how can I verify that my Arena model (serial supply chain) is within a steady-stated (closed) system? I got from the simulation reports: number in (614 entities), number out (602 entities) and WIP (average inventory) of around 12.67. Can this used as a proof? because this is according to my understanding: 614 total entities enter the model, within are on avg 12.67 and until the end of the simulation leave about 602. Is this right? I couldnt find anything in Kelton / Altiok etc
For a queueing simulation, if the long-term average arrival rate is less than the long-term average service rate for all sub-queues it will be a stable system. If the rates are constant, the ratio of arrival rate over service rate is called the traffic intensity of the queue. If any queues within your model have a traffic intensity greater than or equal to 1, they will grow in an unbounded fashion over time.
If the rates vary based on time or state, then you may not know what the traffic intensity actually is. In that case, you can empirically check queue lengths (WIP) and see if it is showing an increasing trend line over time. Note, though, that for high traffic intensities a few hundred entities may be nowhere near enough to analyze your system. For example, an M/M/1 queue with traffic intensity of 0.95 takes as much as 4000 to 5000 observations to even get warmed up.