Is the concept of Rx debounce possible in a distributed environment?

I am building a server-side system that handles streams of time-series events from multiple users and I'd like to perform an action after a certain quiet period has elapsed in the event stream of every user.

For example, a user emits this stream of data:

-[5]------[4]-[3]--[2][1]-->

My consumer will handle this stream of data, but will also perform an operation if X time has passed after [4] and before [5].

When looking at the issue Rx debounce immediately comes to mind.

But is Rx fit for an environment where I run more than one consumer for the streams?

To my understanding, multiple consumers means that individual consumers potentially may be exposed only to parts of the time-series, making it impossible to know when a specific user's stream has started or ended.

For example:

User | Applications -[5]----[4]-[3]--[2][1]-> | ---> [4]--[2]-[1] ---> CONSUMER 1 | \ | \-> [5]------[3] ---> CONSUMER 2 

So can I handle streams with more than one consumer but still harness the power or Rx and debounce?

Is there a more fitting solution for this issue?