Arena Simulation (Rockwell) - steady -state / model verification

Question

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

Answer 1

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.

Answer 2

"Steady" state in your case means that state variable averaged over small period of time is constant over long periods of time. If you measure some output f(t) then you would have to show that f averaged over N (like 15 or 100) time steps no longer significantly changes as function of time. I'm assuming you are dealing with a stochastic system in which case you will always have small variations in time (for non-stochastic, i.e. deterministic system, the system will reach a truly constant value of each of its state variable(s)).

So you have to instrument your Arena model so you can measure the quantity that represents steady state. Your question doesn't make it clear what that is but perhaps WIP: continue the simulation, providing entities to supply chain, and if WIP is as I describe above then you have reached steady state.

Answer 3

ok, I change the replication length from 100 to 10000 and the WIP output changed from 12.67 to 12.604, which should be okay. I didnt use any time arrival etc. I only got from the report: Other Time, WIP (represents average inventory), number in & number out and some specifiet cost related data.

I also try to argue with littles law, WIP / CT = TH to show that it is closed. I used various demand variability types.