Discrete flow networks: bottleneck analysis and fluid approximations
Mathematics of Operations Research
An algorithm for a class of continuous linear programs
SIAM Journal on Control and Optimization
On the Solutions of a Class of Continuous Linear Programs
SIAM Journal on Control and Optimization
Forms of Optimal Solutions for Separated Continuous Linear Programs
SIAM Journal on Control and Optimization
A Duality Theory for Separated Continuous Linear Programs
SIAM Journal on Control and Optimization
A New Algorithm for State-Constrained Separated Continuous Linear Programs
SIAM Journal on Control and Optimization
Polynomial time algorithms for some evacuation problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Faster Algorithms for the Quickest Transshipment Problem
SIAM Journal on Optimization
The Quickest Multicommodity Flow Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Fluid Heuristic for Minimizing Makespan in Job Shops
Operations Research
Dynamic Programming
Scheduling multiclass queueing networks and job shops using fluid and semidefinite relaxations
Scheduling multiclass queueing networks and job shops using fluid and semidefinite relaxations
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We give an approximation algorithm for the optimal control problem in fluid networks. Such problems arise as fluid relaxations of multiclass queueing networks, and are used to find approximate solutions to complex job shop scheduling problems. In a network with linear flow costs and linear, per-unit-time holding costs, our algorithm finds a drainage of the network, that for given constants ε 0 and δ 0 has total cost (1 + ε)OPT + δ, where OPT is the cost of the minimum cost drainage. The complexity of our algorithm is polynomial in the size of the input network, 1/ε and log 1/δ. The fluid relaxation is a continuous problem. While the problem is known to have a piecewise constant solution, it is not known to have a polynomially-sized solution. We introduce a natural discretization of polynomial size and prove that this discretization produces a solution with low cost. This is the first polynomial time algorithm with a provable approximation guarantee for fluid relaxations.