A bandwidth allocation apparatus for a relay transmission system that relays radio communication in a communication system configured to perform the radio communication according to a time-division duplex scheme, the relay transmission system comprising the bandwidth allocation apparatus and at least one terminating apparatus, the communication system comprising an upper-level apparatus and at least one lower-level apparatus, the upper-level apparatus being connected to the bandwidth allocation apparatus, the bandwidth allocation apparatus being connected to the at least one lower-level apparatus via the at least one terminating apparatus, the bandwidth allocation apparatus comprising: a traffic information acquisition unit configured to acquire, from the at least one terminating apparatus, traffic information indicating a traffic amount between the bandwidth allocation apparatus and the at least one terminating apparatus in a case in which the at least one lower-level apparatus performs communication with the upper-level apparatus via the at least one terminating apparatus; a traffic starting position detection unit configured to detect a start timing of burst traffic on a basis of the traffic information; a traffic information extraction unit configured to extract information on a traffic amount of each of traffic allocation periods from the traffic information extracted for each of the at least one lower-level apparatus; a traffic amount estimation unit configured to calculate, for each of the at least one lower-level apparatus, an average value and a standard deviation of the traffic amount in the traffic allocation periods on a basis of the traffic information and calculate a surplus bandwidth in an uplink between the bandwidth allocation apparatus and the at least one terminating apparatus by subtracting a sum of at least one first bandwidth that is an allocation bandwidth based on the average value for the at least one lower-level apparatus and a sum of at least one second bandwidth that is an allocation bandwidth based on the standard deviation for the at least one lower-level apparatus from an allocatable bandwidth in a bandwidth allocation period; a bandwidth allocation unit configured to allocate the at least one first bandwidth to the at least one terminating apparatus from a start of the bandwidth allocation period, the start timing detected by the traffic starting position detection unit being used as a start timing of the bandwidth allocation period; and a newly-connected terminating apparatus authentication unit configured to set an activation window in which a newly-connected terminating apparatus sends an authentication request signal to the bandwidth allocation apparatus in the surplus bandwidth in the uplink. a traffic information acquisition unit configured to acquire, from the at least one terminating apparatus, traffic information indicating a traffic amount between the bandwidth allocation apparatus and the at least one terminating apparatus in a case in which the at least one lower-level apparatus performs communication with the upper-level apparatus via the at least one terminating apparatus; a traffic starting position detection unit configured to detect a start timing of burst traffic on a basis of the traffic information; a traffic information extraction unit configured to extract information on a traffic amount of each of traffic allocation periods from the traffic information extracted for each of the at least one lower-level apparatus; a traffic amount estimation unit configured to calculate, for each of the at least one lower-level apparatus, an average value and a standard deviation of the traffic amount in the traffic allocation periods on a basis of the traffic information and calculate a surplus bandwidth in an uplink between the bandwidth allocation apparatus and the at least one terminating apparatus by subtracting a sum of at least one first bandwidth that is an allocation bandwidth based on the average value for the at least one lower-level apparatus and a sum of at least one second bandwidth that is an allocation bandwidth based on the standard deviation for the at least one lower-level apparatus from an allocatable bandwidth in a bandwidth allocation period; a bandwidth allocation unit configured to allocate the at least one first bandwidth to the at least one terminating apparatus from a start of the bandwidth allocation period, the start timing detected by the traffic starting position detection unit being used as a start timing of the bandwidth allocation period; and a newly-connected terminating apparatus authentication unit configured to set an activation window in which a newly-connected terminating apparatus sends an authentication request signal to the bandwidth allocation apparatus in the surplus bandwidth in the uplink.