The stochastic multicommodity flow problem

This paper formulates and classifies some multicommodity flow problems (MFP) on “stochastic networks.” Here, the arc attributes are not necessarily deterministic, but, rather, are allowed to be probabilistic. Some special cases of the stochastic multicommodity flow problems (SMFP) are considered where the resultant formulations are solvable by existing algorithms for MFP. Specifically, we consider the following problems: SMFP‐FLOW INDEPENDENT, where the arc travel attributes are random but not dependent on the flows in the network, and SMFP‐FLOW DEPENDENT, where the stochasticity of arc travel attributes is either due to random demands or due to arc free‐flow travel attributes being probabilistic. The scenario where the cost function c(w) , of travel attribute w , is linear is fully explored‐for both the above problems. Also, some special cases of the problems are studied when c(w) is exponential or quadratic in w . As an illustrative application, some traffic assignment problems on stochastic networks are formulated and solved as SMFPs.