Fluid analysis of an input control problem

A two-station network with controllable inputs and sequencing control, proposed by Wein (Oper. Res. 38:1065–1078, 1990), is analyzed. A control is sought to minimize holding cost subject to a throughput constraint. In a Lagrangian formulation, input vanishes in the fluid limit. Several alternative fluid models, including workload formulations, are analyzed to develop a heuristic policy for the stochastic network. Both the fluid heuristic and Wein’s diffusion solution are compared with the optimal policy by solving the dynamic program. Examples with up to six customer classes, using Poisson arrival and service processes, are presented. The fluid heuristic does well at sequencing control but the diffusion gives additional, and better, information on input control. The fluid analysis, in particular whether the fluid priorities are greedy, aids in determining whether the fluid heuristic contains useful information.