Product-form node metrics add into network metrics. The total mean count and total mean time are exact fractions for the pinned tandem. The lesson interprets L as the mean number in the whole network and W as the corresponding time through the network by Little's law.

highlighted = computed this step

Node mean counts

Mean count at station A is 1/2 and mean count at station B is 1. Why: each node uses its own exact utilization, so congestion is not evenly spread just because the same jobs visit both stations. A node mean count is the long-run average number of jobs at that station, including any waiting and service there.

LA=1/2LB=1L_A=1/2\quad L_B=1
Network mean counts and timesNode and network metrics are exact fractions.nodeA nodeB totalnodeAnodeBtotal1/213/21/213/2

Network mean count

The total mean number in the network is 3/2. Why: add the mean counts across stations because a job in either node is still a job inside the network. This total is the network-level workload snapshot: how many jobs, on average, are somewhere in the tandem system.

L=LA+LB=3/2L=L_A+L_B=3/2
Network mean counts and timesNode and network metrics are exact fractions.nodeA nodeB totalnodeAnodeBtotal1/213/21/213/2

Node mean times

Mean time at station A is 1/2 and mean time at station B is 1. Why: each station contributes its own sojourn time, and a job experiences those times in sequence along the route. The per-node times help explain where the total delay comes from rather than hiding everything in one aggregate.

WA=1/2WB=1W_A=1/2\quad W_B=1
Network mean counts and timesNode and network metrics are exact fractions.nodeA nodeB totalnodeAnodeBtotal1/213/21/213/2

Network mean time

The mean time through the network is 3/2. Why: Little's law gives total count divided by external arrival rate, so W is the average time a job spends from entry through exit. This connects the product-form count calculation back to an operational time quantity. Diagram note: all metric entries are exact fractions for the pinned stable tandem. Pixel positions are rounded for layout; every number shown is exact.

W=L/λ=3/2W=L/\lambda=3/2
Network mean counts and timesNode and network metrics are exact fractions.nodeA nodeB totalnodeAnodeBtotal1/213/21/213/2