What are the equivalent concepts for packet switching in programming?

I am new to intermediate programming and couldn't find the concepts that I have learned in engineering. I have searched them with keywords such as "dispatching, switching, handling, session" but no success in finding the concepts/methods that I have in my mind. I have found some documents about nessage switching and packet forwaring but they are all related to networking area not the algorithm that I am looking for.

I have two groups of customers and customer representatives who need to communicate with each other through REST API. A middle man who need to handle the communication with 2 different REST APIs, one for incoming messages and one for the forwarding one. They are not allowed to communicate without the middle man.

I have created a REST API to receive 2K messages per second as a JSON file. I need to assign a representative to each customer. There are more than 2K representative but only a few of them will be available at one time. So I have to create some sessions for this purpose to avoid assigning offline representatives to customers. My questions is how to handle these processes? What are the exact terms that programmers are using for this type of message handling? It would be appreciated if you could suggest some books and documentations in Python or any other programming languages.