How to trace Simultaneous User in performance testing

Requirement:

1. Monthly Users: (50% of total Estimated)
• Users are expected to login when they purchase
• Purchase Cycles are spread over 20 days in a month
• Customers are in a single Time Zone
• Access Times each day is divided over a 4 hour interval (5pm – 9pm) at 50%
• 4 Hour Interval to be distributed at 15-50-25-10 with a peak of 50% (meaning the traffic is a bell curve with a maximum anticipated load of 50% users to be on the system at a given hour.
• Remaining 30% spread over the day (at work, work at home) over a 10 hour day.
• User Session Takes an Average of 2-5 Minutes depending on user type/class

2. Weekly Users: (20% of total Estimated)
• Users are expected to login on the weekend to check their usage
• Access Time distribution over 10 hour period
• Bell Curve is not necessary for this User Type

3. Daily Users: (20% of total Estimated) – These are the users that want to improve their usage and control costs.
• Access Time distribution over 4 hour period
• Users have a smaller Transactions list


Calculation Equation:
Where K is the Required User Usage:
the 50% are spread over 20 days and the weekly are spread over 2 days) and that only 50% of the 60% are active in the peak after work period
so I get

((((K * 0.5 Monthly)/20 days) * 0.6 weight * 0.5 peak)) / (60 Minutes * 5 Minute Session)) +
((K * 0.2 Weekly)/2 days)) / (10 hours * (60 Minutes * 5 Minute Session))) +
(((K * 0.1 Daily))) / (4 hours * (60 Minutes * 5 Minute Session)))

 10,000 Users : 1.196 Simultaneous Users