DESCRIPTION TITLE: AVAILABLE BANDWIDTH ESTIMATING DEVICE TECHNICAL FIELD [0001] The present invention relates to an available bandwidth estimating device which estimates an available bandwidth in a communication network. BACKGROUND ART [0002] When a transmitting device transmits data to a receiving device via a communication network, part of the data may be lost in the communication network (data loss occurs, e.g., packet loss may occur in a case that the communication network is the IP (Internet Protocol) network). Moreover, a delay time, which is a time before the receiving device receives data after the data is transmitted from the transmitting device, may become excessive. [0003] Particularly in a case that the transmitting device transmits data representing multimedia that the real time property of video, audio or the like is high, when data loss occurs and/or when a delay time becomes excessive, the quality of experience relatively largely decreases. [0004] Therefore, it is thought to be preferred to accurately estimate an available bandwidth, which is a communication bandwidth available in a communication path between the transmitting device and the receiving device, and properly determine a transmission rate based on the estimated available bandwidth. Here, a transmission rate is the amount of data transmitted by the transmitting device to the receiving device per unit time. [0005] Accordingly, a technique for estimating an available bandwidth has been developed. As this type of techniques, "Pathload" described in Non-Patent Document 1, "pathChirp" described in Non-Patent Document 2, "IGI" described in Non-Patent Document, and so on are known. [0006] An available bandwidth estimating device to which these techniques are applied is configured to estimate an available bandwidth based on an equation 1 and an equation 2. At first, this available bandwidth estimating device estimates an available bandwidth Aj(t) in a section i that is one of a plurality of sections configuring a communication path from the transmitting device to the receiving device, based on the equation 1. [Equation 1] Ai{t) = Ci{l-ui) [0007] The available bandwidth estimating device described above uses, as Ci*Ui, an average value in a preset period of a communication bandwidth already used in the section i. Next, the available bandwidth estimating device estimates an available bandwidth A(t) in a communication path based on the equation 2. [Equation 2] A{t) = mm{Ai(t)} [0008] Thus, the available bandwidth estimating device described above calculates a value as the result of subtracting an already used communication bandwidth from a physical bandwidth for each of the sections configuring the communication path, and estimates the minimum value of the calculated values as an available bandwidth for the communication path. [0009] [Non-Patent Document 1] M. Jain, C. Dovrolis, "End-to-End Available Bandwidth: Measurement Methodology, Dynamics, and Relation with TCP Throughput," Proc. SIGCOMM 2002, the Association for Computing Machinery, Vol. 32, pp. 295-308, October 2002 [Non-Patent Document 2] V. J. Ribeiro, R. H. Riedi, R. G Baraniuk, J. Navratil, L. Cottrell, "pathChirp: Efficient Available Bandwidth Estimation for Network Paths," Rice University, [searched on December 3, 2009], Internet [Non-Patent Document 3] N.Hu, P. Steenkiste, "Evaluation and Characterization of Available Bandwidth Probing Techniques," Proc. IEEE journal on selected areas in communications, the Institute of Electrical and Electronics Engineers, Inc., Vol.21, No.6, pp. 879-893, August 2003. [0010] Data transmitted by a target device will be referred to as self-traffic. Moreover, data transmitted by another device by using a communication path that shares at least one section with a communication path from the target device to the receiving device will be referred to as cross traffic. [0011] As a communication bandwidth used in a certain section increases, a data loss ratio and delay time relating to data flowing through the section increase. Therefore, in a case that the target device increases a transmission rate (a communication bandwidth to be used) relating to self-traffic, a data loss ratio and delay time relating to cross traffic increase. [0012] On the other hand, in a case that the other device transmits data in compliance with TCP (Transmission Control Protocol), the other device is often configured to control to change the transmission rate depending on a data loss ratio, which is a ratio of occurrence of data loss, and/or a delay time. [0013] Therefore, when the target device increases the transmission rate relating to self-traffic, the other device decreases the transmission rate relating to cross traffic. On the other hand, when the target device decreases the transmission rate relating to self-traffic, the other device increases the transmission rate relating to cross traffic. Thus, when the target device changes the transmission rate relating to self-traffic, the other device changes the transmission rate relating to cross traffic. [0014] Therefore, the available bandwidth estimating device described above has a problem that it is impossible to estimate, with high accuracy, an available bandwidth when the transmission rate relating to self-traffic is changed. SUMMARY [0015] Accordingly, an object of the present invention is to provide an available bandwidth estimating device that is capable of solving the aforementioned problem, "it is impossible to estimate, with high accuracy, an available bandwidth when the transmission rate relating to self-traffic is changed." [0016] In order to achieve the object, an available bandwidth estimating device as an exemplary embodiment of the present invention includes: a transmission rate acquiring means for acquiring a transmission rate, which is an amount of data transmitted by a transmitting device per unit time to a receiving device connected so as to be capable of communicating via a communication network; and an available bandwidth estimating means for estimating an available bandwidth, which is a communication bandwidth available in a communication path between the transmitting device and the receiving device, based on: a mathematical model constructed by representing a relation between the available bandwidth and the transmission rate by a dynamic model including a mobile body that can move in a preset moving direction and an elastic body that transforms in the moving direction by a movement amount of movement of the mobile body in the moving direction; and the acquired transmission rate. [0017] Further, an available bandwidth estimating method as another exemplary embodiment of the present invention is a method including: acquiring a transmission rate, which is an amount of data transmitted by a transmitting device per unit time to a receiving device connected so as to be capable of communicating via a communication network; and estimating an available bandwidth, which is a communication bandwidth available in a communication path between the transmitting device and the receiving device, based on: a mathematical model constructed by representing a relation between the available bandwidth and the transmission rate by a dynamic model including a mobile body that can move in a preset moving direction and an elastic body that transforms in the moving direction by a movement amount of movement of the mobile body in the moving direction; and the acquired transmission rate. [0018] Further, a program as another exemplary embodiment of the present invention is a program for causing an available bandwidth estimating device to realize: a transmission rate acquiring means for acquiring a transmission rate, which is an amount of data transmitted by a transmitting device per unit time to a receiving device connected so as to be capable of communicating via a communication network; and an available bandwidth estimating means for estimating an available bandwidth, which is a communication bandwidth available in a communication path between the transmitting device and the receiving device, based on: a mathematical model constructed by representing a relation between the available bandwidth and the transmission rate by a dynamic model including a mobile body that can move in a preset moving direction and an elastic body that transforms in the moving direction by a movement amount of movement of the mobile body in the moving direction; and the acquired transmission rate. [0019] With the configurations described above, the present invention can estimate, with high accuracy, an available bandwidth when the transmission rate relating to self-traffic is changed. BRIEF DESCRIPTION OF DRAWINGS [0020] Fig. 1 is a diagram showing a schematic configuration of a content delivery system according to a first exemplary embodiment of the present invention; Fig. 2 is a block diagram schematically showing a function of the content delivery system according to the first exemplary embodiment of the present invention; Fig. 3 is an explanation view conceptually showing a dynamic model according to the first exemplary embodiment of the present invention; Fig. 4 is an explanation view conceptually showing a dynamic model according to a modified example of the first exemplary embodiment of the present invention; Fig. 5 is an explanation view conceptually showing a dynamic model according to a modified example of the first exemplary embodiment of the present invention; Fig. 6 is an explanation view conceptually showing a communication status of a communication network according to the first exemplary embodiment of the present invention; Fig. 7 is a graph showing a change of a transmission rate; Fig. 8 is a graph showing a change of a reception rate in a case that the number of cross traffic is 10; Fig. 9 is a table showing model parameters estimated by a transmitting device in cases that the numbers of cross traffic are 1,2, 3, 5, 7,10,15,20 and 30, respectively; Fig. 10 is a graph showing a change of a data loss ratio in a case that the number of cross traffic is 10; Fig. 11 is a block diagram schematically showing a function of a content delivery system according to a second exemplary embodiment of the present invention; and Fig. 12 is a block diagram schematically showing a function of an available bandwidth estimating device according to a third exemplary embodiment of the present invention. EXEMPLARY EMBODIMENTS [0021] Below, exemplary embodiments of an available bandwidth estimating device, an available bandwidth estimating method and a program according to the present invention will be described with reference to Figs. 1 to 12. [0022] As shown in Fig. 1, a content delivery system 1 according to a first exemplary embodiment includes a transmitting device (an available bandwidth estimating device) 100 and a receiving device 200. The transmitting device 100 and the receiving device 200 are connected so as to be capable of communicating with each other via a communication network NW configuring the IP (Internet Protocol) network. [0023] The transmitting device 100 is a server device. The transmitting device 100 is equipped with a central processing unit (CPU) and a storage device (a memory and a hard disk drive (HDD)), which are not shown in the drawing. The transmitting device 100 is configured to realize a function described later by execution of a program stored in the storage device by the CPU. [0024] The receiving device 200 is a personal computer. The receiving device 200 may be a mobile phone terminal, a PHS (Personal Handyphone System), a PDA (Personal Data Assistance, Personal Digital Assistant), a car navigation terminal, a game terminal, or the like. The receiving device 200 is equipped with a CPU, a storage device (a memory and an HDD), an input device (a keyboard, a mouse, and the like) and an output device (a display, or the like), which are not shown in the drawing. [0025] The receiving device 200 is configured to realize a function described later by execution of a program stored in the storage device by the CPU. [0026] Fig. 2 is a block diagram showing a function of the content delivery system 1 configured as described above. The function of the transmitting device 100 includes a data transmitting part 101, a transmission rate acquiring part (a transmission rate acquiring means) 102, a reception rate acquiring part (a reception rate acquiring means) 103, a model parameter estimating part (a model parameter estimating means) 104, an available bandwidth estimating part (an available bandwidth estimating means) 105, and a reception characteristic information estimating part (a reception characteristic information estimating means) 106. [0027] Further, the function of the receiving device 200 includes a data receiving part 201 and a reception information transmitting part 202. [0028] The data transmitting part 101 transmits data to the receiving device 200. In this exemplary embodiment, the data transmitting part 101 transmits multimedia data representing video or sound. The data transmitting part 101 transmits data in compliance with RTP (Real-time Transport Protocol). [0029] The data transmitting part 101 may transmit data other than multimedia data (e.g., probe data: data itself does not have any meaning). Moreover, the data transmitting part 101 may transmit data in compliance with a communication protocol other than RTP. It is preferred that the data transmitting part 101 transmits data in compliance with UDP (User Datagram Protocol)/IP or TCP/IP. [0030] The transmission rate acquiring part 102 calculates (acquires) a transmission rate, which is the amount (the size) of data transmitted by the data transmitting part 101 to the receiving device 200 per unit time, every time a preset operation period h elapses. [0031] The data receiving part 201 receives data transmitted by the transmitting device 100. The reception information transmitting part 202 extracts reception information relating to data transmitted by the transmitting device 100, from among reception information relating to all data received by the data receiving part 201. [0032] Reception information has only to include information that enables calculation of a reception rate, which is the amount of data received by the receiving device 200 from the transmitting device 100 per unit time. In this exemplary embodiment, reception information is a pair of: time when the reception information has been acquired (sampled); and the amount of data received within a period from previous time when the reception information has been acquired to present time. Reception information may include time when the reception information has been acquired, the maximum value of a sequence number included in the received data, and the amount of data loss. [0033] The data receiving part 201 transmits the extracted reception information to the transmitting device 100 every time the operation period h elapses. In this exemplary embodiment, the data receiving part 201 transmits reception information in compliance with RTCP (RTP Control Protocol). Furthermore, the data receiving part 201 transmits the reception information in the form of an RTCP RR packet (Receiver Report Packet). [0034] The reception rate acquiring part 103 receives reception information from the receiving device 200. The reception rate acquiring part 103 calculates (acquires) a reception rate, which is the amount of data received by the receiving device 200 from the transmitting device 100 per unit time, based on the received reception information. [0035] The model parameter estimating part 104 estimates a model parameter based on a transmission rate acquired by the transmission rate acquiring part 102, a reception rate acquired by the reception rate acquiring part 103, and a mathematical model. A model parameter is a parameter for specifying a mathematical model, and includes a force-free distance, an elastic modulus, and a viscosity coefficient. [0036] Below, a mathematical model will be described. As mentioned above, with an available bandwidth estimating device configured to calculate a value as the result of subtracting an already used communication bandwidth from a physical bandwidth for each of sections configuring a communication path and estimate the minimum value of the calculated values as an available bandwidth in the communication path, it is impossible to highly accurately estimate an available bandwidth because a change of a transmission rate relating to cross traffic in accordance with a change of a transmission rate relating to self-traffic is not taken into consideration. [0037] Actually, as a transmission rate relating to self-traffic (the flow of self-traffic) becomes large, a data loss ratio and delay time relating to cross traffic increase. Consequently, a transmission rate relating to cross traffic (the flow of cross traffic) decreases. As a result, a communication bandwidth that is available for communication relating to self-traffic (i.e., an available bandwidth) increases. [0038] On the other hand, as the flow of self-traffic becomes small, a data loss ratio and delay time relating to cross traffic decrease. Consequently, the flow of cross traffic increases. As a result, a communication bandwidth that is available for communication relating to self-traffic (i.e., an available bandwidth) decreases. [0039] Thus, it can be said that a qualitative relation between the flow of self-traffic and the flow of cross traffic is a relation of thrusting the flows with each other (decreasing one when the other increases, and increasing one when the other decreases). [0040] Then, by representing a relation between an available bandwidth and a transmission rate by using a dynamic model (a viscoelastic model) including a mobile body Ml, a spring M2 as an elastic body (an elastic element) and a dashpot M3 as a viscous body (a viscous element) shown in Fig. 3, a mathematical model will be constructed. [0041] This dynamic model is a model in which data transmitted from the transmitting device 100 to the receiving device 200 is simulated by a fluid flowing in a passage zoned by a wall face Wl and the mobile body Ml. The mobile body Ml is a plate-like body that is placed within the ) passage and movable in a moving direction set in advance (in the vertical direction in Fig. 3). [0042] The spring M2 is a coil spring having a spring constant (an elastic modulus) K. The spring M2 has one end fixed to the mobile body Ml and the other end fixed to the wall face W2. With such a configuration, the spring M2 transforms, by the amount of movement of the mobile body Ml in a moving direction, in the moving direction. [0043] The dashpot M3 has a viscosity coefficient D. The dashpot M3 has one end fixed to the mobile body Ml and the other end fixed to the wall face W2. With such a configuration, the dashpot M3 delays the movement in the moving direction of the mobile body Ml due to external force applied to the mobile body Ml. [0044] In this exemplary embodiment, both the spring constant K and the viscosity coefficient D are constant values (have a linear characteristic). The spring constant K and/or the viscosity coefficient may have a nonlinear characteristic. [0045] The dynamic model is a model in which it is assumed that external force applied to the mobile body Ml in the moving direction by a fluid corresponding to data transmitted at a transmission rate u (unit is [bps]) from the transmitting device 100 to the receiving device 200 has a magnitude f(u) corresponding to the transmission rate u, and it is assumed that a distance in the moving direction between a reference position pref set in advance (in this exemplary embodiment, a position of the wall face Wl) and a position p of the mobile body Ml is an available bandwidth w ) (unit is [bps]). That is to say, this dynamic model is a model representing a relation between the available bandwidth and the transmission rate. [0046] Further, in this dynamic model, in a case that the mobile body Ml is located in a position po (a force-free position) away from the reference position pref in the moving direction by a distance (a force-free distance) wo, the spring M2 does not generate an elastic force (a restoring force). Moreover, an elastic force generated by the spring M2 has a magnitude of a value as the result of multiplying a movement amount w-wo of the mobile body Ml from the force-free position po by the elastic modulus K that is a proportionality factor, and works in the opposite direction to a direction in which the mobile body Ml moves from the mobile body Ml. [0047] In addition, in this dynamic model, when the mobile body Ml is still in the moving direction (speed is 0), the dashpot M3 does not generate resistance force. Moreover, resistance force generated by the dashpot M3 has a magnitude of a value as the result of multiplying a movement speed of the mobile body Ml in the moving direction by the viscosity coefficient D that is a proportionality factor, and works in the opposite direction to the direction that the mobile body Ml moves. [0048] In this dynamic model, an equation governing a motion of the mobile body Ml is written as an equation 3. A term dw/dt denotes the derivative of the distance (i.e., the available bandwidth) w in the moving direction between the reference position pref and the position p of the mobile body Ml with respect to time t. ) [Equation 3] [0049] Further, a reception rate v (unit is [bps]) coincides with the available bandwidth w when the transmission rate u is larger than the available bandwidth w and, on the other hand, coincides with the transmission rate u when the transmission rate u is equal to or less than the available bandwidth w, as shown by an equation 4. [Equation 4] [0050] It can be thought that the spring constant K in this viscoelastic model represents "being hard to thrust" of cross .traffic. Moreover, it can be thought that the viscosity coefficient D represents the "degree of viscosity" or "weak response" of cross traffic. [0051] As the dynamic model, it is possible to use another model. For example, a model that also takes the inertia force of the mobile body Ml into consideration can be employed as the dynamic model. By the inertial force of the mobile body Ml, it is possible to represent a change that a transmission rate relating to cross traffic overshoots. In this dynamic model, an equation governing a motion of the mobile body Ml is written as an equation 5. In the equation, M denotes the mass of the mobile body Ml. Moreover, dV/dt2 denotes the second derivative of the distance (the available bandwidth) w in the moving direction between the reference position pref and the position p of the mobile body Ml with respect to time t. [Equation 5] [0052] As mentioned above, the viscoelastic model in which the spring M2 and the dashpot M3 are connected to the mobile body Ml in parallel is called the Kelvin-Voigt model. Moreover, as shown in Fig. 4, the dynamic model may be a viscoelastic model in which the spring M2 and the dashpot M3 are connected to the mobile body Ml in series. This viscoelastic model is called the Maxwell model. [0053] Further, as shown in Fig. 5, the dynamic model may be a viscoelastic model (a four-element model) including a plurality of (in this example embodiment, two) springs M2 and M4 and a plurality of (in this exemplary embodiment, two) dashpots M3 and M5. In this exemplary embodiment, the spring M2 and the dashpot M3 are connected in series to the mobile body Ml, and the spring M4 and the dashpot M5 are connected in parallel to the Spring M4 and the dashpot M5. [0054] Further, an equation governing a motion of the mobile body Ml in the dynamic model may include a term including the third derivative (the jerk) of the distance (the available bandwidth) w in the moving direction between the reference position pref and the position p of the mobile body Ml with respect to time t, or may include a term including the third or higher derivative. [0055] As mentioned above, the model parameter estimating part 104 estimates a model parameter based on the mathematical model formed by the equations 4 and 5, a transmission rate acquired by the transmission rate acquiring part 102, and a reception rate acquired by the reception rate acquiring part 103. A model parameter includes the force-free distance wo, the elastic modulus K, and the viscosity coefficient D. [0056] In this exemplary embodiment, the model parameter estimating part 104 estimates a model parameter by using the least squares method. Here, for convenience, equations 6 and 7, which linearly approximate the equations 3 and 4, will be used as a mathematical model. [Equation 6] [Equation 7] v = w [0057] The reception rate acquiring part 103 calculates a reception rate every time the operation period h elapses. Then, the equation 6 will be rewritten to a difference equation. In this exemplary embodiment, as shown by an equation 8, the operation period (a sampling interval) h is a time interval (a time step), and a backward difference is used. [Equation 8] [0058] Here, by solving the equation 8 for w(k), an equation 9 is obtained. [Equation 9] [0059] From the equation 9, Next, a content delivery system according to a second exemplary embodiment of the present invention will be described. The content delivery system according to the second exemplary embodiment is different from the content delivery system according to the first exemplary embodiment in that the transmitting device changes redundancy relating to an error correction process based on a data loss ratio. Therefore, a description will be made focusing on a different point. [0095] As shown in Fig. 11, a function of the transmitting device 100 according to the second exemplary embodiment includes a transmission parameter determining part (a transmission parameter determining means) 107 in addition to the function of the first exemplary embodiment. [0096] The transmission parameter determining part 107 determines a transmission rate and redundancy (in this exemplary embodiment FEC (Forward Error Correction) redundancy) for transmitting data to the receiving device 200 based on a data loss ratio estimated by the reception characteristic information estimating part 106. [0097] The data transmitting part 101 encodes transmission information to generate data having the redundancy determined by the transmission parameter determining part 107 so that the receiving device 200 can execute an error correction process (in this exemplary embodiment, a forward error correction process). The data transmitting part 101 transmits the generated data to the receiving device 200 at a transmission rate determined by the transmission parameter determining part 107. [0098] The data receiving part 201 acquires the transmission information by executing the error correction process based on the data received from the transmitting device 100. In this exemplary embodiment, the content delivery system 1 is configured to execute an error correction process using Reed-Solomon codes. Alternatively, the content delivery system 1 may be configured to execute an error correction process using codes other than Reed-Solomon codes. [0099] Here, the transmission parameter determining part 107 will be described in more detail. When the amount of data (net data) corresponding to the transmission information that is the basis of data transmitted by the transmitting device 100 to the receiving device 200 per unit time among the data (i.e., a net transmission rate) is un [bps ] and the amount of a portion (redundant data) other than the net data among the data transmitted by the transmitting device 100 to the receiving device 200 per unit time (i.e., a redundant transmission rate) is Ur [bps], a relation shown by an equation 26 is satisfied. [Equation 26] [0100] Redundancy dr is defined as shown by an equation 27 as a ratio of the redundant transmission rate ur to the transmission rate u. [Equation 27] ur ar = — u [0101] The upper limit value of a data loss ratio that allows restoration of the transmission information by execution of the error correction process varies with the redundancy dr. Here, the average value (an average data loss ratio) of the data loss ratio that allows restoration of the transmission information will be denoted by rc(dr). [0102] In this case, by determining the redundancy dr so as to satisfy rc(dr)> p(t) based on the data loss ratio p(t) estimated by the reception characteristic information estimating part 106, it is possible to cause the receiving device 200 to restore the transmission information even when data loss occurs. [0103] The data loss ratio p(t) varies with time. However, it is difficult to change the redundancy dr in accordance with the data loss ratio p(t) within a relatively short time period. Thus, the transmission parameter detennining part 107 calculates an average value pa (an average data loss ratio) of a data loss ratio in a preset change cycle. Then, the transmission parameter determining part 107 determines the redundancy dr so as to satisfy an equation 28. The transmission parameter determining part 107 may be configured to use a movement average value as the average data loss ratio pa. [Equation 28] rc(dr) > pa [0104] Thus, the transmission parameter determining part 107 determines the redundancy dr of data so that the receiving device 200 can restore the transmission information by executing the error correction process based on received data in a case that part of data is lost in the communication network NW at the data loss ratio estimated by the reception characteristic information estimating part 107. [0105] According to this, even when data loss occurs, it is possible to restore transmission information (in this exemplary embodiment, multimedia data) based on the data received by the receiving device 200. As a result, it is possible to securely prevent decrease of the quality of transmission information acquired by the receiving device 200. [0106] Furthermore, the transmission parameter determining part 107 determines a pair of the transmission rate u and the redundancy dr so as to maximize the net transmission rate u„ (i.e., the amount of transmission information transmitted per unit time) within a range satisfying the equation 28. [0107] Accordingly, it is possible to maximize the amount of transmission information transmitted per unit time within a rage that the receiving device 200 can restore the transmission information by executing the error correction process based on received data. [0108] As described above, with the transmitting device 100 according to the second exemplary embodiment, it is possible to estimate, with high accuracy, an available bandwidth in a case that transmission rate relating to self-traffic is changed. As a result, it is possible to properly set a transmission rate relating to self-traffic based on the estimated available bandwidth. [0109] In a case that the transmitting device 100 is configured to transmit any of transmission information encoded at a plurality of media rates different from each other (encoding rates, e.g., 384 [kbps], 1 [Mbps]) to the receiving device 200, the transmitting device 100 may be configured to determine a pair of the transmission rate u and the redundancy dr so as to maximize the media rate in a range satisfying the equation 28. In this case, it is possible to make the quality of reception information received by the receiving device 200 high. [0110] The whole or part of the exemplary embodiments disclosed above can be described as, but not limited to, the following supplementary notes. [0118] (Supplementary Note 1) An available bandwidth estimating device, comprising: a transmission rate acquiring means for acquiring a transmission rate, which is an amount of data transmitted by a transmitting device per unit time to a receiving device connected so as to be capable of communicating via a communication network; and an available bandwidth estimating means for estimating an available bandwidth, which is a communication bandwidth available in a communication path between the transmitting device and the receiving device, based on: a mathematical model constructed by representing a relation between the available bandwidth and the transmission rate by a dynamic model including a mobile body that can move in a preset moving direction and an elastic body that transforms in the moving direction by a movement amount of movement of the mobile body in the moving direction; and the acquired transmission rate. [0119] A change of a transmission rate relating to cross traffic caused by a change of a transmission rate relating to self-traffic is well represented by elastic force of an elastic body. Therefore, by configuring the available bandwidth estimating device as described above, it is possible to estimate, with high accuracy, an available bandwidth in a case that a transmission rate relating to self-traffic is changed. As a result, for example, it is possible to properly set a transmission rate relating to self-traffic based on the estimated available bandwidth. Moreover, for example, it is possible to estimate, with high accuracy, reception characteristic information representing a characteristic (e.g., a reception rate, a data loss ratio, a data delay time, or the like) of reception of data by the receiving device. [0120] (Supplementary Note 2) The available bandwidth estimating device according to Supplementary Note 1, wherein the mathematical model is constructed on the assumption that external force applied to the mobile body in the moving direction has a magnitude depending on the transmission rate, and that a ) distance in the moving direction between a preset reference position and a position of the mobile body is the available bandwidth. [0121] (Supplementary Note 3) The available bandwidth estimating device according to Supplementary Note 2, wherein the mathematical model is constructed on the assumption that elastic force generated by the elastic body has a magnitude of a value as the result of multiplying an amount of movement of the mobile body from a force-free position, which is a position of the mobile body where the elastic force becomes 0, by an elastic modulus, which is a proportionality factor, and that the elastic force works in a direction opposite to a direction in which the mobile body moves from the force-free position. [0122] (Supplementary Note 4) The available bandwidth estimating device according to Supplementary Note 3, comprising: a reception rate acquiring means for acquiring a reception rate, which is an amount of data received by the receiving device from the transmitting device per unit time; and a model parameter estimating means for estimating a distance between the reference position and the force-free position and the elastic modulus based on the acquired reception rate, the acquired transmission rate, and the mathematical model. [0123] (Supplementary Note 5) The available bandwidth estimating device according to any of Supplementary Notes 1 to > 3, wherein the dynamic model includes a viscous body that delays movement of the mobile body in the moving direction due to external force applied to the mobile body. [0124] From change of a transmission rate relating to self-traffic by a target device to change of a transmission rate relating to cross traffic by another device, a delay time is required. This delay time is well represented by resistance force of a viscous body. Therefore, by configuring the available bandwidth estimating device as described above, it is possible to estimate, with high accuracy, an available bandwidth in a case that a transmission rate relating to self-traffic is changed. [0125] (Supplementary Note 6) The available bandwidth estimating device according to Supplementary Note 5, wherein the mathematical model is constructed on the assumption that resistance force generated by the viscous body has a magnitude of a value as the result of multiplying a speed of movement of the mobile body in the moving direction by a viscosity coefficient, which is a proportionality factor, and that the resistance force works in a direction opposite to a direction in which the mobile body moves. [0126] (Supplementary Note 7) The available bandwidth estimating device according to Supplementary Note 6, comprising: a reception rate acquiring means for acquiring a reception rate, which is an amount of data received by the receiving device from the transmitting device per unit time; and a model parameter estimating means for estimating the viscosity coefficient based on the acquired reception rate, the acquired transmission rate, and the mathematical model. [0127] (Supplementary Note 8) The available bandwidth estimating device according to any of Supplementary Notes 1 to 7, comprising: a reception characteristic information estimating means for estimating reception characteristic information representing a characteristic of reception of the data by the receiving device based on the estimated available bandwidth. [0128] (Supplementary Note 9) The available bandwidth estimating device according to Supplementary Note 8, wherein the reception characteristic information includes information representing at least one of: a reception rate, which is an amount of data received by the receiving device from the transmitting device per unit time; a data loss ratio, which is a ratio of an amount of data lost in the communication network among the data transmitted by the transmitting device to a total amount of the data transmitted by the transmitting device; and a data delay time, which is a time from a moment of transmission of the data from the transmitting device to a moment of reception of the data by the receiving device. [0129] (Supplementary Note 10) The available bandwidth estimating device according to Supplementary Note 9, wherein: the available bandwidth estimating device configures the transmitting device; and the reception characteristic information includes information representing the data loss ratio, the available bandwidth estimating device, comprising: a transmission parameter detennining means for determining redundancy of the data so that, in a case that part of the data is lost in the communication network at the estimated data loss ratio, the receiving device can restore transmission information by executing an error correction process based on the received data; and a data transmitting means for encoding the transmission information to generate the data having the determined redundancy and transmit the generated data to the receiving device so that the receiving device can execute the error correction process. [0130] According to this, even when data loss occurs, the receiving device can restore transmission information (e.g., multimedia data) based on received data. As a result, it is possible to securely prevent decrease of the quality of transmission information acquired by the receiving device. [0131] (Supplementary Note 11) The available bandwidth estimating device according to Supplementary Note 10, wherein the transmission parameter determining means determines a pair of the transmission rate and the redundancy so as to maximize an amount of the transmission information transmitted per unit time within a range that the receiving device can restore the transmission information by executing the error correction process based on the received data. [0132] When it is assumed that redundancy is constant, the amount of transmission information transmitted per unit time becomes large as a transmission rate relating to self-traffic becomes high. On the other hand, as the transmission rate becomes high, a data loss ratio also becomes high. Therefore, redundancy that allows the receiving device to restore transmission information based on received data becomes large. Moreover, when it is assumed that the transmission rate is constant, the amount of transmission information transmitted per unit time becomes small as the redundancy becomes large. [0133] Therefore, by configuring the available bandwidth estimating device as described above, it is possible to maximize the amount of transmission information transmitted per unit time within a range that the receiving device can restore transmission information by executing the error correction process based on received data. [0134] (Supplementary Note 12) An available bandwidth estimating method, comprising: acquiring a transmission rate, which is an amount of data transmitted by a transmitting device per unit time to a receiving device connected so as to be capable of communicating via a communication network; and estimating an available bandwidth, which is a communication bandwidth available in a communication path between the transmitting device and the receiving device, based on: a mathematical model constructed by representing a relation between the available bandwidth and the transmission rate by a dynamic model including a mobile body that can move in a preset moving direction and an elastic body that transforms in the moving direction by a movement amount of movement of the mobile body in the moving direction; and the acquired transmission rate. [0135] (Supplementary Note 13) The available bandwidth estimating method according to Supplementary Note 12, wherein the mathematical model is constructed on the assumption that external force applied to the mobile body in the moving direction has a magnitude depending on the transmission rate, and that a distance in the moving direction between a preset reference position and a position of the mobile body is the available bandwidth. [0136] (Supplementary Note 14) The available bandwidth estimating method according to Supplementary Note 12 or 13, wherein the dynamic model includes a viscous body that delays movement of the mobile body in the moving direction due to external force applied to the mobile body. [0137] (Supplementary Note 15) The available bandwidth estimating method according to any of Supplementary Notes 12 to 14, comprising: estimating a data loss ratio, which is a ratio of an amount of data lost in the communication network among the data transmitted by the transmitting device to a total amount of the data transmitted by the transmitting device based on the estimated available bandwidth; determining redundancy of the data so that, in a case that part of the data is lost in the communication network at the estimated data loss ratio, the receiving device can restore transmission information by executing an error correction process based on the received data; and encoding the transmission information to generate the data having the determined redundancy and transmit the generated data to the receiving device so that the receiving device can execute the error correction process. [0138] (Supplementary Note 16) A computer program, comprising instructions that cause an available bandwidth estimating device to realize: a transmission rate acquiring means for acquiring a transmission rate, which is an amount of data transmitted by a transmitting device per unit time to a receiving device connected so as to be capable of communicating via a communication network; and an available bandwidth estimating means for estimating an available bandwidth, which is a communication bandwidth available in a communication path between the transmitting device and the receiving device, based on: a mathematical model constructed by representing a relation between the available bandwidth and the transmission rate by a dynamic model including a mobile body that can move in a preset moving direction and an elastic body that transforms in the moving | direction by a movement amount of movement of the mobile body in the moving direction; and the acquired transmission rate. [0139] (Supplementary Note 17) The computer program according to Supplementary Note 16, wherein the mathematical model is constructed on the assumption that external force applied to the mobile body in the moving direction has a magnitude depending on the transmission rate, and that a distance in the moving direction between a preset reference position and a position of the mobile body is the available bandwidth. [0140] (Supplementary Note 18) The computer program according to Supplementary Note 16 or 17, wherein the dynamic model includes a viscous body that delays movement of the mobile body in the moving direction due to external force applied to the mobile body. [0141] (Supplementary Note 19) The computer program according to any of Supplementary Notes 16 to 18, comprising instructions that cause the available bandwidth estimating device to realize: a reception characteristic information estimating means for estimating a data loss ratio, which is a ratio of an amount of data lost in the communication network among the data transmitted by the transmitting device to a total amount of the data transmitted by the transmitting device based on the estimated available bandwidth; a transmission parameter determining means for determining redundancy of the data so that, in a case that part of the data is lost in the communication network at the estimated data loss ratio, the receiving device can restore transmission information by executing an error correction process based on the received data; and a data transmitting means for encoding the transmission information to generate the data having the determined redundancy and transmit the generated data to the receiving device so that the receiving device can execute the error correction process. [0142] The present invention is based upon and claims the benefit of priority from Japanese patent application No. 2009-282617, filed on December 14, 2009, the disclosure of which is incorporated herein in its entirety by reference. INDUSTRIAL APPLICABILITY [0143] The present invention can be applied to an available bandwidth estimating device that estimates an available bandwidth in a communication network, a server device that delivers content data representing content, or the like. DESCRIPTION OF REFERENCE NUMERALS [0144] 1 content delivery system 100 transmitting device (available bandwidth estimating device) 101 data transmitting part 102 transmission rate acquiring part 103 reception rate acquiring part 104 model parameter estimating part 105 available bandwidth estimating part 106 reception characteristic information estimating part 107 transmission parameter determining part 200 receiving device 201 data receiving part 202 reception information transmitting part 300 available bandwidth estimating device 301 transmission rate acquiring part 302 available bandwidth estimating part Amendment (IN) CLAIMS 1. An available bandwidth estimating device, comprising: a transmission rate acquiring means for acquiring a transmission rate, which is an amount of data transmitted by a transmitting device per unit time to a receiving device connected so as to be capable of communicating via a communication network; and an available bandwidth estimating means for estimating an available bandwidth, which is a communication bandwidth available in a communication path between the transmitting device and the receiving device, based on: a mathematical model representing a relation between the available bandwidth and the transmission rate and constructed by assuming that a function including at least one of a term proportional to the available bandwidth and a term proportional to a time derivative of the available bandwidth is equal to a function in which the transmission rate is a variable; and the acquired transmission rate. 2. The available bandwidth estimating device according to Claim 1, wherein the mathematical model is constructed by representing the relation between the available bandwidth and the transmission rate by a dynamic model including a mobile body that can move in a preset moving direction and an elastic body that transforms in the moving direction by a movement amount of movement of the mobile body in the moving direction. 3. The available bandwidth estimating device according to Claim 2, wherein the mathematical model is constructed on the assumption that external force applied to the mobile body in the moving direction has a magnitude depending on the transmission rate, and that a distance in the moving direction between a preset reference position and a position of the mobile body is the available bandwidth. 4. The available bandwidth estimating device according to Claim 3, wherein the mathematical model is constructed on the assumption that elastic force generated by the elastic body has a magnitude of a value as the result of multiplying an amount of movement of the mobile body from a force-free position, which is a position of the mobile body where the elastic force becomes 0, by an elastic modulus, which is a proportionality factor, and that the elastic force works in a direction opposite to a direction in which the mobile body moves from the force-free position. 5. The available bandwidth estimating device according to Claim 4, comprising: a reception rate acquiring means for acquiring a reception rate, which is an amount of data received by the receiving device from the transmitting device per unit time; and a model parameter estimating means for estimating a distance between the reference position and the force-free position and the elastic modulus based on the acquired reception rate, the acquired transmission rate, and the mathematical model. 6. The available bandwidth estimating device according to any of Claims 2 to 5, wherein the dynamic model includes a viscous body that delays movement of the mobile body in the moving direction due to external force applied to the mobile body. 7. The available bandwidth estimating device according to Claim 6, wherein the mathematical model is constructed on the assumption that resistance force generated by the viscous body has a magnitude of a value as the result of multiplying a speed of movement of the mobile body in the moving direction by a viscosity coefficient, which is a proportionality factor, and that the resistance force works in a direction opposite to a direction in which the mobile body moves. 8. The available bandwidth estimating device according to Claim 7, comprising: a reception rate acquiring means for acquiring a reception rate, which is an amount of data received by the receiving device from the transmitting device per unit time; and a model parameter estimating means for estimating the viscosity coefficient based on the acquired reception rate, the acquired transmission rate, and the mathematical model. 9. The available bandwidth estimating device according to any of Claims 1 to 8, comprising: a reception characteristic information estimating means for estimating reception characteristic information representing a characteristic of reception of the data by the receiving device based on the estimated available bandwidth. 10. The available bandwidth estimating device according to Claim 9, wherein the reception characteristic information includes information representing at least one of: a reception rate, which is an amount of data received by the receiving device from the transmitting device per unit time; a data loss ratio, which is a ratio of an amount of data lost in the communication network among the data transmitted by the transmitting device to a total amount of the data transmitted by the transmitting device; and a data delay time, which is a time from a moment of transmission of the data from the transmitting device to a moment of reception of the data by the receiving device. 11. The available bandwidth estimating device according to Claim 10, wherein: the available bandwidth estimating device configures the transmitting device; and the reception characteristic information includes information representing the data loss ratio, the available bandwidth estimating device, comprising: a transmission parameter determining means for deterrnining redundancy of the data so that, in a case that part of the data is lost in the communication network at the estimated data loss ratio, the receiving device can restore transmission information by executing an error correction process based on the received data; and a data transmitting means for encoding the transmission information to generate the data having the determined redundancy and transmit the generated data to the receiving device so that the receiving device can execute the error correction process. ) 12. The available bandwidth estimating device according to Claim 11, wherein the transmission parameter determining means determines a pair of the transmission rate and the redundancy so as to maximize an amount of the transmission information transmitted per unit time within a range that the receiving device can restore the transmission information by executing the error correction process based on the received data. 13. An available bandwidth estimating method, comprising: acquiring a transmission rate, which is an amount of data transmitted by a transmitting device per unit time to a receiving device connected so as to be capable of communicating via a communication network; and estimating an available bandwidth, which is a communication bandwidth available in a communication path between the transmitting device and the receiving device, based on: a mathematical model representing a relation between the available bandwidth and the transmission rate and constructed by assuming that a function including at least one of a term proportional to the available bandwidth and a term proportional to a time derivative of the available bandwidth is equal to a function in which the transmission rate is a variable; and the acquired transmission rate. 14. The available bandwidth estimating method according to Claim 13, wherein the mathematical model is constructed by representing the relation between the available bandwidth and the transmission rate by a dynamic model including a mobile body that can move in a preset moving direction and an elastic body that transforms in the moving direction by a movement amount of movement of the mobile body in the moving direction. 15. The available bandwidth estimating method according to Claim 14, wherein the mathematical model is constructed on the assumption that external force applied to the mobile body in the moving direction has a magnitude depending on the transmission rate, and that a distance in the moving direction between a preset reference position and a position of the mobile body is the available bandwidth. 16. The available bandwidth estimating method according to Claim 15, wherein the mathematical model is constructed on the assumption that elastic force generated by the elastic body has a magnitude of a value as the result of multiplying an amount of movement of the mobile body from a force-free position, which is a position of the mobile body where the elastic force becomes 0, by an elastic modulus, which is a proportionality factor, and that the elastic force works in a direction opposite to a direction in which the mobile body moves from the force-free position. 17. A computer program, comprising instructions that cause an available bandwidth estimating device to perform operations including: acquiring a transmission rate, which is an amount of data transmitted by a transmitting device per unit time to a receiving device connected so as to be capable of communicating via a communication network; and estimating an available bandwidth, which is a communication bandwidth available in a communication path between the transmitting device and the receiving device, based on: a mathematical model representing a relation between the available bandwidth and the transmission rate and constructed by assuming that a function including at least one of a term proportional to the available bandwidth and a term proportional to a time derivative of the available bandwidth is equal to a function in which the transmission rate is a variable; and the acquired transmission rate. 18. The computer program according to Claim 17, wherein the mathematical model is constructed by representing the relation between the available bandwidth and the transmission rate by a dynamic model including a mobile body that can move in a preset moving direction and an elastic body that transforms in the moving direction by a movement amount of movement of the mobile body in the moving direction. 19. The computer program according to Claim 18, wherein the mathematical model is constructed on the assumption that external force applied to the mobile body in the moving direction has a magnitude depending on the transmission rate, and that a distance in the moving direction between a preset reference position and a position of the mobile body is the available bandwidth. 20. The computer program according to Claim 19, wherein the mathematical model is constructed on the assumption that elastic force generated by the elastic body has a magnitude of a value as the result of multiplying an amount of movement of the mobile body from a force-free position, which is a position of the mobile body where the elastic force becomes 0, by an elastic modulus, which is a proportionality factor, and that the elastic force works in a direction opposite to a direction in which the mobile body moves from the force-free position.