, 2, …, f. is the number of ambulances that the primary fire station can call upon in scenario l. is the number of ambulances that the backup fire station can call upon in scenario l. D is the set of the number of minor and severe injuries in the j-th affected area, denoted by {(,)|j}. uminor; usevere is the number of minor / severe injuries that can be immediately transported by an ambulance. νj,q: The number of lightly or severely injured patients assigned to the j-th affected area from the q-th fire station (FS). γq,j: The number of journeys required from the q-th fire station (FS) to the j-th affected area. (D, s, f)-UB: The maximum rescue vector, representing the travel time for each transport edge with f fire stations (FS) to successfully rescue all patients D and achieve survival rate s. RD,s,f: The probability of successfully satisfying the set of patients D and achieving survival rate s using ambulances at the primary and backup fire stations (FS).

[0020] Assume that X = (x1, x2, ..., xn) and Y = (y1, y2, ..., yn) are both rescue vectors. The vector operations are calculated according to the following rules: (1) X ≧ Y: (x1, x2, …, xn) ≧ (y1, y2, …, yn) if and if xi ≧ yi, for i = 1, 2, …, n. (2) X > Y: (x1, x2, …, xn) > (y1, y2, …, yn) if and if X ≧ Y and xi > yi, for i = 1, 2, …, n. Construct a multi-level rescue network

[0021] Following a disaster, such as an earthquake, the first step in planning rescue operations is to confirm the number of casualties and the location of triage stations (CCPs). The injured will gather at designated locations near the disaster area, awaiting ambulance transport to CCPs for initial treatment. Rescue commanders must assess the number of casualties in each affected area (disaster zone) and allocate limited ambulance resources to transport them, while ensuring a certain survival rate. Furthermore, the uncertainty of traffic conditions on every road and the availability of ambulances at fire stations during earthquakes or natural disasters further complicates this task.

[0022] To evaluate the performance of rescue operations, this invention first establishes a Random Ambulance Dispatch Rescue Network (SARRN), denoted as G≡(A, M, N), providing detailed data for each road. The set A = {ai | i = 1, 2, …, n} represents the set of roads used to transport the injured, where ai represents a specific road. The travel time X = (xi | i = 1, 2, …, n) along each road ai is considered as a multi-level state, taking into account different degrees of damage in the disaster scenario. The set M = {Mi | i = 1, 2, …, n}, where Mi represents the maximum travel time for each road ai. Additionally, N = {Nj | j = 1, 2, …, m} represents the set of affected areas. The Random Ambulance Dispatch Rescue Network (SARRN) uses transmission edges (arcs) representing roads between fire stations, affected areas, and triage stations (CCPs) to describe ambulance transport. Nodes represent the connection between two transmission edges. For example, Figure 1 shows the relative positions of the wounded points (10a, 10b), the triage station (20), and the fire station (30a, 30b) when a disaster occurs.

[0023] Figure 2 is a random ambulance dispatch rescue network (SARRN) constructed for the situation in Figure 1, i.e., the network diagram of the emergency rescue system. The random ambulance dispatch rescue network (SARRN) satisfies the following assumptions: (1) All injured persons will gather at disaster area assembly points (e.g., injured person point 1, injured person point 2) and wait for ambulances. (2) The travel time of each transmission edge is measured in seconds, ensuring that the total travel time of all transmission edges is an integer value. (3) The travel times of different ai are statistically independent. (4) The specified survival rate refers to the minimum survival rate of all injured persons as a group rather than each individual. The actual survival rate of each injured person may vary depending on the order in which they are transported to the triage station (CCP).

[0024] Figure 2 uses a network topology to structure the relative positions of the injured and hospitals (triage stations), where ai represents the route traveled by ambulances. Based on this information, Table 1 shows the distribution of minor and serious injuries at each patient location during the disaster; Table 2 presents the number of ambulances available at different fire stations and their corresponding probabilities, represented in multi-level states. In addition, the multi-level travel time and corresponding probability of each route ai are obtained from historical data, as shown in Table 3, and the rescue routes connecting fire stations (as shown in Figure 2, including main fire stations and backup fire stations) with the injured and with the triage stations are represented by and , respectively. [Table 1]: Patient Information Affected areas () 1 (6, 3) 2 (9, 2) [Table 2]: Probability of the Number of Ambulances at Each Fire Station Main fire stations backup fire station Number of ambulances probability Number of ambulances probability 3 0.05 1 0.75 4 0.20 2 0.25 5 0.75 [Table 3]: Parameters of the Construction Time Probability Table a i Travel time (seconds) probability a i Travel time (seconds) probability a1 twenty four 0.75 a 10 51 0.75 25 0.125 52 0.08 26 0.125 53 0.17 a2 21 0.75 a 11 43 0.75 22 0.08 44 0.08 23 0.17 45 0.17 a3 13 0.75 a 12 38 0.90 14 0.08 39 0.03 15 0.17 40 0.07 a4 31 0.83 a 13 38 0.90 32 0.17 39 0.03 a5 50 0.75 40 0.07 51 0.125 a 14 18 0.83 52 0.125 19 0.17 a6 52 0.83 a 15 20 0.90 53 0.17 21 0.75 a7 26 0.75 22 0.125 27 0.08 a 16 25 0.125 28 0.17 26 0.08 a8 26 0.90 27 0.17 27 0.03 a 17 8 0.90 28 0.07 9 0.03 a9 52 0.83 10 0.07 53 0.17

[0025] To obtain the feasibility of the above-mentioned emergency rescue system being able to rescue 6 lightly injured () and 3 seriously injured () from two injury points (injury point 1 and 2) under the condition that the patient survival rate s is 0.75, and to rescue 9 lightly injured () and 2 seriously injured () from injury point 2, the present invention will complete the system reliability calculation through a two-stage procedure. The above two-stage procedure includes, firstly, obtaining the upper bound vector (D, f, s)-UBs (or the maximum rescue vector) for rescuing all patients under the constraints set by the commander for each road, then calculating the success probability under each scenario, and finally summing them into the system reliability. The complete steps are as follows: I. Obtaining the upper bound vector (D, f, s)-UBs (using the first algorithm) Step (1). Calculate the rescue time T according to the given patient survival rate s using (Mathematical Formula 1), where S0 is the initial survival rate and λ represents the decay rate of survival ability. [Mathematical Formula 1] Step (2). Based on the number of light and severe injured patients at each injury site, enumerate all possible patient deployment candidate solutions using (Mathematical Formula 2). Here, and represent the number of light / severe injured patients assigned to the j-th affected area by ambulances departing from the q-th fire station (FS), respectively. [Mathematical Formula 2] Step (3). Obtain feasible ambulance deployments and corresponding patient deployments under different ambulance numbers. First, in step (3.1), enumerate possible ambulance deployment candidate solutions using (Mathematical Formula 3). Here, represents the k-th pseudo-allocation candidate solution for ambulances from the main fire station to the j-th affected area; represents the k-th pseudo-allocation candidate solution for ambulances from the backup fire station to the j-th affected area; is the number of ambulances that can be called up by the main fire station in scenario l; is the number of ambulances that can be called up by the backup fire station in scenario l. [Mathematical Formula 3] Next, in step (3.2), the screening process proposed in this invention, when the ratio of the number of injured to the number of ambulances (equivalent to the number of ambulance trips required) is greater than the constraint, shows that the allocation candidates cannot transport all the injured within the rescue time and are removed because they are infeasible. Here, Si is the travel time required at transmission edge i in the most optimistic case (no road damage), and represents the number of trips required in the most optimistic case (no road damage). Therefore, the number of trips (the number of round trips required for ambulances) for each allocation candidate should be less than or equal to this value. This screening process is used to remove infeasible candidate solutions. Through (Mathematical Formula 4), infeasible ambulance allocation and injured candidate solutions can be removed simultaneously to obtain feasible ambulance and corresponding injured configuration solutions.[Mathematical Formula 4] Step (4). Calculate the candidate solutions for the upper bound vector (D, f, s)-UBs based on the feasible ambulance and patient configuration obtained in step (3). First, in step (4.1), based on the principle of three minor injuries sharing one ambulance and serious injuries traveling alone in an ambulance, calculate the number of round trips required for each ambulance on each rescue route using the number of minor and serious injuries (dminor, dsevere) and the number of ambulances cq,j, as shown in (Mathematical Formula 5). Whereinor and usevere represent the number of minor / severe patients who can be immediately transported by an ambulance; and represent the number of minor / severe patients assigned to the j-th affected area by the ambulance departing from the q-th fire station (FS). γq,j is the number of trips required from the q-th fire station (FS) to the j-th affected area. [Mathematical Formula 5] Following step (4.2), a pseudo-time vector is generated based on (Mathematical Formulas 6 and 7) to represent the total time T spent on each rescue path. Here, represents the set of transmission edges on the rescue path from the fire station (FS) to the j-th affected area; represents the set of transmission edges on the rescue path from the j-th affected area to the casualty collection point (CCP). [Mathematical Formula 6], for all i [Mathematical Formula 7] In step (4.3), the pseudo-time vector Zq,j generated above is converted into a travel time vector Xq,j according to the time probability (Mathematical Formula 8). , for all i [Mathematical Formula 8] where is the possible travel time of ai under different degrees of damage (severe damage, minor damage, no damage). In step (4.4), the upper bound vectors (travel time vectors Xq,j) of all rescue paths in the affected area obtained in step (4.3) are merged (Mathematical Formula 9) to obtain the combined upper bound vector X that can complete the rescue within the rescue time limit in the entire rescue operation. [Mathematical Formula 9] By performing the above four steps for all possible ambulance numbers in the emergency rescue system, we can obtain the combined upper bound vectors that satisfy the specified survival rate under different scenarios, as shown in Table 4. This table presents the combined upper bound vectors that satisfy the given conditions under this scenario (5 ambulances in the jurisdiction and 2 ambulances at the backup fire station). [Table 4]: Combined upper bound vectors obtained under the scenarios of 5 ambulances and 2 ambulances. Ψ 5,2 {(26, 53, 28, 40, 23, 15, 26, 51, 38, 8, 22, 19, 27, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 28, 51, 38, 8, 22, 19, 27, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 28, 53, 38, 8, 22, 19, 27, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 28, 51, 40, 8, 22, 19, 27, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 28, 53, 39, 8, 22, 19, 25, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 28, 52, 40, 8, 22, 19, 25, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 26, 53, 40, 8, 22, 19, 27, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 27, 53, 40, 8, 22, 19, 25, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 28, 53, 38, 10, 22, 19, 26, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 28, 51, 40, 10, 22, 19, 26, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 28, 51, 39, 10, 22, 19, 27, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 27, 53, 39, 8, 22, 19, 27, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 26, 53, 40, 9, 22, 19, 27, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 28, 52, 39, 10, 22, 19, 26, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 27, 52, 40, 10, 22, 19, 26, 32, 52, 53, 45) (26, 53, 28, 40, 23, 15, 27, 52, 40, 9, 22, 19, 27, 32, 52, 53, 45)} II. Calculating System Reliability (Using the Second Algorithm) Step (1). Remove duplicate terms and non-maximal combination upper bound vectors from X to obtain (D, f, s)-UBs. Step (2). Using the obtained (D, f, s)-UBs, calculate the success probability under different scenarios using the existing set algorithm (Mathematical Formula 10), as shown in Table 5. [Mathematical Formula 10] [Table 5]: Success Probability of Rescue under Different Scenarios b l Success rate of rescue 3 1 0.1297 2 0.4283 4 1 0.6761 2 0.9785 5 1 1.0000 2 1.0000 Step (3). Compile all possible scenarios using conditional probability and calculate the system reliability, referring to (Mathematical Formula 11). , ===[Mathematical Formula 11] Through the above steps, the system reliability can be calculated to be 0.91058, which means that in this emergency rescue system, given the patient survival rate and a backup fire station, the probability of successfully transporting all patients within the time limit is 0.91058. System reliability can be provided to the rescue commander as a performance indicator to evaluate system effectiveness, and appropriate management decisions can be made based on the changes in system reliability calculated under different resource allocations, such as the number of fire stations participating in the rescue, ambulance assignment, and the expected patient survival rate, etc. Data-driven management methods can effectively reduce the risk costs brought about by post-disaster uncertainty and further establish appropriate decision-making methods.

[0026] Based on the above description of the first algorithm, the second algorithm, and the actual numerical examples of applying the algorithms, and referring to Figure 3, a flowchart of the method for evaluating the system reliability of the random ambulance dispatch rescue network proposed in this invention is summarized. This invention considers the number of ambulances that one or more fire stations can provide and the probability of ambulance travel time on each route for the random ambulance dispatch rescue network. Using the aforementioned first and second algorithms, the processor 405 (referring to Figure 4) accesses and executes the first and second algorithms to simultaneously calculate all feasible allocation candidates and system reliability, thereby evaluating network performance. The method for evaluating the system reliability of the random ambulance dispatch rescue network includes the following steps performed by the processor 405 (referring to Figure 4): Step S30: Construct the random ambulance dispatch rescue network as a network topology, including nodes that ambulances can access, multiple rescue paths connecting each node, and the travel time of each rescue path. Step S31: Based on the above network topology, list the number of available ambulances and all rescue routes in each fire station, and construct a multi-order probability table of the number of ambulances in each fire station and a multi-order travel time and corresponding probability table of individual rescue routes. Step S32: Calculate the upper bound vector (D, f, s)-UBs (maximum rescue vector) for each rescue route to meet rescue requirements; this step includes (1) calculating the rescue time based on the given patient survival rate; (2) enumerating all possible patient configuration candidate solutions based on the number of each patient point; (3) obtaining feasible ambulance configurations and corresponding patient configurations under different ambulance numbers, including (i) enumerating all possible ambulance configuration candidate solutions, and (ii) obtaining feasible ambulance and corresponding patient configuration solutions according to a screening process; (4) calculating the upper bound vector (D, f, s) based on the feasible ambulance configurations and corresponding patient configurations obtained above. The candidate solutions (i.e., the maximum travel time vector) of s)-UBs include (i) calculating the number of round trips required for each ambulance on each rescue route using the number of light and severe injuries and the number of ambulances, (ii) generating a pseudo-time vector of the total time spent on each rescue route, (iii) converting the pseudo-time vector generated above into a time vector according to a time probability table, and (iv) combining the time vectors of the different affected areas to obtain a combined upper bound vector of the rescue operation that can be completed within the rescue time limit.Step S33: Calculate the system reliability, which represents the probability that the Random Ambulance Dispatch and Rescue Network (SAARN) will successfully rescue all patients within the rescue time limit. This step includes (1) removing duplicate terms and non-maximum combined upper bound vectors from the combined upper bound vector X to obtain the upper bound vector (D, f, s)-UBs; (2) using the obtained upper bound vectors (D, f, s)-UBs, calculating the success probability under different scenarios using the existing set algorithm (Mathematical Formula 10); and (3) summarizing all possible scenarios using conditional probability to calculate the system reliability. Step S34: Based on the above system reliability results, evaluate the network performance and make corresponding rescue decisions based on the changes in system reliability, such as rescue route selection, ambulance dispatch, and rescue time limit planning.

[0027] This invention mainly proposes a method for evaluating the performance of the corresponding emergency rescue system for the Random Ambulance Dispatch and Rescue Network (SAARN). The emergency rescue system is constructed into a network topology that includes nodes that ambulances can access, rescue paths connecting each node, and travel time for each rescue path. This allows the emergency rescue system to evaluate and calculate the travel efficiency of each rescue path. By evaluating the travel time required for each road under normal conditions, minor damage, and severe damage, a post-disaster emergency rescue system is constructed into a multi-level rescue network. The upper bound vector of the network's ability to successfully transport all patients to the hospital within the rescue time limit is calculated, and the system reliability, i.e., the probability that the emergency rescue system successfully rescues all patients within the rescue time limit, is calculated through the upper bound vector.

[0028] In this invention, system reliability is obtained using the Recursive Disjoint Summation Method (RSDP). Please refer to Figure 4, which shows a schematic diagram of a computing device used to evaluate the system reliability of the Random Ambulance Dispatch Rescue Network (SAARN) in an embodiment of the present invention, i.e., a computing device 400 for predicting system reliability. As shown in the figure, the computing device 400 for predicting system reliability applied in this invention may include at least an input device 401, a memory 403, a processor 405, and an output device 407. The input device 401 is electrically connected to the memory 403. The input device 401 may include various input interfaces of a computer device or a file receiving device. It can receive information about the architecture of the nodes and transmission edges of the Random Ambulance Dispatch Rescue Network (SAARN) 4031 (i.e., the SAARN network topology 4031) through the input device 401 and store it in the memory 403. Memory 403 can store the algorithm for the system reliability calculation method developed for the aforementioned Random Ambulance Dispatch and Rescue Network (SAARN) 4031, including a first algorithm 4032 and a second algorithm 4033, which can calculate the accurate system reliability (RD,s) using the process steps disclosed in the foregoing embodiments.

[0029] In a preferred embodiment, memory 403 may include read-only memory, flash memory, disk or cloud database, etc.

[0030] In a preferred embodiment, the processor 405 is electrically connected to the memory 403. The processor 405 includes a central processing unit, a video processor, a microprocessor, etc., and may include a multi-core processing unit or a combination of multiple processing units. The processor 405 can access the random ambulance dispatch rescue network (SAARN) 4031 in the memory and the first algorithm 4032 and the second algorithm 4033 for reliability calculation methods to perform system reliability estimation.

[0031] In a preferred embodiment, the result of the calculation by the processor 405 can be output by the output device 407. The output device 407 can be a display that presents the calculation result, such as an LCD, LED or OLED display screen, or a wired / wireless network transmission device that transmits the calculation result to a remote user.

[0032] This invention aims at disaster relief and rescue, taking into account the difficulties that ambulances may encounter due to road damage and other factors when traveling on roads. It incorporates the uncertainty of road conditions into the calculation and adds the concept of patient survival rate. Rescue commanders need to ensure that the rescue strategy can improve the patient survival rate within the time limit, given that the probability of patient survival decreases over time. The performance indicators proposed in this invention aim to quantify the probability of successfully rescuing patients and help rescue commanders evaluate and adjust rescue operations. This invention has the following characteristics compared to previous technologies: (1) It constructs the emergency rescue system as a multistate network. For example, it considers different degrees of road damage and calculates the travel time of each road segment under normal, slightly damaged, and severely damaged conditions, reflecting the uncertainty caused by the disaster to the road, so that the travel time of each road segment presents a multistate state. (2) Expanding from deterministic factors such as fixed road damage levels and fixed ambulance speeds to uncertain factors, the degree of road damage and the probability of occurrence for each road segment are transformed into vehicle travel speeds, and the travel time and probability of occurrence for each road segment are calculated accordingly, presenting a multi-level state. (3) Proposing system reliability performance indicators to quantify the probability of successfully evacuating the injured within the time limit for rescue operations. Rescue commanders can adjust the system reliability threshold to determine whether it is necessary to increase the number of ambulances or change the rescue route, thereby flexibly planning a more comprehensive rescue strategy.

[0033] The above description is a preferred embodiment of the present invention. Those skilled in the art should understand that it is used to illustrate the present invention and not to limit the scope of the patent rights claimed by the present invention. The scope of patent protection shall be determined by the appended claims and their equivalent fields. Any modifications or refinements made by those skilled in the art without departing from the spirit or scope of this patent are equivalent changes or designs made under the spirit disclosed in the present invention and should be included in the scope of the following claims. [Simplified Explanation of the Diagram]

[0034] [Figure 1] shows an example of the relative positions of the injury site, triage station and fire station when a disaster occurs.

[0035] [Figure 2] shows the relative positions of the injured and the hospital using the network topology architecture of the present invention.

[0036] [Figure 3] shows a flowchart of the present invention for evaluating a random ambulance dispatch rescue network.

[0037] [Figure 4] shows a schematic diagram of the computing device of the present invention for evaluating a random ambulance dispatch rescue network.

Claims

1. A method for evaluating the system reliability of a random ambulance dispatch and rescue network, wherein the random ambulance dispatch and rescue network is constructed as a network topology and stored in a readable medium, and the following steps are performed by a processor: Constructing the network topology, including network nodes accessible to ambulances, multiple rescue paths connecting each network node, and the travel time of each of the multiple rescue paths; Listing all rescue paths, patient information, constructing a multi-order probability table of the number of ambulances in each fire station, and a multi-order travel time and corresponding probability table for each of the multiple rescue paths; Calculating a combined upper bound vector of the network topology for successfully rescuing all patients within the rescue time limit; and calculating the system reliability using the combined upper bound vector; wherein the performance of the random ambulance dispatch and rescue network is evaluated based on the system reliability results, and corresponding rescue decisions are made based on changes in the system reliability.

2. The method for assessing the system reliability of a random ambulance dispatch and rescue network as described in claim 1, wherein the network nodes include at least a plurality of nodes consisting of a plurality of fire stations, a plurality of affected areas, and triage stations.

3. The method for evaluating the system reliability of a random ambulance dispatch rescue network as described in claim 2, wherein the combined upper bound vector is obtained by the processor performing the following steps: calculating the rescue time based on a given patient survival rate; enumerating all candidate solutions for patient configuration based on the number of minor and severe patients at each patient point in the complex affected area; obtaining feasible ambulance configurations and corresponding patient configurations under different ambulance number scenarios; and calculating candidate solutions for the upper bound vector based on the ambulance configuration and the patient configuration, thereby deriving the aforementioned combined upper bound vector.

4. The method for evaluating the system reliability of a random ambulance dispatch network as described in claim 3, wherein the steps for obtaining feasible ambulance configurations and corresponding patient configurations include: Enumerate all possible candidate solutions for ambulance configuration; And through a screening process, feasible ambulance configuration solutions and corresponding patient configuration solutions are obtained.

5. The method for evaluating the system reliability of a random ambulance dispatch network as described in claim 4, wherein the screening process can remove infeasible ambulance configurations when the ratio of the number of injured to the number of ambulances is greater than the constraint of the number of trips required for ambulances to travel on roads without damage.

6. The method for evaluating the system reliability of a random ambulance dispatch and rescue network as described in claim 5, wherein the step of calculating the candidate solution of the upper bound vector includes: Using the number of patients with minor and severe injuries and the number of ambulances, calculate the number of round trips required for each ambulance on each of the multiple rescue routes; generate a pseudo-time vector within a time limit on each of the multiple rescue routes; convert the generated pseudo-time vector into a time vector according to a time probability table; and combine the time vectors of different affected areas into the combined upper bound vector.

7. The method for evaluating the system reliability of a random ambulance dispatch and rescue network as described in claim 6, wherein the steps for calculating system reliability include: Remove duplicate and non-maximum terms from the above combined upper bound vectors to obtain a complex number of upper bound vectors; Using the derived complex upper bound vectors, the success probability under different ambulance configuration scenarios is calculated using the recursive disjoint sum method (RSDP); and all possible scenarios are aggregated using conditional probability to calculate the reliability of the above system.

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