I would have to guess that this all happens in an instant? If not, they may have already had the funeral for the patient by the time all this plays out.
Less than a minute.
....under OPTIMUM conditions. Otherwise, the term, "next available," or "no unit available" is used.
NYC*EMS is not sitting around waiting for runs, for the most part. It's not like those old black-and-white movies, where the ambulance crew is sitting around in the hospital and then run out. They very often go to run, after run, after run, etc, sometimes all night.
And always remember something else: no one has a Constitutional right to ambulance service, or, for that matter, Police or Fire responses. It is what it is when the first call comes in. "No one available" means just that: no one is coming right away.
And, in the state of affairs NYC is in right now, that may happen more often than not in the near future.