Scheduling networks of queues: heavy traffic analysis of a simple open network
Queueing Systems: Theory and Applications
A theory of rolling horizon decision making
Annals of Operations Research
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Least controls for a class of constrained linear stochastic systems
Mathematics of Operations Research
Dynamic scheduling of a multiclass fluid network
Operations Research
Heavy Traffic Analysis of a Controlled Multiclass Queueing Network via Weak Convergence Methods
SIAM Journal on Control and Optimization
Heavy Traffic Convergence of a Controlled, Multiclass Queueing System
SIAM Journal on Control and Optimization
The Complexity of Optimal Queuing Network Control
Mathematics of Operations Research
Sequencing and Routing in Multiclass Queueing Networks Part I: Feedback Regulation
SIAM Journal on Control and Optimization
A Multiclass Feedback Queueing Network with a Regular Skorokhod Problem
Queueing Systems: Theory and Applications
Stability of two families of queueing networks and a discussion of fluid limits
Queueing Systems: Theory and Applications
An invariance principle for semimartingale reflecting Brownian motions in an orthant
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
State space collapse with application to heavy traffic limits for multiclass queueing networks
Queueing Systems: Theory and Applications
Dynamic scheduling in multiclass queueing networks: Stability under discrete-review policies
Queueing Systems: Theory and Applications
Sequencing and Routing in Multiclass Queueing Networks Part II: Workload Relaxations
SIAM Journal on Control and Optimization
A Fluid Heuristic for Minimizing Makespan in Job Shops
Operations Research
In Search of Sensitivity in Network Optimization
Queueing Systems: Theory and Applications
Two Workload Properties for Brownian Networks
Queueing Systems: Theory and Applications
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This paper is concerned with dynamic control of stochastic processing networks. Specifically, it follows the so called “heavy traffic approach,” where a Brownian approximating model is formulated, an associated Brownian optimal control problem is solved, the solution of which is then used to define an implementable policy for the original system. A major challenge is the step of policy translation from the Brownian to the discrete network. This paper addresses this problem by defining a general and easily implementable family of continuous-review tracking policies. Each such policy has the following structure: at each point in time t, the controller observes the current vector of queue lengths q and chooses (i) a target position z(q) of where the system should be at some point in the near future, say at time t+l, and (ii) an allocation vector v(q) that describes how to split the server's processing capacity amongst job classes in order to steer the state from q to z(q). Implementation of such policies involves the enforcement of small safety stocks. In the context of the “heavy traffic” approach, the solution of the approximating Brownian control problem is used in selecting the target state z(q). The proposed tracking policy is shown to be asymptotically optimal in the heavy traffic limiting regime, where the Brownian model approximation becomes valid, for multiclass queueing networks that admit orthant Brownian optimal controls; this is a form of pathwise, or greedy, optimality. Several extensions are discussed.