It's night and it's an emergency! The Joker is loose! Gotham needs Batman. But there isn't a cloud in the sky. How does Commissioner Gordon summon him?
Assuming he doesn't have a red phone line directly to Batman like in the old TV show, obviously.
Plot twist: Gordon doesn't actually need the bat signal to contact him. It's there to drive fear to street criminals when they see the sign and think that the Bat is heading their way.
Also Gordon prefers talking to the man dressed like a bat on the rooftop rather than in his small office.
Wayne Enterprises maintains a cloud machine so their spoiled, good-for-nothing, CEO can always see at least 1 cloud when he looks out the windows of his manner house. Batman should really do something about that guy.
He is on top of the police precinct, which is not the highest building in the city. All he needs to do is project it against the highest building in the city: Wayne Tower.
The batsignal has often been described as a way to instill fear in the criminals, not as the most effective way to summon Batman per se. Certainly Batman doesn't just watch fhe sky all night long to wait for the batsignal to come up, he has ways to get notified without seeing it.
The commissioner and his friend snoop take some huge rips and make their own clouds of gange that billow out into the sky. The commissioner forgets what all the fuss is about when batman turns up