Just wait it out?
How many cops should be sitting on the house waiting? Overtime or pulled off the road? Should you keep SWAT onsite in case he starts taking shots again and you need to move quickly? Medical? Fire?
Should neighbors be displaced? How far out should you push the cordon? How long can you reasonably expect to keep people out of their own homes? Do you let some get in to get important medicines, stuff for work, etc? If so, do you have to send an officer with them to babysit?
Should roads be blocked off? How many additional cops will you need to man the roadblocks? Will they be overtime or pulled off the road?
Assuming the guy doesn't give up or go to sleep in a few hours, when do you finally order guys through the door? If he looks like he's sleeping do you just send a Uniform through and hope for the best or do you use SWAT?
While you have most of your resources parked at one guy's house, how do you handle the other calls that come in? "Sorry, we're waiting for a trigger-happy grandpa to go to sleep. Good luck with your problem."
There's more to waiting than just waiting. It is good and appropriate to give some situations more time, but in a case like this the guy punched his own ticket. We're not talking about someone who was just threatening to hurt himself or just threatening to come kick someone's dog. He threatened a couple of folks with a gun, then actually shot at two police officers when they announced themselves. He then had three hours during which he had every opportunity to stop being a jackass. He didn't.
The only thing that makes this case even worthy of comment is the guy's age, and I'm not sure why that entitles him to special treatment after he tries to kill folks. I doubt many of you would be calling for a police siege of indeterminate length if the guy were 17 years old but the situation was otherwise identical. Sure, the 17 year old might be able to stay awake a little longer, but he'll go to sleep eventually, and is his life really worth less? Indeed, if we're willing to spend the extra money and time to give a 107 year old attempted murderer a better chance at living another year or two, why not spend many times that to give a 17 year old shooter a chance at 90 more years?