A method for performing by a network side device random access based on multiple uplink timing advances comprising: in response to acquiring that a user equipment, UE, has multiple uplink timing advances, initiating, by a network side, a random access on a designated carrier of a secondary cell, SCell, for the UE; wherein initiating the random access on the designated carrier of the SCell for the UE comprises: determining, by the network side, a carrier for transmitting a random access resource allocation message Msg0 according to whether cross-carrier scheduling is configured for the designated carrier on which the random access is to be initiated; transmitting, by the network side, the random access resource allocation message, Msg0, on a scheduling carrier configured in response to determining that a cross-carrier scheduling is configured for a designated carrier on which a random access of a secondary cell, SCell, is to be initiated for the UE, and transmitting, by the network side, the Msg0 on a downlink carrier of the SCell in which the random access is to be initiated in response to determining that the cross-carrier scheduling is not configured for the designated carrier on which the random access is to be initiated; and the method further comprises: transmitting, by the network side, a random access response message, Msg2, Media Access Control, MAC, Protocol Data Unit, PDU, on the downlink carrier of the SCell in which the random access is initiated; or transmitting, by the network side, an Msg2 MAC PDU on the same carrier as a Msg2 scheduling command. in response to acquiring that a user equipment, UE, has multiple uplink timing advances, initiating, by a network side, a random access on a designated carrier of a secondary cell, SCell, for the UE; wherein initiating the random access on the designated carrier of the SCell for the UE comprises: determining, by the network side, a carrier for transmitting a random access resource allocation message Msg0 according to whether cross-carrier scheduling is configured for the designated carrier on which the random access is to be initiated; transmitting, by the network side, the random access resource allocation message, Msg0, on a scheduling carrier configured in response to determining that a cross-carrier scheduling is configured for a designated carrier on which a random access of a secondary cell, SCell, is to be initiated for the UE, and transmitting, by the network side, the Msg0 on a downlink carrier of the SCell in which the random access is to be initiated in response to determining that the cross-carrier scheduling is not configured for the designated carrier on which the random access is to be initiated; and determining, by the network side, a carrier for transmitting a random access resource allocation message Msg0 according to whether cross-carrier scheduling is configured for the designated carrier on which the random access is to be initiated; transmitting, by the network side, the random access resource allocation message, Msg0, on a scheduling carrier configured in response to determining that a cross-carrier scheduling is configured for a designated carrier on which a random access of a secondary cell, SCell, is to be initiated for the UE, and transmitting, by the network side, the Msg0 on a downlink carrier of the SCell in which the random access is to be initiated in response to determining that the cross-carrier scheduling is not configured for the designated carrier on which the random access is to be initiated; and the method further comprises: transmitting, by the network side, a random access response message, Msg2, Media Access Control, MAC, Protocol Data Unit, PDU, on the downlink carrier of the SCell in which the random access is initiated; or transmitting, by the network side, an Msg2 MAC PDU on the same carrier as a Msg2 scheduling command. transmitting, by the network side, a random access response message, Msg2, Media Access Control, MAC, Protocol Data Unit, PDU, on the downlink carrier of the SCell in which the random access is initiated; or transmitting, by the network side, an Msg2 MAC PDU on the same carrier as a Msg2 scheduling command.