Scheduling networks of queues: heavy traffic analysis of a simple open network
Queueing Systems: Theory and Applications
Routing and singular control for queueing networks in heavy traffic
SIAM Journal on Control and Optimization
Brownian networks with discretionary routing
Operations Research
Operations Research - Supplement to Operations Research: stochastic processes
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Introduction to Linear Optimization
Introduction to Linear Optimization
Critical Thresholds for Dynamic Routing in Queueing Networks
Queueing Systems: Theory and Applications
Two Workload Properties for Brownian Networks
Queueing Systems: Theory and Applications
Optimal Routing In Output-Queued Flexible Server Systems
Probability in the Engineering and Informational Sciences
Queueing Systems: Theory and Applications
Stochastic analysis of multiserver systems
ACM SIGMETRICS Performance Evaluation Review
Managing Response Time in a Call-Routing Problem with Service Failure
Operations Research
Limited choice and locality considerations for load balancing
Performance Evaluation
Queueing Systems: Theory and Applications
Dynamic Control of a Make-to-Order, Parallel-Server System with Cancellations
Operations Research
Simplified Control Problems for Multiclass Many-Server Queueing Systems
Mathematics of Operations Research
Asymptotically optimal parallel resource assignment with interference
Queueing Systems: Theory and Applications
Control of systems with flexible multi-server pools: a shadow routing approach
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Dynamic server allocation for unstable queueing networks with flexible servers
Queueing Systems: Theory and Applications
Asymptotic Optimality of Balanced Routing
Operations Research
Asymptotically tight steady-state queue length bounds implied by drift conditions
Queueing Systems: Theory and Applications
Heavy traffic optimal resource allocation algorithms for cloud computing clusters
Proceedings of the 24th International Teletraffic Congress
Product mix optimization for a semiconductor fab: modeling approaches and decomposition techniques
Proceedings of the Winter Simulation Conference
Queueing system topologies with limited flexibility
Proceedings of the ACM SIGMETRICS/international conference on Measurement and modeling of computer systems
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We consider a queueing system with r non-identical servers working in parallel, exogenous arrivals into m different job classes, and linear holding costs for each class. Each arrival requires a single service, which may be provided by any of several different servers in our general formulation; the service time distribution depends on both the job class being processed and the server selected. The system manager seeks to minimize holding costs by dynamically scheduling waiting jobs onto available servers. A linear program involving only first-moment data (average arrival rates and mean service times) is used to define heavy traffic for a system of this form, and also to articulate a condition of overlapping server capabilities which leads to resource pooling in the heavy traffic limit. Assuming that the latter condition holds, we rescale time and state space in standard fashion, then identify a Brownian control problem that is the formal heavy traffic limit of our rescaled scheduling problem. Because of the assumed overlap in server capabilities, the limiting Brownian control problem is effectively one-dimensional, and it admits a pathwise optimal solution. That is, in the limiting Brownian control problem the multiple servers of our original model merge to form a single pool of service capacity, and there exists a dynamic control policy which minimizes cumulative cost incurred up to any time t with probability one. Interpreted in our original problem context, the Brownian solution suggests the following: virtually all backlogged work should be held in one particular job class, and all servers can and should be productively employed except when the total backlog is small. It is conjectured that such ideal system behavior can be approached using a family of relatively simple scheduling policies related to the c\mu rule.