Comparison of Fluid Approximations for Service Systems with State-Dependent Service Rates and Return Probabilities

•We analyze the impact of inserting a delay between service completion and return.•Inserting a constant delay does not change fluid approximation equilibrium points.•A constant delay does changes the fluid approximation transient behavior.•Simulations indicate less impact on transient behavior if delay is exponential.•Bistable behavior can occur if return and service rates are state-dependent.