As far as I know, there is no easy way to model your requirements with built-in blocks. Have you tried using the custom SimEvents block authoring environment viz. 'MATLAB Discrete Event System' OR 'Discrete Event chart'?
I believe using one of the above should help you achieve what you want. You can start with 'Custom Server' available in SimEvents Design Patterns and modify it to suit your needs.
If you have any questions please feel free to ask here, we can help you.