What limits flow through parallel paths?

Two conveyor branches can carry items side by side, yet a slower belt feeding both can still limit the whole route. Parallel paths add carrying capacity only where the rest of the system can supply and receive their combined flow. Capacity is an upper bound; throughput is the amount actually passing through the complete network each minute.

This directed network has one source connection, two independent branches, and one shared exit after the branches rejoin. In steady flow with no loss or storage, the incoming amount equals the outgoing amount at each split or merge. Neither branch may exceed its capacity, and their combined flow cannot exceed either shared connection.

For this arrangement, greatest feasible throughput is the smallest of source capacity, the sum of branch capacities, and exit capacity. The illustration gives 8 items per minute at the source, branch capacities of 5 and 4, and an exit capacity of 10. Although the branches could together carry 9, the shared source limits throughput to 8.

A stated routing rule fills the upper branch first, then the lower. The 8-item total therefore divides into 5 upper and 3 lower. Extra lower-branch capacity does not create another item or bypass the source limit. With different capacities, the combined branches or shared exit could become the bottleneck instead.

Widening the lower branch alone would not raise the eight-item total while the source stays limited to eight. If the source became faster, the combined branch capacity could become the next limit; a smaller exit could instead hold everything back after the paths rejoin. The bottleneck belongs to the connected route, so adding capacity in one place helps only when that place is limiting the whole flow.