Manage Timestamp of Multiple Actors

I’m trying to generate synthetic logs of different types and push to a Kafka topic. In my current implementation, I have actors for each log type. Each log type is having a start/end timestamps. There are several log types each of them having different timestamp ranges. There may be cases where timestamp ranges of different log types overlap each other. I was able to generate logs with the current implementation, but I need to have all these logs generated in time series manner.

Can someone direct me the best way to achieve this?