Emergency server site selection and scheduling method and device considering space-time queuing mechanism

Abstract

The invention provides an emergency server site selection and scheduling method and device considering a space-time queuing mechanism, and relates to the technical field of emergency rescue, and the method comprises the steps: constructing an optimization model of a server position and a scheduling priority, and replacing a nonlinear constraint through an auxiliary variable to obtain a converted linear constraint condition; constructing a target function, wherein the target of the target function is to minimize the fire loss; solving the target function under the constraint of the constraint condition according to an algorithm based on a Lagrangian relaxation framework so as to obtain the position and scheduling strategy of the server; and setting the servers according to the positions of the servers, and scheduling the servers according to the scheduling strategy. By constructing an optimization model and converting nonlinear constraints, optimization of server positions and scheduling strategies is realized, optimization problems in a traditional method are avoided, optimal configuration of the servers is realized by minimizing a target function of regional fire loss and solving by a Lagrange relaxation algorithm, and emergency response efficiency and system reliability are improved.

Description

Technical Field

[0001] The present application relates to the field of emergency rescue technology, and in particular to a method and device for selecting and scheduling an emergency server in consideration of a spatiotemporal queuing mechanism. Background Art

[0002] The general dispatch strategy for emergency servers is the principle of nearest dispatch, that is, deploying the nearest server as the primary responder.

[0003] Although this approach is widely adopted, research shows that it may not minimize average response time. This is because the nearest station and its service efficiency are often unable to cope with the high incidence of rescue incidents and service time, resulting in the need to dispatch additional resources, which in turn affects the efficiency and effectiveness of rescue. Summary of the invention

[0004] The present application aims to solve one of the technical problems in the related art at least to some extent.

[0005] To this end, the first purpose of the present application is to propose an emergency server site selection and scheduling method that takes into account the spatiotemporal queuing mechanism.

[0006] The second object of the present application is to provide a device.

[0007] The third objective of the present application is to provide an electronic device.

[0008] A fourth objective of the present application is to provide a computer-readable storage medium.

[0009] A fifth object of the present application is to provide a computer program product.

[0010] To achieve the above-mentioned purpose, the first embodiment of the present application proposes an emergency server site selection and scheduling method considering the spatiotemporal queuing mechanism, including:

[0011] Constructing an optimization model of server location and scheduling priority, and replacing nonlinear constraints in the optimization model with auxiliary variables to obtain converted linear constraints;

[0012] Constructing an objective function, wherein the objective of the objective function is to minimize fire losses;

[0013] Solving the objective function subject to the constraints according to an algorithm based on a Lagrangian relaxation framework to obtain the location and scheduling strategy of the server;

[0014] The servers are set according to the locations of the servers, and each server is scheduled according to the scheduling strategy.

[0015] The optimization model includes:

[0016] Steady-state equilibrium equation:

[0017]

[0018] In the formula, For the system in region m to be in state e m The probability of J m is the set of demand points in area m, and j is m index; is the arrival rate of demand point j in region m, is the status of server i in region m. If server i is busy, otherwise is the service rate of server i in region m, which follows a negative exponential distribution; Indicates whether there is a server at location i in region m. If there is a server at location i in region m, then Otherwise E m is the system state set consisting of all possible system states in region m, For the system in region m, the state The probability of is the system state transition variable. If the server completes the service in area m, the system state changes from e ′m Convert to e m ,but otherwise is the demand point j m The resulting system conversion variables, if the area m is due to demand point j m The occurrence demand causes the system state to change from e ′m Convert to e m ,but otherwise M is the service area set, indexed by m;

[0019] Among them, in formula (1) The location decision is described. Only when a site is built at this location, the service efficiency of this location is Otherwise, it is 0, which means that a server with a service efficiency of 0 is built at this location;

[0020] Server status constraints:

[0021]

[0022] Among them, formula (2) shows that the variable is a binary variable;

[0023] Precedence table indicator constraints:

[0024]

[0025] In the formula, is the priority table indicator. In region m, when server i m is the demand point j m When the qth responder is otherwise I m is the potential server set in region m, with i m Index; card(I m ) is the set I m The cardinality of the set I m The number of elements in

[0026] Among them, formula (3) shows that is a binary variable;

[0027] System state transition constraints:

[0028]

[0029] System state transition verification parameter constraints:

[0030]

[0031] In the formula, C is any sufficiently large positive number;

[0032] Among them, equations (4) and (5) indicate that the system state transition will only occur when it is feasible, that is, when When ′m and e m Only one server is different and all servers with higher priority than this server in the priority table are busy;

[0033] Server scheduling order uniqueness constraints:

[0034]

[0035] Demand point responder assignment uniqueness constraint:

[0036]

[0037] Among them, equations (6) and (7) guarantee the order of server scheduling and the uniqueness of the assignment of the qth responder of demand point j. Equation (6) ensures that server i has one and only one position in the priority list of demand point j, while equation (7) ensures that for demand point j, only one server is designated as the qth responder;

[0038] Normalized equation:

[0039]

[0040] Wherein, equation (8) ensures that the sum of the probabilities of all system states in region m is equal to 1.

[0041] Optionally, replacing the nonlinear constraints in the optimization model with auxiliary variables includes:

[0042] By substitution variables To replace and The product of

[0043] By substitution variables To replace and The product of

[0044] By substitution variables To replace and The product of .

[0045] Optionally, the transformed linear constraints include:

[0046] System state probability and server efficiency matching constraints:

[0047]

[0048] System state transition constraints:

[0049]

[0050] System state transition verification parameter constraints:

[0051]

[0052] The upper bound constraint of transition probability is:

[0053]

[0054] Consistency constraints between transition probability and state probability:

[0055] The non-negativity constraint of transition probability is:

[0056]

[0057] The lower bound constraint of transition probability is:

[0058]

[0059] Response priority matching constraints:

[0060]

[0061] Response priority order constraints:

[0062]

[0063] Response priority combination constraints:

[0064]

[0065] Server deployment and state probability matching constraints:

[0066] Server deployment status probability consistency constraints:

[0067] Non-negativity constraints on server deployment status:

[0068] The lower limit constraints of server deployment state:

[0069] Response priority binary constraints:

[0070]

[0071] Optionally, the objective function is:

[0072] Minimize:

[0073]

[0074] Among them, z is the total loss, that is, the fire loss, α s is the system saturation loss parameter, which is used to represent the loss caused by the inability to respond to fire due to system saturation; is the probability that all servers in region m are busy, Represents all demand points J in region m m The total demand fulfillment rate, α rf In response to the fire cost parameter, it is used to indicate the degree of influence of server traffic travel time delay on the extent of fire damage; is the arrival rate of demand point j in region m, Indicates which station should be dispatched for rescue in the current system state e; Represents the functional relationship between site response distance and fire loss.

[0075] Optionally, the constraint condition also includes:

[0076] Government budget constraints:

[0077]

[0078] Where F is the maximum number of servers that the budget can afford.

[0079] Optionally, solving the objective function under the constraints of the constraints according to the algorithm based on the Lagrangian relaxation framework to obtain the location and scheduling strategy of the server includes:

[0080] Set the initial number of servers to be deployed in each region R m And calculate the minimum total loss when each region fully builds servers Iteratively reduce the number of servers to minimize the total loss increment and update When the number of servers in all regions R m The solution ends when the sum is equal to the number of servers F in the total plan, and the initial feasible solution is output;

[0081] Integrating the government budget constraint and the Lagrange multiplier θ into the objective function, we get the relaxation problem. The new objective function of the relaxation problem is:

[0082] Minimize:

[0083]

[0084] Among them, the optimal value z of the new objective function for solving the relaxation problem LR (θ) needs to satisfy constraints (2), (3), (6) to (23), and (27). Formula (27) is a constraint on the Lagrange multiplier, requiring the Lagrange multiplier to be greater than or equal to 0, which can be expressed as:

[0085] θ ≥ 0 (27)

[0086] The relaxation problem is decomposed into subproblems for each region and solved using a commercial optimization solver to obtain the Lagrangian relaxation solution, where the optimal value z of the new objective function is LR (θ) represents a lower bound of the original objective function;

[0087] Generate a feasible solution to the original problem based on the Lagrangian relaxation solution and calculate the upper bound z UB ;

[0088] The subgradient method is used to update the Lagrange multiplier, and the optimization is iteratively performed until the relative error of the upper and lower bounds drops below the preset threshold, and the target feasible solution is output as the final server location and scheduling strategy.

[0089] Optionally, also include:

[0090] The sub-problems of each region are expressed by equation (28):

[0091]

[0092] In the formula, z LR m (θ) is the optimal value in region m;

[0093] The objective function of each sub-problem is:

[0094]

[0095] In the formula, min represents the minimization function.

[0096] Optionally, the updating of the Lagrange multiplier by using a subgradient method includes:

[0097] The subgradient method is used to update the Lagrange multiplier θ, and θ is initially set to 0. In the kth iteration, θ is updated by equation (30), and the expression of equation (30) is:

[0098]

[0099] In the formula, θ k+1 is the Lagrange multiplier after k iterations, θ k+1 is the Lagrange multiplier at the kth iteration, ξ k is the step size for k iterations, which is updated by scaling parameter ρ. If Z LR If (θ) does not improve, the scaling parameter ρ is gradually adjusted downward;

[0100] Step length k The update formula is:

[0101]

[0102] In the formula, z LR,k (θ) is the optimal value of the new objective function after k iterations.

[0103] To achieve the above-mentioned purpose, the second embodiment of the present application proposes an emergency server site selection and scheduling device considering the time-space queuing mechanism, including:

[0104] A constraint condition acquisition module is used to construct an optimization model of server location and scheduling priority, and replace the nonlinear constraints in the optimization model with auxiliary variables to obtain converted linear constraints;

[0105] An objective function building module, used to build an objective function, wherein the objective of the objective function is to minimize fire losses;

[0106] a solving module, for solving the objective function under the constraints of the constraints according to an algorithm based on a Lagrangian relaxation framework to obtain the location and scheduling strategy of the server;

[0107] The scheduling module is used to set up the server according to the location of the server and schedule each server according to the scheduling strategy.

[0108] To achieve the above-mentioned purpose, the third aspect of the present application provides an electronic device, including: a processor, and a memory communicatively connected to the processor;

[0109] The memory stores computer-executable instructions;

[0110] The processor executes the computer-executable instructions stored in the memory to implement the method as described in any one of the first aspects.

[0111] To achieve the above-mentioned purpose, the fourth aspect embodiment of the present application proposes a computer-readable storage medium, in which computer-readable storage medium is stored computer execution instructions, and when the computer execution instructions are executed by a processor, they are used to implement the method as described in any one of the first aspects.

[0112] To achieve the above-mentioned purpose, the fifth aspect of the present application proposes a computer program product, which implements any method in the first aspect when executed by a processor.

[0113] The emergency server site selection and scheduling method, device, electronic device and storage medium that consider the spatiotemporal queuing mechanism provided in this application realize the optimization of server location and scheduling strategy by constructing an optimization model and converting nonlinear constraints, avoiding the optimization problems in traditional methods; improve the efficiency of emergency response by minimizing the objective function of regional fire losses; achieve the optimal configuration of servers by solving the Lagrangian relaxation algorithm; and achieve efficient operation of the emergency system by reasonably setting and scheduling servers, avoiding response delays and improving the efficiency and reliability of emergency rescue.

[0114] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:

[0116] Figure 1 A flow chart of an emergency server site selection and scheduling method considering a spatiotemporal queuing mechanism provided in an embodiment of the present application;

[0117] Figure 2 A schematic diagram of the flow of the initial solution generation algorithm provided in the embodiment of the present application;

[0118] Figure 3 A schematic diagram of a flow chart of generating a feasible solution to the original problem based on the Lagrangian relaxation solution provided in an embodiment of the present application;

[0119] Figure 4 A schematic diagram of the distribution of servers and demand points provided in the embodiment of the present application;

[0120] FIG5( a ) is a three-dimensional schematic diagram of the optimal dispatch rule variation surface provided by an embodiment of the present application;

[0121] FIG5( b ) is a top view of the optimal dispatching rule changing surface provided by an embodiment of the present application;

[0122] Figure 6 The impact of server efficiency variance on system saturation loss under the three strategy scenarios provided in the embodiments of this application;

[0123] FIG. 7( a ) is a schematic diagram of the system layout of scenario I provided in an embodiment of the present application;

[0124] FIG7( b ) is a schematic diagram of the system layout of scenario II provided in an embodiment of the present application;

[0125] FIG7( c ) is a schematic diagram of the system layout of scenario III provided in an embodiment of the present application;

[0126] Figure 8 The relationship between the response fire loss and the sum of the server service efficiency in the three scenarios provided in the embodiments of the present application;

[0127] Fig. 9 A schematic diagram of the structure of an emergency server site selection and scheduling device taking into account a spatiotemporal queuing mechanism provided in an embodiment of the present application. DETAILED DESCRIPTION

[0128] Embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0129] The general dispatch strategy of emergency servers is the principle of nearest dispatch, that is, deploying the nearest server as the first responder. Although this method is widely adopted, research shows that it may not minimize the average response time. This is because the nearest site and its service efficiency are often unable to cope with the high incidence and service time of rescue incidents, resulting in the need to dispatch additional resources, which in turn affects the efficiency and effectiveness of rescue.

[0130] To address this problem, the present application provides an emergency server site selection and scheduling method that takes into account the time-space queuing mechanism. Figure 1 The flowchart of the method for selecting and scheduling an emergency server site considering the time-space queuing mechanism provided by the embodiment of the present application is as follows. Figure 1 As shown, the method comprises the following steps:

[0131] Step 101, construct an optimization model of server location and scheduling priority, and replace the nonlinear constraints in the optimization model with auxiliary variables to obtain converted linear constraints.

[0132] In the embodiment of the present application, the optimization model constructs a service system optimization framework, which has several sub-areas, and each sub-area m∈M has an independent server group balanced response system. The service demand of area m∈M comes from different demand points j in the area. m ∈J m These demand arrivals follow an independent Poisson distribution, with an average arrival rate of Potential server i in region m m ∈I m The service duration of follows a negative exponential distribution, and the average service efficiency is Binary variables represents position i in region m m Whether there is a server, where 1 means that a server is planned to be set up, and 0 means no. F represents the upper limit of the number of servers, which is constrained by the government budget. Set E m Includes all possible system states in region m. Server i m The state of Indicates that if If it is busy,

[0133] Binary parameters Indicates that the server in region m is from e ′m To e m Is the state transition from busy to idle because one and only one server ends the service? If so, m∈M, then otherwise Then it is 0.

[0134] In contrast, binary variables It means: In area m, if the demand point j m The demand arrives, causing the system state to change from e m′ becomes e m ,but otherwise

[0135] In the present application embodiment, binary variables are used. To express the priority table. If server i m Plan to be the qth responder in the region for demand point j m service), then otherwise

[0136] Table 1 is a table of model variables and parameters in the optimization model proposed in this application.

[0137] Table 1

[0138]

[0139]

[0140]

[0141] The optimization model can be expressed by the following equation:

[0142] It should be noted that under the assumption that demand arrival is Poisson distributed and service time is exponentially distributed, as the system evolves to a steady state over time, the system state probability It can be obtained through a set of steady-state equilibrium equations, as shown in formula (1). The location decision is described. Only when a site is built at this location, the service efficiency of this location is Otherwise, it is 0, which means that a server with a service efficiency of 0 is built at this location, as follows:

[0143] Steady-state equilibrium equation:

[0144]

[0145] In the formula, For the system in region m to be in state e m The probability of J m is the set of demand points in area m, and j is m index; is the arrival rate of demand point j in region m, is the status of server i in region m. If server i is busy, otherwise is the service rate of server i in region m, which follows a negative exponential distribution; Indicates whether there is a server at location i in region m. If there is a server at location i in region m, then Otherwise E m is the system state set consisting of all possible system states in region m, For the system in region m, The probability of is the system state transition variable. If the server completes the service in area m, the system state changes from e ′m Convert to e m ,but otherwise is the demand point j m The resulting system conversion variables, if the area m is due to demand point j m The occurrence demand causes the system state to change from e ′m Convert to e m ,but otherwise M is the service area set, indexed by m.

[0146] In addition, for the constraints in the optimization model, constraints (2) and (3) indicate the variables and is a binary variable, and constraints (4) and (5) ensure that the system state transition only occurs when it is feasible, that is, when When ′m and e m Only one server is different and all servers with higher priority than this server in the priority table are busy.

[0147] Use the following formula to ensure the correct operation of the priority table:

[0148]

[0149] The value of this formula is 1 only when all servers with higher priority than this server are busy. Otherwise, the value of this formula is other numbers.

[0150] Constraints (2), (3), (4), and (5) are as follows:

[0151] Server status constraints:

[0152]

[0153] Precedence table indicator constraints:

[0154]

[0155] In the formula, is the priority table indicator. In region m, when server i m is the demand point j m When the qth responder is otherwise I m is the potential server set in region m, with i m Index; card(I m ) is the set I m The cardinality of the set I m The number of elements in .

[0156] System state transition constraints:

[0157]

[0158] System state transition verification parameter constraints:

[0159]

[0160] Where C is any sufficiently large positive number.

[0161] Constraints (6) and (7) guarantee the order of server scheduling and the uniqueness of the assignment of the qth responder to demand point j. Constraint (6) ensures that server i has one and only one position in the priority list of demand point j. Constraint (7) ensures that for demand point j, only one server is assigned as the qth responder.

[0162] Constraints (6) and (7) are as follows:

[0163] Server scheduling order uniqueness constraints:

[0164]

[0165] Demand point responder assignment uniqueness constraint:

[0166]

[0167] Normalizing equation (8) ensures that the sum of the probabilities of all system states in region m is equal to 1, as follows:

[0168] Normalized equation:

[0169]

[0170] It should be noted that the optimization model proposed in this application is a highly nonlinear mixed integer programming, which brings great challenges to model optimization. However, all nonlinear constraints in the model are the product of two variables, and at least one of the variables is binary. This feature allows the introduction of auxiliary variables to replace nonlinear terms, thereby achieving the linearization of the original model without expanding the feasible solution space. Table 2 shows the details of this linearization process.

[0171] Table 2

[0172]

[0173] As shown in Table 2, by replacing the variables To replace and The product of To replace and The product of To replace and The product of .

[0174] In the embodiment of the present application, equations (1), (4), and (5) are reconstructed by linearization method to obtain a set of variables Therefore, the original optimization model is transformed into a mixed integer linear programming model, which greatly simplifies the planning and solving process. The converted linear constraints are now:

[0175] System state probability and server efficiency matching constraints:

[0176]

[0177] System state transition constraints:

[0178]

[0179] System state transition verification parameter constraints:

[0180]

[0181] The upper bound constraint of transition probability is:

[0182]

[0183] Consistency constraints between transition probability and state probability:

[0184]

[0185] The non-negativity constraint of transition probability is:

[0186]

[0187] The lower bound constraint of transition probability is:

[0188]

[0189] Response priority matching constraints:

[0190]

[0191] Response priority order constraints:

[0192]

[0193] Response priority combination constraints:

[0194]

[0195] Server deployment and state probability matching constraints:

[0196]

[0197] Server deployment status probability consistency constraints:

[0198]

[0199] Non-negativity constraints on server deployment status:

[0200]

[0201] The lower limit constraints of server deployment state:

[0202]

[0203] Response priority binary constraints:

[0204]

[0205] Step 102, constructing an objective function, the goal of which is to minimize regional fire losses.

[0206] It can be understood that the model goal is to optimize the total system cost based on the model constraints. The core is to determine the deployment location of the server and the corresponding priority list under the premise of limited resources, in order to reduce the probability of system downtime and reduce the loss of the responded fire.

[0207] Specifically, the objective function proposed in this application requires that while minimizing the total system cost defined in equation (24), i.e., the regional fire loss, constraints (2), (3) and (6) to (23) are satisfied, and the additional constraints given in equation (25) are complied with.

[0208] The objective function is:

[0209] Minimize:

[0210]

[0211] At the same time, constraints (2), (3), (6) to (23) and (25) are satisfied. Constraint (25) is the government budget constraint, as follows:

[0212]

[0213] In the formula, z is the total loss, that is, the fire loss, and F is the maximum number of servers that the budget can bear.

[0214] It can be understood that for a service system, its core purpose is to reduce the fire loss in the area. Considering the availability of the server, this application further divides this indicator into two categories.

[0215] The first category is when all servers in the system are busy. If a fire occurs at this time, the system cannot dispatch servers for rescue, resulting in losses, which is the system saturation loss rate. The specific expression is as follows:

[0216]

[0217] Among them, α s Represents the system saturation loss parameter, which is used to indicate the loss caused by the inability to respond to fire due to system saturation. represents the probability that all servers in region m are busy, Represents the total demand achievement rate in region m.

[0218] The second category refers to the loss caused by responding to fires, that is, the system dispatches servers to rescue fire demand points, and the time required for the server to travel from the site to the fire scene increases the loss caused by the fire damage. The specific expression is as follows:

[0219]

[0220] Among them, α rf represents the fire response cost parameter, reflecting the impact of server traffic travel time delay on the extent of fire damage. represents the arrival rate of demand point j in region m, Indicates which station should be sent for rescue in the current system state e. It represents the functional relationship between the site response distance and the fire loss, which can be set according to different fire scenarios. In this application, it is assumed that the relationship formula is a quadratic function, which means that as the response distance increases, the fire loss will increase more rapidly.

[0221] Step 103 , solving the objective function under the constraints of the constraints according to the algorithm based on the Lagrangian relaxation framework to obtain the location and scheduling strategy of the server.

[0222] In order to solve the computational complexity of the model and its corresponding mixed integer programming model, this application also proposes a set of sequential search algorithms. This algorithm integrates the neighborhood search algorithm into the Lagrangian relaxation framework, obtains feasible solutions through the neighborhood search algorithm and commercial solvers, and iterates under the Lagrangian relaxation framework. The heuristic method is combined with the Lagrangian relaxation algorithm to estimate the upper and lower bounds of the model, and the gap between the upper and lower bounds is narrowed through iteration.

[0223] Specifically, step 103 also includes:

[0224] Step 201: Set the initial number of servers R to be deployed for each region. m And calculate the minimum total loss when each region fully builds servers Iteratively reduce the number of servers to minimize the total loss increment and update When the number of servers in all regions R m The process ends when the sum of the total number of servers F in the total plan, and the initial feasible solution is output.

[0225] It is understandable that in order to obtain a high-standard feasible solution and reduce the algorithm calculation time, a sufficiently high-quality initial feasible solution is required. To this end, this application designs a set of sequential solution algorithms, such as Figure 2 As shown in Figure 2, the algorithm gradually reduces the problem size to quickly find a feasible solution.

[0226] The specific sequential solution algorithm is as follows:

[0227] 1) Initialization. Set the initial number of servers R m , the value is the total number of potential servers in the area, i.e., card (I m ) and calculate the minimum total loss when each region is fully built with servers

[0228] 2) Calculation. For each region m, calculate the number of servers R in the current plan m The minimum total loss that can be achieved when reducing one.

[0229] 3) Update. Evaluate the total loss increment for each region. Select the region with the smallest loss increment and increase its server number R m Reduce one and update the area at the same time

[0230] 4) Judge. Judge the R of all regions m Is the sum equal to the total number of servers F in the plan?

[0231] 5) Iteration: Repeat steps (2), (3), and (4) until R m When the sum is equal to the number of servers F, the selection process ends, the algorithm terminates, and the initial feasible solution is output.

[0232] Step 202, integrate the government budget constraint and the Lagrange multiplier θ into the objective function to obtain a relaxed problem.

[0233] In order to estimate the lower bound of the objective function, this application adopts the Lagrange relaxation method, which relaxes the constraint by integrating constraint (25) and Lagrange multiplier θ into the original objective function. The new objective function of the relaxed problem is:

[0234] Minimize:

[0235]

[0236] Among them, the optimal value z of the new objective function for solving the relaxation problem LR (θ) needs to satisfy constraints (2), (3), (6) to (23), and (27). Formula (27) is a constraint on the Lagrange multiplier, requiring the Lagrange multiplier to be greater than or equal to 0, which can be expressed as:

[0237] θ ≥ 0 (27)

[0238] Step 203, decompose the relaxation problem into sub-problems for respective regions and solve them using a commercial optimization solver to obtain a Lagrangian relaxation solution, where the optimal value z of the new objective function is LR (θ) represents a lower bound of the original objective function.

[0239] In the embodiment of the present application, after relaxation, the dual problem (26) is decomposed into M sub-problems for respective regions, the sub-problems for respective regions are expressed by formula (28), and the objective of each sub-problem is given by formula (29).

[0240] The sub-problems of each region are expressed by equation (28):

[0241]

[0242] In the formula, z LRm (θ) is the optimal value in region m;

[0243] The objective function of each sub-problem is:

[0244]

[0245] In the formula, min represents the minimization function.

[0246] Compared to the original problem, the size of the variables and constraints in the dual subproblem is significantly reduced and can now be solved using a commercial optimization solver. The optimal value of the relaxed objective function z LR (θ) represents a lower bound of the original objective function.

[0247] Step 204: Generate a feasible solution to the original problem based on the Lagrangian relaxation solution and calculate the upper bound z UB .

[0248] It should be noted that the solutions to the dual problem may not be applicable to the original problem. However, these solutions can be used to generate feasible solutions, thereby providing an upper bound on the optimal objective value z UB This approach is similar to the algorithm used to generate an initial feasible solution, such as Figure 3 As shown, this application will not repeat the description.

[0249] Step 205, using the subgradient method to update the Lagrange multiplier, and iteratively optimize until the relative error between the upper and lower bounds drops below a preset threshold, and outputs a target feasible solution as the final server location and scheduling strategy.

[0250] In the embodiment of the present application, the subgradient method is used to update the Lagrangian multiplier θ, and θ=0 is initially set.

[0251] In the kth iteration, θ is updated by equation (30), which is expressed as:

[0252]

[0253] In the formula, θ k+1 is the Lagrange multiplier after k iterations, θ k+1 is the Lagrange multiplier at the kth iteration, ξ k is the step size for k iterations, which is updated by scaling parameter ρ.

[0254] If after a predefined number of iterations Z LR (θ) does not improve, the scaling parameter ρ is adjusted downward step by step, with a step size ξ k The update formula is:

[0255]

[0256] In the formula, zLR,k (θ) is the optimal value of the new objective function after k iterations.

[0257] Once the relative error between the upper and lower bounds drops below the preset threshold, the iteration ends and the target feasible solution is finally output as the final server location and scheduling strategy.

[0258] In a possible embodiment, the preset threshold is set to 0.5%, that is, once the relative error between the upper and lower bounds drops below 0.5%, the iteration ends.

[0259] Step 104, setting the server according to the location of the server, and scheduling each server according to the scheduling strategy.

[0260] Finally, the server is set according to the server location obtained in step 103, and each server is scheduled according to the scheduling strategy.

[0261] Furthermore, the present application performs a sensitivity analysis on the emergency server site selection and scheduling method considering the spatiotemporal queuing mechanism.

[0262] The optimization model and heuristic algorithm established by the present application enable the present application to optimize the efficiency of the rescue system by adjusting the location and scheduling strategy of the site. Further, two aspects are discussed in the embodiment: the impact of the scheduling rules on the system saturation loss, and how the service efficiency of the site affects the performance of the entire system.

[0263] 1) Impact of dispatch rules on system saturation losses

[0264] Among all the current dispatching rules, the nearest dispatch strategy, that is, dispatching the nearest station for rescue, is the most commonly used one. Therefore, the embodiment of the present application constructs a simple scenario to test whether the nearest dispatch solution is the optimal strategy, and analyzes the performance of the strategy under different workloads.

[0265] In order to avoid introducing interference factors such as geographical differences in sensitivity analysis, the case constructed a one-dimensional model with a length of 100 units, with two servers at the left and right ends. Two dynamic demand points were set along this line, named Fire Risk Point I and Fire Risk Point II. Figure 4 It shows the relative position relationship between the server and the demand point.

[0266] The case assumes that the service efficiency of all servers in the system and the arrival rate of the demand point are the same. By adjusting the distance between the demand point and the left station and the ratio of the arrival rate to the service rate, the impact of the nearest dispatch strategy on the system saturation loss in different scenarios is explored. Figure 5(a) shows the change surface of the optimal dispatch preference, which reveals the optimality of the nearest dispatch strategy in different scenarios. Figure 5(b) is a top view of the curve, which more comprehensively shows the dynamic changes of the dispatch strategy in space.

[0267] In Figure 5(a), the area above the curve indicates that the nearest dispatch strategy is not the optimal dispatch strategy when the objective function is the system saturation loss. In contrast, the area below the curve shows that under these conditions, the nearest dispatch strategy is still the best choice. The curve itself represents the key moment of strategy transition. The color gradient on the curve shows the change in the applicability of the nearest priority dispatch strategy under different demand layouts. The transition to yellow implies the increased applicability of the nearest dispatch strategy, while the transition to purple indicates that in these layouts, the nearest dispatch strategy often leads to suboptimal results.

[0268] Figure 5(a) also shows that as the ratio of arrival rate to service rate increases, the area above the surface gradually expands, indicating that the effectiveness of the nearest dispatch strategy gradually decreases under heavier system loads. This decrease comes from the disproportionate demand for some server resources, causing them to be overloaded while other resources are underutilized. As the system becomes busier, this imbalance in resource utilization becomes more obvious. Figure 5(b) shows that different server layouts have different sensitivities to the ratio of arrival rate to service rate. When some demand points are close to specific servers and other demand points are equidistant from all servers, nearest dispatch is more likely to lead to suboptimal results, especially when the system workload increases.

[0269] 2) Impact of server efficiency differences on system saturation loss

[0270] In a real system, the rescue efficiency of each site often varies, given the personnel and equipment configuration of different sites and the fire load of the corresponding responsible area. These differences may affect the overall effectiveness of the system. The embodiment of this application will focus on analyzing the specific impact of these differences on system saturation loss. For this purpose, this application designs a system with 3 servers and demand points.

[0271] Assume that the total server efficiency remains unchanged at 180, and the arrival rate of each demand point is 20. While keeping the efficiency of the second server at 60, change the efficiency of the first and third servers to observe their impact on the system saturation loss and the optimal dispatch strategy in this scenario. The specific results are shown in Table 3, where the horizontal axis is the variance of the efficiency of the three servers, and the vertical axis is the system saturation loss rate of this system.

[0272] Table 3 shows that as the variance of server efficiency increases, the system saturation loss first decreases and then increases. This shows that the uniformity of server efficiency does not always ensure the optimal performance of the system; introducing diversity in service efficiency actually helps to reduce system saturation loss. In particular, service sites with higher efficiency are always given priority when allocating tasks, which further emphasizes the key role of the choice of scheduling strategy in minimizing system saturation loss.

[0273] Table 3

[0274]

[0275] In order to further analyze the role of the scheduling strategy, the embodiment of the present application compares the system loss when the optimal scheduling strategy is adopted and the loss when the two strategies of random allocation and giving priority to the service site with the lowest efficiency are adopted. The comparison results are as follows: Figure 6 As shown in Figure 2, as the difference in server efficiency increases, the difference in system saturation loss between different strategies becomes more obvious. This shows that although the uniformity of server efficiency can weaken the impact of scheduling strategy selection to a certain extent, the importance of scheduling strategy optimization cannot be ignored when pursuing the minimization of system saturation loss.

[0276] Furthermore, the embodiment of the present application analyzes the impact of the total server efficiency on the response to fire losses.

[0277] The higher the rescue efficiency of the site, the better the performance of the system is generally. However, this situation is also affected by the geographical distribution of the site and the demand point. This application embodiment aims to explore the impact of the site's service efficiency response to fire losses in different scenarios. To this end, this application embodiment constructs a service system model including three demand points and three servers, and sets up three classic scenario layouts, as shown in Figure 7. Each demand node is set at the three vertices of an equilateral triangle.

[0278] Scenario I: All three servers are placed at the center of the triangle.

[0279] Scenario II: Three servers are located at the midpoints of the three sides of the triangle.

[0280] Scenario III: The servers are placed on the extension lines of the triangle sides.

[0281] Figure 8 The correlation between the sum of the service efficiency of the servers in the three scenarios and the system's ability to respond to fire losses is shown in detail. When the service efficiency is initially improved, the response fire losses surge. This phenomenon is because higher service efficiency makes service responses more frequent. However, when the efficiency improvement exceeds a certain threshold, the availability of closer idle response units increases, allowing faster service, thereby reducing the response fire losses. In scenario I, since the sites are equidistant from the demand points, the increase in service efficiency will not reduce the fire losses. In addition, the study analyzes the relationship between the ranking of the optimal priority list and its distance in scenarios II and III. As shown in Table 4, the analysis results show that in these two scenarios, the ranking of the optimal priority follows the principle of nearest dispatch.

[0282] Table 4

[0283]

[0284] In order to implement the above-mentioned embodiment, the present application also proposes an emergency server site selection and scheduling device that takes into account the time-space queuing mechanism. Fig. 9 The structure diagram of an emergency server site selection and scheduling device 10 considering the time-space queuing mechanism provided in the embodiment of the present application is shown in FIG. Fig. 9 As shown, the device comprises:

[0285] The constraint condition acquisition module 100 is used to construct an optimization model of server location and scheduling priority, and replace the nonlinear constraints in the optimization model with auxiliary variables to obtain the converted constraint conditions;

[0286] An objective function building module 200 is used to build an objective function, wherein the objective of the objective function is to minimize regional fire losses;

[0287] A solution module 300 for solving the objective function under the constraints of the constraints according to an algorithm based on the Lagrangian relaxation framework to obtain the location and scheduling strategy of the server;

[0288] The scheduling module 400 is used to set up the servers according to the locations of the servers and schedule the servers according to the scheduling policies.

[0289] In order to implement the above embodiments, the present application also proposes an electronic device, comprising: a processor, and a memory communicatively connected to the processor; the memory stores computer-executable instructions; the processor executes the computer-executable instructions stored in the memory to implement the method provided by the above embodiments.

[0290] In order to implement the above embodiments, the present application also proposes a computer-readable storage medium, in which computer-executable instructions are stored. When the computer-executable instructions are executed by a processor, they are used to implement the methods provided by the above embodiments.

[0291] In order to implement the above embodiments, the present application also proposes a computer program product, including a computer program, which implements the methods provided by the above embodiments when executed by a processor.

[0292] The collection, storage, use, processing, transmission, provision and disclosure of user personal information involved in this application are in compliance with relevant laws and regulations and do not violate public order and good morals.

[0293] It should be noted that personal information from users should be collected for legitimate and reasonable purposes and should not be shared or sold outside of these legitimate uses. In addition, such collection / sharing should be carried out after receiving the user's informed consent, including but not limited to notifying the user to read the user agreement / user notice and sign the agreement / authorization including authorization of relevant user information before the user uses the function. In addition, any necessary steps should be taken to protect and safeguard access to such personal information data and ensure that others who have access to personal information data comply with its privacy policy and procedures.

[0294] The present application is expected to provide an implementation scheme for users to selectively block the use or access of personal information data. That is, the present disclosure is expected to provide hardware and / or software to prevent or block access to such personal information data. Once the personal information data is no longer needed, the risk can be minimized by limiting data collection and deleting the data. In addition, when applicable, such personal information is de-identified to protect the privacy of the user.

[0295] In the description of the aforementioned embodiments, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0296] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In the description of this application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0297] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or more executable instructions for implementing the steps of a custom logical function or process, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may not be performed in the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by technicians in the technical field to which the embodiments of the present application belong.

[0298] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by an instruction execution system, device or apparatus (such as a computer-based system, a system including a processor, or other system that can fetch instructions from an instruction execution system, device or apparatus and execute the instructions), or in combination with these instruction execution systems, devices or apparatuses. For the purpose of this specification, "computer-readable medium" can be any device that can contain, store, communicate, propagate or transmit a program for use by an instruction execution system, device or apparatus, or in combination with these instruction execution systems, devices or apparatuses. More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk box (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium and then editing, interpreting or processing in other suitable ways if necessary, and then stored in a computer memory.

[0299] It should be understood that the various parts of the present application can be implemented by hardware, software, firmware or a combination thereof. In the above-mentioned embodiments, multiple steps or methods can be implemented by software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented by hardware, as in another embodiment, it can be implemented by any one of the following technologies known in the art or their combination: a discrete logic circuit having a logic gate circuit for implementing a logic function for a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0300] A person skilled in the art may understand that all or part of the steps in the method for implementing the above-mentioned embodiment may be completed by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, which, when executed, includes one or a combination of the steps of the method embodiment.

[0301] In addition, each functional unit in each embodiment of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into one module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0302] The storage medium mentioned above may be a read-only memory, a magnetic disk or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be understood as limiting the present application. A person of ordinary skill in the art may change, modify, replace and modify the above embodiments within the scope of the present application.

Claims

1. A method for selecting and scheduling emergency servers considering a spatiotemporal queuing mechanism, characterized in that: The following steps are involved: Constructing an optimization model of server location and scheduling priority, and replacing nonlinear constraints in the optimization model with auxiliary variables to obtain converted linear constraints; Constructing an objective function, wherein the objective of the objective function is to minimize fire losses; Solving the objective function subject to the constraints according to an algorithm based on a Lagrangian relaxation framework to obtain the location and scheduling strategy of the server; The servers are set according to the locations of the servers, and each server is scheduled according to the scheduling strategy.

2. The method according to claim 1, characterized in that The optimization model includes: Steady-state equilibrium equation: In the formula, For the system in region m to be in state e m The probability of J m is the set of demand points in area m, and j is m index; is the arrival rate of demand point j in region m, is the status of server i in region m. If server i is busy, otherwise is the service rate of server i in region m, which follows a negative exponential distribution; Indicates whether there is a server at location i in region m. If there is a server at location i in region m, then Otherwise is the system state set consisting of all possible system states in region m, For the system in region m, The probability of is the system state transition variable. If the server completes the service in area m, the system state changes from e ′m Convert to e m ,but otherwise is the demand point j m The resulting system conversion variables, if the area m is due to demand point j m The occurrence demand causes the system state to change from e ′m Convert to e m ,but otherwise M is the service area set, indexed by m; Among them, in formula (1) The location decision is described. Only when a site is built at this location, the service efficiency of this location is Otherwise, it is 0, which means that a server with a service efficiency of 0 is built at this location; Server status constraints: Among them, formula (2) shows that the variable is a binary variable; Precedence table indicator constraints: In the formula, is the priority table indicator. In region m, when server i m is the demand point j m When the qth responder is otherwise I m is the potential server set in region m, with i m Index; card(I m ) is the set I m The cardinality of the set I m The number of elements in Among them, formula (3) shows that is a binary variable; System state transition constraints: System state transition verification parameter constraints: In the formula, C is any sufficiently large positive number; Among them, equations (4) and (5) indicate that the system state transition will only occur when it is feasible, that is, when When ′m and e m Only one server is different and all servers with higher priority than this server in the priority table are busy; Server scheduling order uniqueness constraints: Demand point responder assignment uniqueness constraint: Among them, equations (6) and (7) guarantee the order of server scheduling and the uniqueness of the assignment of the qth responder of demand point j. Equation (6) ensures that server i has one and only one position in the priority list of demand point j, while equation (7) ensures that for demand point j, only one server is designated as the qth responder; Normalized equation: Wherein, equation (8) ensures that the sum of the probabilities of all system states in region m is equal to 1.

3. The method according to claim 2, characterized in that The replacing the nonlinear constraints in the optimization model by auxiliary variables comprises: By substitution variables To replace and The product of By substitution variables To replace and The product of By substitution variables To replace and The product of .

4. The method according to claim 3, characterized in that The converted linear constraints include: System state probability and server efficiency matching constraints: System state transition constraints: System state transition verification parameter constraints: The upper bound constraint of transition probability is: Consistency constraints between transition probability and state probability: The non-negativity constraint of transition probability is: The lower bound constraint of transition probability is: Response priority matching constraints: Response priority order constraints: Response priority combination constraints: Server deployment and state probability matching constraints: Server deployment status probability consistency constraints: Non-negativity constraints on server deployment status: The lower limit constraints of server deployment state: Response priority binary constraints:

5. The method according to claim 4, characterized in that The objective function is: Minimize: Among them, z is the total loss, that is, the fire loss, α s is the system saturation loss parameter, which is used to represent the loss caused by the inability to respond to fire due to system saturation; is the probability that all servers in region m are busy, Represents all demand points J in area m m The total demand fulfillment rate, α rf In response to the fire cost parameter, it is used to indicate the degree of influence of server traffic travel time delay on the extent of fire damage; is the arrival rate of demand point j in region m, Indicates which station should be dispatched for rescue in the current system state e; Represents the functional relationship between site response distance and fire loss.

6. The method according to claim 5, characterized in that The constraints also include: Government budget constraints: Where F is the maximum number of servers that the budget can afford.

7. The method according to claim 6, characterized in that The algorithm based on the Lagrangian relaxation framework solves the objective function under the constraints of the constraints to obtain the location and scheduling strategy of the server, including: Set the initial number of servers to be deployed in each region R m And calculate the minimum total loss when each region fully builds servers Iteratively reduce the number of servers to minimize the total loss increment and update When the number of servers in all regions R m The solution ends when the sum is equal to the number of servers F in the total plan, and the initial feasible solution is output; Integrating the government budget constraint and the Lagrange multiplier θ into the objective function, we get the relaxation problem. The new objective function of the relaxation problem is: Minimize: Among them, the optimal value z of the new objective function for solving the relaxation problem LR (θ) needs to satisfy constraints (2), (3), (6) to (23), and (27). Formula (27) is a constraint on the Lagrange multiplier, requiring the Lagrange multiplier to be greater than or equal to 0, which can be expressed as: θ ≥ 0 (27) The relaxation problem is decomposed into subproblems for each region and solved using a commercial optimization solver to obtain the Lagrangian relaxation solution, where the optimal value z of the new objective function is LR (θ) represents a lower bound of the original objective function; Generate a feasible solution to the original problem based on the Lagrangian relaxation solution and calculate the upper bound z UB ; The subgradient method is used to update the Lagrange multiplier, and the optimization is iteratively performed until the relative error of the upper and lower bounds drops below the preset threshold, and the target feasible solution is output as the final server location and scheduling strategy.

8. The method according to claim 7, characterized in that Also includes: The sub-problems of each region are expressed by equation (28): In the formula, z LR m (θ) is the optimal value in region m; The objective function of each sub-problem is: In the formula, min represents the minimization function.

9. The method according to claim 8, characterized in that The method of updating the Lagrange multiplier using the subgradient method includes: The subgradient method is used to update the Lagrange multiplier θ, and θ is initially set to 0. In the kth iteration, θ is updated by equation (30), and the expression of equation (30) is: In the formula, θ k+1 is the Lagrange multiplier after k iterations, θ k+1 is the Lagrange multiplier at the kth iteration, ξ k is the step size for k iterations, which is updated by scaling parameter ρ. If Z LR If (θ) does not improve, the scaling parameter ρ is gradually adjusted downward; Step length k The update formula is: In the formula, z LR,k (θ) is the optimal value of the new objective function after k iterations.

10. An emergency server site selection and scheduling device considering the time-space queuing mechanism, characterized in that: include: A constraint condition acquisition module is used to construct an optimization model of server location and scheduling priority, and replace the nonlinear constraints in the optimization model with auxiliary variables to obtain converted linear constraints; An objective function building module, used to build an objective function, wherein the objective of the objective function is to minimize fire losses; a solving module, for solving the objective function under the constraints of the constraints according to an algorithm based on a Lagrangian relaxation framework to obtain the location and scheduling strategy of the server; The scheduling module is used to set up the server according to the location of the server and schedule each server according to the scheduling strategy.

Images