Frequently I have had to use queuing analysis to determine a best policy. Let's consider a simple example. Let us say you went to a bank. In the old days each teller had a separate line. After decades of analysis it was clear that the average wait/delay was maximum this way as compared to a single line and then the next in line served by the next available teller. For those too young to remember, too bad.
Now the next step was instead of just having one massive bank with lots of tellers they built branch banks with fewer tellers and often at less cost. Thus distributed banks with multiple tellers and a single queue line optimized the process. Then along cam ATM, then bitcoin, and it is all virtual. By the way, Post Offices now work the same way, not as nice as a bank though.
Now how does this apply to the vaccines. Well just look at today, we have "The Banker" opening his two mega sites and the queues are not lines but the old fashion one, where you pick a line and hope the server does not decide on lunch before you get served!
Government has made vaccines the DMV Office, not even the Post Office. Pity.