A many-server fluid limit for the Gt/GI/st+GIGt/GI/st+GI queueing model experiencing periods of overloading

A many-server heavy-traffic functional weak law of large numbers is established for the Gt/GI/st+GIGt/GI/st+GI queueing model, which has customer abandonment (the +GI+GI), time-varying arrival rate and staffing (the subscript tt) and non-exponential service and patience distributions (the two GIGI’s). This limit provides support for a previously proposed deterministic fluid approximation, and extends a previously established limit for the special case of exponential service times.