Our swat team members, are not just setting at home awaiting a call, they are out patrolling like all the other officers, but are ready at a moments notice to respond to a swat situation.
This is precisely what I wanted to indicate is the case in Canada in my experience. Tactical, and containment team members are 'mobile' out on patrol. Dispatch centres (tech), as well as training helps direct the assets quickly - 'unit xxxx, we're starting to take calls of a man with a knife, in the general area of c st & d st, if you can start heading that way..'. This one single detail, in my experience gets us 'there' much faster than a dispatcher dicking around trying to get 'all' the details, or a precise location. It's like an early warning system .. a bull horn screaming 'over here!'. Every available officer listening, or actively dispatched races to that area, and enroute all the other details become available, including a more precise location, descriptions, weapons and on and on.
But, having said that, when we watch some of the active shooters incidents play out, and autopsy them afterwards we realize that it's usually beat cops that are first on scene. And unfortunately for them, they're it for a while and need to be on their game, alone (likely) until other units arrive. We cannot rely on specialized teams to save the day...