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

2. 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.

3. 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 }.

4. 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

5. 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).

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

8. 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).

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

10. Advanced incremental assignment

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