Product Form
Node Utilizations
Each station behaves like an exact stable node once its effective arrival rate is known. The node traffic intensities are exact fractions, and their interpretation is a busy fraction rather than a job count. This lesson checks local stability before using network-level product form.
Station A utilization
Station A utilization is 1/3. Why: divide station A arrivals by station A service capacity to get the long-run fraction of time that station is busy. A utilization is not a count of jobs; it is a load ratio that tells whether the node has enough service capacity for its effective arrivals.
Station B utilization
Station B utilization is 1/2. Why: station B is slower, so the same effective arrivals create heavier traffic there. That is the first network lesson: two stations can see the same flow but have different congestion because their service rates differ.
Both stations stable
Both utilizations are below 1. Why: each station must have service capacity above its effective arrival rate before a steady-state product-form calculation is claimed. Stability is checked locally at every node, because one unstable station would make the network mean grow without bound.
Diagram note
The table recomputes both utilizations from exact arrival and service rates. Read rho as a busy-fraction at a node, not as a network probability by itself. The exact network results that follow rely on these stable node loads inside an idealized open Jackson tandem. Pixel positions are rounded for layout; every number shown is exact.