Anna says:
You have those I ask for size
Though not everything inside
Completing the order of queue
That's how I acquire you
Alex says:
Number of queues I cannot count
Joined to pose you, a new fount
Another copy of you
That's completion to go through
Tommy says:
Already so complete own
No breakage when let alone
Ironic, 'cause of the queue
Totally broken in you
What are you?
Subtle hint:
Focus on how "queue" is pronounced.
Moderate hint:
For each speakers of the poem, the first two letters of their name are a clue.