Before revision:  In this context, we consider the  M/G/1-FCFS queue endowed with an arbitrarily-designed cost function for the waiting times of the incoming jobs , and we study an undiscounted value function integrating the total cost surplus expected from each state relative to the steady-state costs.
After revision:  In this context, we consider the continuous-space M/G/1-FCFS queue endowed with an arbitrarily-designed cost function for the waiting times of the incoming jobs , and we study an undiscounted value function integrating the total cost surplus expected from each state relative to the steady-state costs.