# How to predict how long a worker will take to perform a task when performance on the task is only known for other workers?

I am trying to model a queue system (via simulation) to see if I can make different work assignments to improve the overall performance (based on a number of metrics). I have historical records of past tasks which includes when they entered the system, who was assigned to perform to the task, and the service time. In my simulator I want to have the option of replaying back these historical records to quantify how different assignment policies could have effected the performance measures in these counterfactuals.

The workers perform at different speeds (i.e. have different service time distributions), so I would like to take this into account in my counterfactual simulations.

• What is the best way to predict how longer worker $A$ will take on task $X$ when all I know about task $X$ is how long it took worker $B$ to complete it?
• In other words, I have two distributions of the same type but with different parameters and given $x$ came from distribution $A$, what would $x'$ be if it instead came from distribution $B$?

My current approach is to find the probability of $x$ in $A$, and then get a number for $x'$ that has similar probability in $B$.

As an aside, I am very new to simulators and queuing theory in general so feel free to provide additional advice or links to resources if you think I could approach this a better way.