B. Buke, Hasenbein, J. J., and Morton, D. P., “Minimizing Makespan in a Multiclass Fluid Network with Parameter Uncertainty,” Probability in the Engineering and Informational Sciences, vol. 23, pp. 457-480, 2009.
We introduce and investigate a new type of decision problem related to multiclass fluid networks. Optimization problems arising from fluid networks with known parameters have been studied extensively in the queueing, scheduling, and optimization literature. In this paper, we explore the makespan problem in fluid networks, with the assumption that the parameters are known only through a probability distribution. Thus the decision maker does not have complete knowledge of the parameters in advance. This problem can be formulated as stochastic nonlinear program. We provide necessary and sufficient feasibility conditions for this class of problems. We also derive a number of other structural results which can be used in developing effective computational procedures for solving stochastic fluid makespan problems.