Patent Publication Number: US-2022222555-A1

Title: Parameter estimation apparatus, congestion estimation apparatus, parameter estimation method, congestion estimation method and program

Description:
TECHNICAL FIELD 
     The present invention relates to a parameter estimation device, a congestion degree estimation device, a parameter estimation method, a congestion degree estimation method, and a program. 
     BACKGROUND ART 
     Problems called theme park problems are conventionally known. Theme park problems are problems for analyzing selection of attractions by visitors, estimating congestion conditions, and considering and evaluating control strategies for reducing congestion, for example, by reproducing congestion conditions of a theme park through multi-agent simulation (MAS). Various conventional technologies have been proposed for such theme park problems. 
     For example, PTL 1 describes a technology for predicting a waiting time of an attraction in a theme park. Also, PTL 2 describes a technology for finding an optimum control strategy for reducing congestion in a theme park or the like. 
     CITATION LIST 
     Patent Literature 
     
         
         [PTL 1] Japanese Patent Application Publication No. 2018-073361 
         [PTL 2] Japanese Patent Application Publication No. 2018-147087 
       
    
     SUMMARY OF THE INVENTION 
     Technical Problem 
     Incidentally, when visitors select attractions in a theme park, commonly, there are individual differences in preference between the visitors. That is, visitors commonly select attractions according to their own preference. However, individual differences in preference between visitors are not taken into consideration in the conventional technologies. Therefore, when congestion degrees such as waiting times of attractions are estimated, the accuracy of estimation may be not high. 
     An embodiment of the present invention was made in view of the foregoing, and has an object of estimating congestion degrees with high accuracy. 
     Means for Solving the Problem 
     In order to achieve the object described above, a parameter estimation device according to an embodiment of the present invention includes parameter estimation means for, assuming that a total number of N selection subjects n (n=1, . . . , N) each select any one of a total number of M selection targets m (m=1, . . . , M), inputting acceptable limits α n,m  of each selection subject n and calculating patience φ n  and a preference vector ψ n , the acceptable limits α n,m  indicating limits of congestion degrees of respective selection subjects m that are acceptable to the selection subject n, the patience φ n  indicating the largest value of the acceptable limits α n,m  of the selection subject n with respect to the selection targets m, the preference vector ψ n  indicating preference of the selection subject n when selecting the selection targets m, and estimating parameters of a model for obtaining acceptable limits α i,m  of each of a total number of I(&gt;N) selection subjects i (i=1, . . . , I) by using the calculated patience φ n  and the calculated preference vector ψ n . 
     Also, a congestion degree estimation device according to an embodiment of the present invention includes: parameter estimation means for, assuming that a total number of N selection subjects n (n=1, . . . , N) each select any one of a total number of M selection targets m (m=1, . . . , M), inputting acceptable limits α n,m  of each selection subject n and calculating patience φ n  and a preference vector ψ n , the acceptable limits α n,m  indicating limits of congestion degrees of respective selection subjects m that are acceptable to the selection subject n, the patience φ n  indicating the largest value of the acceptable limits α n,m  of the selection subject n with respect to the selection targets m, the preference vector ψ n  indicating preference of the selection subject n when selecting the selection targets m, and for estimating parameters of a model for obtaining acceptable limits α i,m  of each of a total number of I(&gt;N) selection subjects i (i=1, . . . , I) by using the calculated patience φ n  and the calculated preference vector ψ n ; calculation means for calculating the acceptable limits α i,m  of each selection subject i by using the model in which the estimated parameters are used; and congestion degree estimation means for estimating congestion degrees of the respective selection targets m at each time point t (t=1, . . . , T) by inputting the acceptable limits α i,m  and simulation conditions and simulating selection of the selection targets m by the selection subjects i at each time point t. 
     Effects of the Invention 
     Congestion degrees can be estimated with high accuracy. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a diagram showing an example of the entire configuration of a congestion degree estimation device according to an embodiment of the present invention. 
         FIG. 2  is a flowchart showing an example of processing for estimating parameters of an acceptable limit model. 
         FIG. 3  is a diagram showing an example of acceptable limit data for parameter estimation. 
         FIG. 4  is a diagram showing an example of patience φ n  and attraction preferences ψ n,m . 
         FIG. 5  is a flowchart showing an example of processing for creating visitor data for simulation. 
         FIG. 6  is a diagram showing an example of creation of an acceptable limit vector α i . 
         FIG. 7  is a diagram showing an example of visitor data for simulation. 
         FIG. 8  is a diagram showing an example of setting of an arrival time I i  and a leave time O i . 
         FIG. 9  is a diagram showing an example of setting of a planned number k i . 
         FIG. 10  is a diagram showing an example of arrangement of attractions. 
         FIG. 11  is a diagram showing an example of movement time data for simulation. 
         FIG. 12  is a diagram showing an example of attraction data for simulation. 
         FIG. 13  is a diagram showing an example of state transition of visitors. 
         FIG. 14  is a flowchart showing an example of processing for estimating congestion degrees through simulation. 
         FIG. 15  is a diagram showing an example of simulation results. 
         FIG. 16  is a diagram showing an example of a hardware configuration of the congestion degree estimation device according to an embodiment of the present invention. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     The following describes an embodiment of the present invention. In the embodiment of the present invention, a congestion degree estimation device  10  that estimates congestion degrees of respective attractions (e.g., waiting times of respective attractions) of a theme park in which a plurality of attractions are arranged will be described, the congestion degree estimation device  10  estimating the congestion degrees through simulation, taking preference of each visitor for an attraction into consideration. Here, the term “theme park” refers to a tourist facility of which a part or the entirety is produced based on a theme, and specific examples of theme parks include amusement parks and the like. Note that a theme park may also be called a leisure land or the like. 
     However, estimation of congestion degrees of attractions in a theme park through simulation is an example, and the embodiment of the present invention can be similarly applied to estimation of congestion degrees of respective targets through simulation in a case where a plurality of targets (e.g., attractions) that can be selected by selection subjects (e.g., visitors) are arranged. For example, the embodiment can be similarly applied to estimation of congestion degrees of respective event booths through simulation in an event site in which a plurality of event booths that can be selected by visitors are arranged. 
     &lt;Theoretical Configuration&gt; 
     The following describes a theoretical configuration of the embodiment of the present invention. 
     &lt;&lt;Estimation of Parameters of Acceptable Limit Model&gt;&gt; 
     Let M be the number of attractions, and m (m=1, . . . , M) be an index of each attraction, and an attraction that has an index m will be referred to as an “attraction m”. Similarly, let n be an index of each visitor, and a visitor who has an index n will be referred to as a “visitor n”. Also, let α n,m  be an acceptable limit of waiting time of the visitor n for the attraction m (i.e., a scalar value that indicates a waiting time that the visitor n can accept for the attraction m). 
     In the embodiment of the present invention, parameters of a model expressed by the following Expressions (1) and (2) (this model will also be referred to as an “acceptable limit model”) are estimated using acceptable limits α n,m  (n=1, . . . , N, m=1, . . . , M) that are acquired in advance from N visitors using questionnaires or the like, for example. 
     
       
         
           
             
               
                 
                   
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     Here, φ n  represents the largest value of acceptable limits of waiting time of the visitor n, and will also be referred to as “patience” in the following description. α n  is an M-dimensional vector that includes an acceptable limit α n,m  (m=1, . . . , M) of the visitor n as the m-th element, and will also be referred to as an “acceptable limit vector” in the following description. ψ n  is an M-dimensional vector that includes a scalar value ψ n,m  that indicates relative preference of the visitor n for the attraction m as the m-th element. In the following description, ψ n,m  will also be referred to as an “attraction preference”, and ψ n  will also be referred to as an “attraction preference vector”. 
     In the embodiment of the present invention, parameters μ and σ 2  are estimated using a maximum likelihood method or the like, assuming that the patience φ n  follows a log-normal distribution, i.e., log(φ n )˜N(μ,σ 2 ). Note that μ and σ 2  are mean and variance of a normal distribution, respectively. 
     Also, in the embodiment of the present invention, a parameter β is estimated using a maximum likelihood method, assuming that the attraction preference vector ψ n  follows a Dirichlet distribution Dir(β), i.e., ψ n ˜Dir(β). Note that β is a parameter of the Dirichlet distribution and is expressed as an M-dimensional vector (β 1 , . . . , β M ). 
     &lt;&lt;Creation of Visitor Data for Simulation&gt;&gt; 
     Let I be the number of visitors used to simulate congestion degrees of attractions, and i be an index of each visitor, and a visitor who has an index i will be referred to as a “visitor i”. Note that the number I of visitors used for the simulation is very large when compared to the number N of visitors used to estimate the parameters of the acceptable limit model. 
     In the embodiment of the present invention, patience φ i  (i=1, . . . , I) and attraction preference vectors ψ i  (i=1, . . . , I) are generated using the parameters μ, σ 2 , and β estimated as described above, and then acceptable limit vectors α i  (i=1, . . . , I) are generated using the following Expression (3). 
     
       
         
           
             
               
                 
                   
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     Then, visitor data for simulation is created using the acceptable limit vectors α i . Note that the visitor data for simulation includes acceptable limits α i,m  of a visitor i for respective attractions m, an arrival time I i  and a leave time O i  of the visitor i, and a planned number k i  of attractions that the visitor i will experience (i.e., a number that indicates how many attractions the visitor i plans to experience). 
     &lt;&lt;Simulation&gt;&gt; 
     Waiting times (an example of congestion degrees) of respective attractions m at each simulation time point t are estimated using the visitor data for simulation, attraction data for simulation, and movement time data for simulation. Note that the attraction data for simulation is data that indicates a processing capacity of each attraction (i.e., the number of people who can experience the attraction in a unit time) in simulation, for example. Also, the movement time data for simulation is data that indicates the time it takes to move between attractions (and the time it takes to move between the entrance of the theme park and an attraction) in simulation, for example. 
     In the embodiment of the present invention, a probability θ i,m,t  of a visitor i selecting an attraction m at a simulation time point t is calculated using a model expressed by the following Expression (4) (this model will also be referred to as a “polynomial linear model”). 
     
       
         
           
             
               
                 
                   
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     Here, A i,m,t =max(0, α i,m -W m,t ), and W m,t  represents a waiting time of the attraction m at the time point t. Note that α i,m  is the m-th element of the acceptable limit vector α i  (i.e., an acceptable limit of the visitor i for the attraction m). 
     Thus, waiting times (an example of congestion degrees) of respective attractions m for which attraction preferences ψ i,m  of each visitor i are taken into consideration are estimated as simulation results. 
     Note that the polynomial linear model expressed by the above Expression (4) is a model that is obtained by extending a conventionally known linear model non-negatively such that conditions of logical consistency are satisfied. The conditions of logical consistency are constraint conditions that, when an option is selected from a finite number of options, the sum of selection probabilities of all options is 1 and the selection probabilities of all options are not negative, under the condition that any one of the options is always selected. 
     &lt;Entire Configuration of Congestion Degree Estimation Device  10 &gt; 
     Next, the entire configuration of the congestion degree estimation device  10  according to the embodiment of the present invention will be described with reference to  FIG. 1 .  FIG. 1  is a diagram showing an example of the entire configuration of the congestion degree estimation device  10  according to the embodiment of the present invention. 
     As shown in  FIG. 1 , the congestion degree estimation device  10  according to the embodiment of the present invention includes a parameter estimation unit  101 , a visitor data creation unit  102 , a simulation unit  103 , and a storage unit  104 . Note that the parameter estimation unit  101 , the visitor data creation unit  102 , and the simulation unit  103  are realized through processing that one or more programs installed in the congestion degree estimation device  10  cause a processor or the like to execute, for example. Also, the storage unit  104  can be realized using a suitable storage device such as an auxiliary storage device of the congestion degree estimation device  10  or a recording medium, for example. 
     Various types of data are stored in the storage unit  104 . Examples of data stored in the storage unit  104  include acceptable limit data for parameter estimation, which will be described later, the parameters μ, σ 2 , and β of the acceptable limit model, the visitor data for simulation, the attraction data for simulation, the movement time data for simulation, and the number I of visitors used for simulation. Also, waiting times W m,t  of respective attractions m at a simulation time point t are stored in the storage unit  104 . 
     The parameter estimation unit  101  estimates the parameters μ, σ 2 , and β of the acceptable limit model expressed by the above Expressions (1) and (2), taking the acceptable limit data for parameter estimation as an input. Here, the acceptable limit data for parameter estimation is data that indicates acceptable limits α n,m  (n=1, . . . , N, m=1, . . . , M) that are acquired in advance from N visitors using questionnaires or the like, for example. 
     The visitor data creation unit  102  generates acceptable limit vectors α i  (i=1, . . . , I), taking the parameters μ, σ 2 , and β estimated by the parameter estimation unit  101  and the number I of visitors used for simulation as inputs. Then, the visitor data creation unit  102  creates visitor data for simulation using the acceptable limit vectors α i  (i=1, . . . , I). 
     The simulation unit  103  estimates waiting times W m,t  of respective attractions m at each simulation time point t, taking the visitor data for simulation, the attraction data for simulation, and the movement time data for simulation as inputs. In the embodiment of the present invention, a simulation time point t is expressed as a non-negative integer value of which unit is “minutes”, and indicates a time [minutes] passed from the start of simulation. Specifically, a simulation end time point is represented by T [minutes], and each simulation time point t is expressed as t=0, 1, 2, . . . , T [minutes]. However, there is no limitation to this example, and the simulation time point t may represent an index of a suitable unit period (e.g., 30 minutes or 1 hour). 
     Note that the entire configuration of the congestion degree estimation device  10  shown in  FIG. 1  is an example, and another configuration is also possible. For example, the parameter estimation unit  101 , the visitor data creation unit  102 , and the simulation unit  103  may be included in difference devices. That is, the congestion degree estimation device  10  shown in  FIG. 1  may be divided into a parameter estimation device that includes the parameter estimation unit  101 , a visitor data creation device that includes the visitor data creation unit  102 , and a simulation device that includes the simulation unit  103 , for example. 
     &lt;Processing for Estimating Parameters of Acceptable Limit Model&gt; 
     The following describes processing for estimating the parameters of the acceptable limit model with reference to  FIG. 2 .  FIG. 2  is a flowchart showing an example of the processing for estimating the parameters of the acceptable limit mode. 
     Step S 101 : The parameter estimation unit  101  inputs acceptable limit data for parameter estimation. As described above, the acceptable limit data for parameter estimation is data that indicates acceptable limits α n,m  (n=1, . . . , N, m=1, . . . , M, e.g., data that is expressed with a N×M matrix in which a (n,m)-component is α n,m ). Note that the parameter estimation unit  101  may input acceptable limit data for parameter estimation that is stored in the storage unit  104  or acceptable limit data for parameter estimation that is transmitted from another device connected via a communication network, for example. 
     Here,  FIG. 3  shows a specific example of the acceptable limit data for parameter estimation in a case where N=5 and M=3. In the case shown in  FIG. 3 , acceptable limit α 1,1 =24.0, acceptable limit α 1,2 =97.8, and acceptable limit α 1,3 =49.7. Similarly, acceptable limit α 2,1 =58.7, acceptable limit α 2,2 =28.7, and acceptable limit α 2,3 =27.6. Acceptable limits of n=3, 4, 5 are as shown in  FIG. 3 . 
     Step S 102 : The parameter estimation unit  101  calculates patience φ n  based on the above Expression (1) and calculates an attraction preference vector ψ n  based on the above Expression (2) by using acceptable limits α n,m  (n=1, . . . , N, m=1, . . . , M) indicated by the acceptable limit data for parameter estimation. That is, with respect to each visitor n, the parameter estimation unit  101  takes the largest value of acceptable limits α n,m  of waiting time for respective attractions m to be the patience en. Also, with respect to each visitor n, the parameter estimation unit  101  takes a ratio of an acceptable limit α n,m  of waiting time for an attraction m relative to all attractions to be an attraction preference ψ n,m . Note that the attraction preference ψ n,m  is no smaller than 0 and no greater than 1, and the closer the value of the attraction preference is to 1, the more preferentially the corresponding attraction is selected. 
     Here,  FIG. 4  shows a specific example of patience φ n  and attraction preferences ψ n,m , which are elements of the attraction preference vector ψ n , in a case where N=5 and M=3. In the case shown in  FIG. 4 , attraction preference ψ 1,1 =0.14, attraction preference ψ 1,2 =0.57, and attraction preference ψ 1,3 =0.29. Similarly, attraction preference ψ 2,1 =0.51, attraction preference ψ 2,2 =0.25, and attraction preference ψ 2,3 =0.24. Attraction preferences of n=3, 4, 5 are as shown in  FIG. 4 . 
     Also, in the case shown in  FIG. 4 , patience ρ 1 =97.8, patience φ 2 =58.7, patience φ 3 =19.3, patience φ 4 =7.5, and patience φ 5 =25.9. 
     Step S 103 : The parameter estimation unit  101  estimates the parameters μ and σ 2  using a maximum likelihood method, assuming that the patience φ n  (n=1, . . . , N) calculated in step S 102  described above follows a log-normal distribution (i.e., log(φ n )˜N(μ,σ 2 )). This estimation can be performed using a method described in ‘C. M. Bishop, “Pattern Recognition and Machine Learning (Vol. 1) Statistical Prediction Using Bayesian Approach”, p. 24 (1.2.4 Gaussian distribution)’, for example. 
     Step S 104 : The parameter estimation unit  101  estimates the parameter β using a maximum likelihood method, assuming that the attraction preference vector ψ n  calculated in step S 102  described above follows a Dirichlet distribution Dir(β) (i.e., ψ n ˜Dir((β)). This estimation can be performed using a method described in ‘Thomas P. Minka, “Estimating a Dirichlet distribution”, &lt;URL:https://tminka.github.io/papers/dirichlet/minka-dirichlet .pdf&gt;’, for example. Note that the parameter β is an M-dimensional vector expressed as β=(β 1 , . . . , β M ), as described above. 
     Through the above, the parameters μ, σ 2 , and β of the acceptable limit model are estimated. These parameters μ, σ 2 , and are stored in the storage unit  104  by the parameter estimation unit  101 , for example. 
     &lt;Processing for Creating Visitor Data for Simulation&gt; 
     The following describes processing for creating visitor data for simulation with reference to  FIG. 5 .  FIG. 5  is a flowchart showing an example of the processing for creating visitor data for simulation. 
     Step S 201 : The visitor data creation unit  102  inputs the number I of visitors used for simulation and the parameters μ, σ 2 , and β of the acceptable limit model. These parameters μ, σ 2 , and β are the parameters estimated by the parameter estimation unit  101 . Note that the visitor data creation unit  102  may input the parameters μ, σ 2 , and β stored in the storage unit  104  or the parameters μ, σ 2 , and β transmitted from another device connected via a communication network, for example. Also, the visitor data creation unit  102  may input the number I of visitors stored in the storage unit  104 , the number I of visitors transmitted from another device connected via a communication network, or the number I of visitors specified through an input device such as a keyboard, for example. 
     Step S 202 : The visitor data creation unit  102  generates random numbers r i  (i=1, . . . , I) that follow a normal distribution N(μ, σ 2 ), and then generates patience φ i  (i=1, . . . , I) from the random numbers r i  (i=1, . . . , I). That is, the visitor data creation unit  102  generates patience φ i  for each i=1, . . . , I, using the following expression: φ i =e ri . Note that e represents the Napier&#39;s constant. 
     Step S 203 : The visitor data creation unit  102  generates I M-dimensional vectors that follow the Dirichlet distribution Dir(β) at random, and take these M-dimensional vectors to be attraction preference vectors ψ i  (i=1, . . . , I). 
     Step S 204 : The visitor data creation unit  102  generates acceptable limit vectors α i  (i=1, . . . , I) based on the above Expression (3) by using the patience φ i  and the attraction preference vectors ψ i . As shown in the above Expression (3), with respect to i=1, . . . , I, the visitor data creation unit  102  normalizes attraction preferences ψ i,m  (m=1, . . . , M) such that the largest value of the attraction preferences ψ i,m  becomes 1, and then generates an acceptable limit vector α i  such that an acceptable limit α i,m  is a product of a normalized ψ i,m  and the patience φ i . 
     Here,  FIG. 6  shows a specific example of generation of the acceptable limit vector α i  in a case where M=3. In  FIG. 6 , in the case of i=1, maxψ 1 =0.57 and φ 1 =97.8. Therefore, acceptable limits α 1,1 , α 1,2 , and α 1,3 , which are elements of an acceptable limit vector α 1 , are as follows: α 1,1 =97.8×(0.14/0.57)=24.0, α 1,2 =97.8×(0.57/0.57)=97.8, and α 1,3 =97.8×(0.29/0.57)=49.7. 
     Similarly, in  FIG. 6 , in the case of i=2, maxψ 2 =0.51 and φ 2 =58.7. Therefore, acceptable limits α 2,1 , α 2,2 , and α 2,3 , which are elements of an acceptable limit vector α 2 , are as follows: α 2,1 =58.7×( 0 . 51 / 0 . 51 )=58.7, α 2,2 =58.7×(0.25/0.51)=28.7, and α 2,3 =58.7×(0.24/0.51)=27.6. With respect to i=3 and the following values of i as well, elements α i,1 , α i,2 , and α i,3  of an acceptable limit vector α i  are calculated in a similar manner. 
     Step S 205 : The visitor data creation unit  102  creates visitor data for simulation using the acceptable limit vectors α i  (i=1, . . . , I). As described above, the visitor data for simulation includes acceptable limits α i,m  of a visitor i for respective attractions m, an arrival time I i  and a leave time O i  of the visitor i, and a planned number k i  of attractions that the visitor i will experience. Note that a pair of the arrival time I i  and the leave time O i  may also be referred to as a “stay time”. 
     Here,  FIG. 7  shows visitor data for simulation in a case where M=3. In  FIG. 7 , in the case of i=1, acceptable limit α 1,1 =24.0, acceptable limit α 1,2 =97.8, acceptable limit α 1,3 =49.7, arrival time I 1 =8:00, leave time O 1 =14:00, and planned number k 1 =2. Similarly, in the case of i=2, acceptable limit α 2,1 =58.7, acceptable limit α 2,2 =28.7, acceptable limit α 2,3 =27.6, arrival time I 2 =8:30, leave time O 2 =16:00, and planned number k 2 =2. Data regarding i=3 and the following values of i is as shown in  FIG. 7 . 
     Although an arrival time I i  and a leave time O i  of a visitor i can be set to suitable time points, it is commonly thought that a peak of the number of visitors staying in an actual theme park often appears in the daytime. Therefore, in the embodiment of the present invention, the arrival time I i  and the leave time O i  of each visitor i are set such that a peak of the number of visitors i staying in the theme park appears in the daytime. Specifically, assuming that the opening time of the theme park is “8:00”, the closing time of the theme park is “21:00”, and a total of 3,000 people visit the theme park per day, the arrival time I i  and the leave time O i  of each visitor i are set such that a peak of the number of visitors staying in the theme park appears between t=300 and t=400 as shown in  FIG. 8 , where the simulation time point t is from 0 [minutes] to T=780 [minutes], and I=3000. Note that T represents the simulation end time point, as described above. 
     Also, although planned numbers k i  of respective visitors i can be set to suitable integer values, in the embodiment of the present invention, the planned numbers k i  are set so as to follow a Poisson distribution of which mean is 3 (however, 0 is excluded).  FIG. 9  shows a histogram of the planned numbers k i  (i=1, . . . , 3000) in a case where I=3000. 
     Through the above, visitor data for simulation is created. The visitor data is stored in the storage unit  104  by the visitor data creation unit  102 , for example. 
     &lt;Simulation Conditions&gt; 
     Before describing processing for estimating congestion degrees through simulation, various conditions of the simulation will be described as presuppositions. 
     &lt;&lt;Movement Time&gt;&gt; 
     The time it takes for each visitor i to move between attractions and the time it takes for each visitor i to move between the entrance of the theme park and an attraction in simulation are given from movement time data for simulation. In the embodiment of the present invention, it is assumed that M=5 and arrangement of the attractions m and movement paths between the attractions and the entrance are as shown in  FIG. 10 . Note that each figure shown in a circle that represents an attraction in  FIG. 10  is the index of the attraction. 
     Assume that movement time data for simulation shown in  FIG. 11  is given. In the movement time data for simulation shown in  FIG. 11 , movement times from origins to destinations of movement are expressed in the form of a matrix. For example, if the origin of movement is the “entrance” and the destination of movement is the “attraction m=l”, the movement time is 30 [minutes]. Similarly, if the origin of movement is the “attraction m=1” and the destination of movement is the “attraction m=5”, the movement time is 10 [minutes]. 
     &lt;&lt;Processing Capacity of Attraction&gt;&gt; 
     A processing capacity of each attraction (i.e., the number of people who can experience the attraction in a unit time) in simulation is given from attraction data for simulation. In the embodiment of the present invention, it is assumed that M=5 and attraction data for simulation shown in  FIG. 12  is given. In the attraction data for simulation shown in  FIG. 12 , experience times [minutes] of respective attractions, capacities [people] of respective attractions, processing capacities [people/minute] of respective attractions, and operation cycles [minutes] of respective attractions are expressed in the form of a matrix. Note that a processing capacity is equal to “capacity/experience time”. 
     For example, in the case of the attraction m=1, the experience time is “5 minutes”, the capacity is “12 people”, the processing capacity is “2.4”, and the operation cycle is “5”. This means that the attraction m=1 operates every 5 minutes, 12 people can experience the attraction m=1 at the same time in a single operation, and the time it takes to experience the attraction m=1 once is 5 minutes. 
     Note that the attraction data for simulation in the embodiment of the present invention includes the “processing capacity”, but there is no limitation thereto, and attraction data for simulation is only required to include at least “information with which the processing capacity can be specified”. The information with which the processing capacity can be specified may be a pair of the “capacity” and the “experience time” or the “processing capacity” itself. 
     &lt;&lt;State Transition and the Like of Visitors i&gt;&gt; 
     In simulation, any one of the states shown in  FIG. 13  (“arrived”, “left”, “selecting attraction”, “moving”, “queuing”, “experiencing”, and “waiting”), a position in the theme park, and the like are associated with each visitor i. That is, for example, the index i of a visitor and the state, position, and the like of the visitor are stored in the storage unit  104  in association with each other. Assume that the state “arrived” and a position “entrance” are associated with each visitor i in an initial state. 
     The state, position, and the like of each visitor i are updated at each simulation time point t, following conditions described below in (C1) to (C9). 
     (C1) Visitor i in the state of “arrived” If the arrival time I i  is before the simulation time point t, the state of the visitor i is updated to “selecting attraction”. This means that, upon the simulation time point t becoming the arrival time I i , the visitor i enters the theme park and starts to select an attraction. 
     (C2) Visitor i who has a planned number k i ≠0 and is in the state of “selecting attraction” 
     A selection probability θ i,m,t  of each attraction m is calculated using the polynomial linear model expressed by the above Expression (4), and an attraction m that the visitor i will experience next is selected based on the probability. Specifically, based on the selection probability θ i,m,t , an attraction m is selected from candidate attractions m for which the following is satisfied: waiting time W m,t &lt;α i,m . 
     If any one of the attractions m is selected, the state of the visitor i is updated to “moving”. At this time, a “movement completion time point” that is obtained by adding a movement time from the current position to the “selected attraction m” to the simulation time point t is associated with the visitor i, and the position of the visitor i is updated to the “selected attraction m”. The movement time is acquired from the movement time data for simulation described above. Note that in order to express individual differences in movement time between visitors i, it is also possible to perform addition, subtraction, multiplication, or division on the movement time acquired from the movement time data for simulation, by using a random number. 
     On the other hand, if none of the actions m is selected (i.e., for all attractions m, W m,t ≥α i,m  and θ i,m,t =0), the state of the visitor i is updated to “waiting”. At this time, a “waiting end time point” that is obtained by adding a waiting time (e.g., “30 minutes”) determined in advance to the simulation time point t is associated with the visitor i. Note that the waiting time may be determined in advance, or a random number may be used as the waiting time. 
     (C3) Visitor i who has a planned number k i =0 and is in the state of “selecting attraction” 
     The state of the visitor i is updated to “left”. Also, the position of the visitor i is updated to the “entrance”. This means that the visitor i has experienced the planned number of attractions and therefore leaves the theme park. 
     (C4) Visitor i in the state of “moving” 
     If the movement completion time point associated with the visitor i is before the simulation time point t, the state of the visitor i is updated to “queuing”. Also, an “experience start time point” that is obtained by adding the waiting time W m,t  of the attraction m that the visitor i will experience to the simulation time point t and an “experience end time point” that is obtained by adding the experience time of the attraction m to the experience start time point are associated with the visitor i. Note that the movement completion time point associated with the visitor i is deleted (or may also be updated to a time point after the closing time). 
     (C5) Visitor i in the state of “queuing” 
     If the experience start time point associated with the visitor i is before the simulation time point t, the state of the visitor i is updated to “experiencing”. Note that the experience start time point associated with the visitor i is deleted (or may also be updated to a time point after the closing time). 
     (C6) Visitor i in the state of “experiencing” 
     If the experience end time point associated with the visitor i is before the simulation time point t, the state of the visitor i is updated to “selecting attraction”. Also, 1 is subtracted from the planned number k i  of the visitor i. 
     (C8) Visitor i in the state of “waiting” 
     If the waiting end time point associated with the visitor i is before the simulation time point t, the state of the visitor i is updated to “selecting attraction”. 
     (C9) Visitors i in all states other than “arrived” and “left” 
     If the leave time O i  is before the simulation time point t, the state of the visitor i is updated to “left”. Also, the position of the visitor i is updated to the “entrance”. This means that, upon the simulation time point t becoming the leave time O i , the visitor i leaves the theme park. 
     &lt;Processing for Estimating Congestion Degree Through Simulation&gt; 
     The following describes processing for estimating congestion degrees through simulation under the various conditions described above in “Simulation Conditions”, with reference to  FIG. 14 .  FIG. 14  is a flowchart showing an example of the processing for estimating congestion degrees through simulation. 
     Step S 301 : The simulation unit  103  inputs visitor data for simulation, attraction data for simulation, and movement time data for simulation. Note that the simulation unit  103  may input these types of data stored in the storage unit  104  or these types of data transmitted from another device connected via a communication network, for example. 
     Step S 302 : The simulation unit  103  initializes the simulation time point t to a simulation start time point, and initializes waiting times W m,t  of respective attractions m to 0. Note that the simulation start time point can be set to t=0, but there is no limitation thereto, and the simulation start time point may be set to a suitable time point. 
     Step S 303 : The simulation unit  103  updates the state, position, and the like of each visitor i, following the conditions described above in (C1) to (C9). 
     Step S 304 : Next, the simulation unit  103  updates the simulation time point t. That is, the simulation unit  103  adds 1 to the simulation time point t. 
     Step S 305 : The simulation unit  103  determines whether or not the simulation time point t is the simulation end time point T. Upon determining that the simulation time point t is not the simulation end time point T, the simulation unit  103  proceeds to step S 306 . On the other hand, upon determining that the simulation time point t is the simulation end time point T, the simulation unit  103  proceeds to step S 307 . 
     Step S 306 : The simulation unit  103  calculate waiting times W m,t  of the respective attractions m, and stores the waiting times in the storage unit  104 . Here, each waiting time W m,t  is calculated as follows: “the number of visitors i who are queuing for the attraction m at the simulation time point t/processing capacity of the attraction m”. Note that the number of visitors i who are queuing for the attraction m at the simulation time point t is the number of visitors i who are in the state of “queuing” and whose positions are the “attraction m” at the simulation time point t. 
     Note that after calculating and storing the waiting times W m,t , the simulation unit  103  returns to step S 303 . As a result, steps S 303  to S 306  are repeatedly executed until the simulation time point t becomes the simulation end time point T. 
     Step S 307 : The simulation unit  103  updates states of all visitors i to “left” and updates their positions to the “entrance”. This is because the simulation time point t is T and corresponds to the closing time of the theme park. 
     Through the above, waiting times W m,t  of respective attractions m at each simulation time point t are obtained as simulation results. These waiting times W m,t  are estimation results of congestion degrees of respective attractions m at each simulation time point t. 
     &lt;Simulation Results&gt; 
     Next, simulation results (i.e., transition of waiting times W m,t  of attractions m at respective simulation time points t) in cases where M=5 and I=1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, or 9000 are shown in  FIG. 15 . Note that the waiting times of m=1 to m=5 shown in  FIG. 15  are each an average value of waiting times W m,t  obtained by performing simulation 10 times while changing the seed of random numbers used to generate patience φ i  and attraction preference vectors ψ i  in steps S 202  and S 203  shown in  FIG. 5 . 
     As shown in  FIG. 15 , waiting times of all attractions m increased as the number I of visitors increased. These results show that congestion degrees (waiting times) of attractions in an actual theme park could be well reproduced and the congestion degrees could be estimated with high accuracy according to the embodiment of the present invention. 
     Therefore, according to the embodiment of the present invention, if acceptable limits α n,m  (n=1, . . . , N, m=1, . . . , M) are acquired in advance from some visitors using questionnaires or the like, it is possible to easily and accurately predict congestion degrees in a case where I (&gt;N) people visit, while taking attraction preference of each visitor into consideration. 
     &lt;Hardware Configuration of Congestion Degree Estimation Device  10 &gt; 
     Lastly, a hardware configuration of the congestion degree estimation device  10  according to the embodiment of the present invention will be described with reference to  FIG. 16 .  FIG. 16  is a diagram showing an example of the hardware configuration of the congestion degree estimation device  10  according to the embodiment of the present invention. 
     As shown in  FIG. 16 , the congestion degree estimation device.  10  according to the embodiment of the present invention includes an input device  201 , a display device  202 , an external I/F  203 , a RAM (Random Access Memory)  204 , a ROM (Read Only Memory)  205 , a processor  206 , a communication I/F  207 , and an auxiliary storage device  208 . These pieces of hardware are communicably connected to each other via a bus B. 
     The input device  201  is a keyboard, a mouse, a touch panel, or the like, and is used by a user to input various operations. The display device  202  is a display or the like, and displays results of processing performed by the congestion degree estimation device  10 , for example. Note that a configuration is also possible in which the congestion degree estimation device  10  does not include either one or both of the input device  201  and the display device  202 . 
     The external I/F  203  is an interface with an external device. Examples of the external device include a recording medium  203   a . The congestion degree estimation device  10  can perform reading from and wiring into the recording medium  203   a  or the like via the external I/F  203 . One or more programs for realizing the functional units (e.g., the parameter estimation unit  101 , the visitor data creation unit  102 , and the simulation unit  103 ) of the congestion degree estimation device  10  may be recorded on the recording medium  203   a . Note that examples of the recording medium  203   a  include a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card, and a USB memory card. 
     The RAM  204  is a volatile semiconductor memory that temporarily stores programs and data. The ROM  205  is a non-volatile semiconductor memory that can hold programs and data even if power is turned off. Setting information regarding an OS (Operating System), setting information regarding a communication network, and the like are stored in the ROM  205 , for example. 
     The processor  206  is a CPU (Central Processing Unit) or the like, and is an arithmetic device that reads programs and data from the ROM  205 , the auxiliary storage device  208 , and the like into the RAM  204  and executes various types of processing. 
     The communication I/F  207  is an interface for connecting the congestion degree estimation device  10  to a communication network. One or more programs for realizing the functional units of the congestion degree estimation device  10  may also be acquired (downloaded) from a predetermined server device or the like via the communication I/F  207 . 
     The auxiliary storage device  208  is an HDD (Hard Disk Drive), an SSD (Solid State Drive), or the like, and is a non-volatile storage device in which programs and data are stored. Examples of the programs and data stored in the auxiliary storage device  208  include an OS, application programs for realizing various functions in the OS, and one or more programs for realizing the functional units of the congestion degree estimation device  10 . 
     The present invention is not limited to the embodiment specifically disclosed above, and various variations and changes can be made without departing from the description of the claims. 
     REFERENCE SIGNS LIST 
     
         
           10  Congestion degree estimation device 
           101  Parameter estimation unit 
           102  Visitor data creation unit 
           103  Simulation unit 
           104  Storage unit