Suppose urgent and non-urgent missions arrive for “processing” according to two independent arrival processes. The processing times of both mission types are IID. At time 0 the system is empty and there are m idle resources; completing a mission requires one resource.
Urgent missions have priority over non-urgent missions, meaning that if a resource becomes idle, it starts processing an urgent mission (if there’s any in the queue). If there are at least m urgent missions in the queue and the total number of resources is m, the total number of resources is doubled to 2m.
The system remains in “expanded” form until the time it empties (i.e., no people in line nor in service); at point the total number of resources becomes m again.
Present an event graph, including state variables, that could be used as a basis to estimate the average time in the system for each mission type.