Network: http://i.imgur.com/uASvza9.png

Every edge has a traversal time attached. These traversal times change over time. An item takes the exact amount of time to traverse an edge as the traversal time at the instant it begins traversing said edge, regardless if this traversal time changes mid-traversal.

We assume that no two items can enter the network simultaneously. The source node "s" is where new items enter, and immediately, one s-P edge has a cost of 0, and all the others infinite, so it is is simply allocated to a P (producer) node. P-Qs nodes have constant weights all the time. The Qs (queue start) node to Qe (queue end) node edges have a cost that varies over time that is estimated based on the items currently traversing between them. The Qs-C edge costs have constant weights all the time. The C-t edge costs change for every item that reaches any Qe node.