How to initialize the queue of queue?

I defined following data structures:

typedef int                 profile_lru_q_t[PROFILE_NUM];   
typedef profile_lru_q_t     vc_lru_queue[$];

vc_lru_queue                vc_lru_queue_inst;

It's a queue of queue. I want to initialize it with the following code but failed. Can anyone help me with it？

for (int i=0; i<PROFILE_NUM; i++) begin
    for (int j=SDP_VC_NUM-1; j>=0; j--) begin
        vc_lru_queue_inst[i].push_back = j;
    end
end

One problem is that you do not have a queue of queues. You have a queue of fixed-sized arrays because this line declares a fixed-sized array, not a queue:

typedef int                 profile_lru_q_t[PROFILE_NUM];   

If you want to initialize the structure you have, here is a way to do it:

module tb;

parameter PROFILE_NUM = 4;
parameter SDP_VC_NUM  = 4;

typedef int                 profile_lru_q_t [PROFILE_NUM];  // array, not a queue
typedef profile_lru_q_t     vc_lru_queue    [$];            // queue

vc_lru_queue                vc_lru_queue_inst;

initial begin
    for (int i=0; i<PROFILE_NUM; i++) begin
        profile_lru_q_t inner;
        for (int j=SDP_VC_NUM-1; j>=0; j--) begin
            inner[j] = j;
        end
        vc_lru_queue_inst.push_back(inner);
    end
    $display("%p", vc_lru_queue_inst);
end

endmodule

This prints:

'{'{0, 1, 2, 3}, '{0, 1, 2, 3}, '{0, 1, 2, 3}, '{0, 1, 2, 3}}

Although, since you declared the array of a fixed size using PROFILE_NUM, it does not make much sense to iterate over SDP_VC_NUM.

Another problem is that push_back = j is incorrect syntax. push_back.(j) is legal.

Refer to IEEE Std 1800-2023 section 7.10 Queues.