Discrete flow networks: bottleneck analysis and fluid approximations
Mathematics of Operations Research
Dynamic scheduling of a multiclass fluid network
Operations Research
A New Algorithm for State-Constrained Separated Continuous Linear Programs
SIAM Journal on Control and Optimization
Sequencing and Routing in Multiclass Queueing Networks Part I: Feedback Regulation
SIAM Journal on Control and Optimization
Sequencing and Routing in Multiclass Queueing Networks Part II: Workload Relaxations
SIAM Journal on Control and Optimization
A simplex based algorithm to solve separated continuous linear programs
Mathematical Programming: Series A and B
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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.