I hung up my phone and started typing. "Jason just called me, ideas for dinner before the movie?" and sent it to Sara. My phone know's a lot about Sara and where she might be. It encrypted the message for her eyes only, indicated that the message will probably be delivered in midtown with a 70% confidence rating. After all it was 4pm on a Thursday, where else would she be?
My office runs a messages hub. It takes messages from nearby devices and puts them on the internet where they're sent to hubs closer to their delivery locations. Midtown is full of hubs and even if it wasn't there's enough people in manhattan that it would only take a few extra seconds to go phone to phone.
My office's hub took at look at the message and queried it's routing database. It didn't have a better idea of where Sara might be so it remembered mine and chose it's favorite hub in midtown the one at Egyptian restaurant down the block. This hub has the best relationship with mine out of all the nearby hubs. It's rarely overloaded, has a decent enough connection and it's pretty close to Sara's phone most of the time. It also knows my hub is in a similar situation when sending me messages.
The Egyptian restaurant's hub broadcasts the message, it's too far away from Sara's phone for it to hear but a business man is walking near by. His phone picks up the message and sends it to everyone on the block. A woman at the far end had recently taken the elevator past Sara's floor of the office and their phone had seen hers. Her phone relays it to the doorman of her building who's still in range. The doorman always kept his phone plugged in and is in a perfect spot to relay messages. He doesn't really know too much about the messaging app, other than it gives him some spending money at the end of the month and people are happier when he keeps it on.
Sara had tried to get reception to put in a hub, or at least keep the messaging app in "hub mode" on their phones. They're plugged in, someone is almost always there and they'd help relay all the messages to the floor of the office. It would be great for everyone! Except one of the receptionists claimed it slowed down his phone. (Probably gave his online games some lag.) And the other one jacked up the price for each relay 100 times the market rate and everyone routed around him. He never made any money and turned it off. Their loss, they can keep paying for their service plans.
The doorman's phone sends the message bouncing up the phones in the elevator cars until it hits someone walking across the office on the floor above who's also in range of Sara. Her phone receives the message with a "Beep Boop" The whole affair took 7 seconds and negligible battery life.
"I just left work. Swinging by comics, then I'll head towards the theater. I had pizza for lunch, what did he say?"