Incremental Assignment (fixed demand) Transportation System Analysis Incremental Assignment (fixed demand)

Concept Assigns a portion of the O-D matrix at each iteration. The travel times are updated & an additional portion of the O-D matrix is loaded onto the network. Thus, the general shape of link performance functions can be "traced" with successive assignments.

Algorithm Step 0: Preliminaries. Divide each origin-destination entry into N equal portions (i.e. set qrsn = qrs /N). Set n := 1 and xa0 = 0 , . Step 1: Update. Set tan =ta (xan-1 ) , . Step 2: Incremental loading. Perform all-or-nothing assignment based on {tan }, but using only trip rates qrsn for each O-D pair. This yields a flow pattern {wan }.

Step 3: Flow summation. Set xan = xan-1 + wan, . Step 4: Stopping rule. If n = N, stop (current link flows = solution); otherwise, set n:= n + 1 & go to step 1. wan : flow on link a from assignment of the nth increment of O-D matrix

In some versions (step 2) O-D pairs are selected in random, with a flow summation phase (as in step 3) and travel-time update (as in step4) following each partial assignment (i.e. after each O-D entry is loaded).

Example: network with 3 links & 1 O-D pair

As evident from the table the two used paths (links 1 and 2) do not exhibit equal travel times. Furthermore these travel times are higher than that of the unused path (link 3).

Advanced incremental assignment Suggestion: Increments: 2 percent in first 10 iterations. 5 percent in next 12 iterations. 2 percent in last 10 iterations.

Advanced incremental assignment

Conclusion The incremental assignment heuristic method reviewed in this presentation may converge by setting a negligible increment and large number of iterations.