Factory Physics: waiting and flow
Live factory: stock movement and congestion
Each block is one unit. Gold blocks wait in FIFO order, blue blocks are processing, green blocks have completed. Both lanes use the capacity, arrival rates and CV settings in the Capacity & Waiting calculator below.
Last event: previous and current state
Recent activity history
This simulation uses independent gamma-distributed arrival intervals and processing times with the specified means and CVs (CV 0 is constant, CV 1 is exponential). One machine per lane, unlimited waiting space, no failures or blocking. Simulation results are finite-run observations, not VUT forecasts. Initial and added stock enter the process at injection time.
Little’s Law uses matched long-run averages. During startup or queue growth, average WIP ÷ observed departures per hour is an implied flow time, and need not match the average time of only the units already completed. At arrivals ≥ capacity with variation, do not interpret growing queues as a stable average.
Compare two workloads on the same machine. Change the inputs, then move time forward to watch an extra queue shrink.
Congestion: average queue before the machine
Waiting blocks use VUT estimates and Little’s Law: average queue = arrival rate × average waiting time. This is separate from the extra-work recovery animation.
Recovery illustration assumes steady normal arrivals, constant machine capacity, and no further interruptions. Fractional units represent a continuous flow approximation. This is the time to clear an extra queue, not the VUT average waiting time.
Show the Factory Physics VUT formula
u = arrival rate ÷ capacity. t = average effective processing time. V = (arrival CV² + processing CV²) ÷ 2. CV = standard deviation ÷ mean.
Single-machine approximation for stable utilization below 100%. Queue waiting excludes processing. Effective capacity and processing time must describe the same workstation. These estimates are separate from the one-off recovery drawing above.
How much is inside, how fast it leaves, how long it stays
Little’s Law connects averages for the same process: I = R × T. Flow time includes both waiting and processing.
Additional assumption for the drawing: flow time consists of processing plus waiting. Little’s Law alone cannot identify this split. Include all active processing within the chosen process boundary.
A flow-time ruler
Gold shows waiting; navy shows processing. Segment lengths show their share of total flow time.
How to explain this in class
“Count the average units inside our process. Divide by the average units completed per hour. That gives the average time a unit spends inside, including waiting and processing.”
Try changing WIP from 100 to 60 while holding throughput at 20/hour. Flow time changes from five hours to three hours. This is a target relationship, not proof that an inventory cut alone will maintain throughput.
Use averages over a representative period with a stable flow. Count inventory and completions at the same process boundary. VUT estimates waiting at one workstation; Little’s Law relates total inventory, throughput and flow time.