Creating discrete events based on a defined distribution

I believe my question is, how do I generate discrete events based on a defined distribution over a time period?

My simulation is modeling a web application that allows a voter to cast their ballot in an election. I am trying to accomplish a way to ingest the voters to my system. I have defined a distribution of voters arriving to the system hourly over a given day and daily over a week. For the purpose of my initial model, I can address each arrival distribution separately. I have imported my arrival distributions into a time series element that represents “change over previous time interval”. The primary output is an instantaneous value that is being used as my event definition for my timed event which is the initial entrance to the system. For the timed event, I have defined the occurrence type as ‘defined cumulative event count’ and the count is defined via the timed series of my arrival times.

My initial entrance to the system is via the timed event element followed by a series of event delay elements to model the workflow of my system.  The event delay elements are responding based on a stochastic element defined by a sampled results distribution.

My overall goal is to determine the required resources in my system to model response times to the voters, total processing time in my system, the required response times of external systems feeding into my system, and the required throughput of external systems receiving data from my system.