The QNET method for two-moment analysis of open queueing networks
Queueing Systems: Theory and Applications
A heavy traffic limit theorem for networks of queues with multiple customer types
Mathematics of Operations Research
Large fluctuations in a deterministic multiclass network of queues
Management Science
A multiclass station with Markovian feedback in heavy traffic
Mathematics of Operations Research
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Stability of two families of queueing networks and a discussion of fluid limits
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Skorohod–Loynes Characterizations of Queueing, Fluid, and Inventory Processes
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
A heavy traffic limit theorem for a class of open queueing networks with finite buffers
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
An overview of Brownian and non-Brownian FCLTs for the single-server queue
Queueing Systems: Theory and Applications
Existence Condition for the Diffusion Approximations of Multiclass Priority Queueing Networks
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Stability of Earliest-Due-Date, First-Served Queueing Networks
Queueing Systems: Theory and Applications
Diffusion Approximation in Overloaded Switching Queueing Models
Queueing Systems: Theory and Applications
Continuous-Review Tracking Policies for Dynamic Control of Stochastic Networks
Queueing Systems: Theory and Applications
Performance Evaluation and Policy Selection in Multiclass Networks
Discrete Event Dynamic Systems
A Brownian model for multiclass queueing networks with finite buffers
Journal of Computational and Applied Mathematics - Selected papers of the international symposium on applied mathematics, August 2000, Dalian, China
In Search of Sensitivity in Network Optimization
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
Dynamic Routing in Large-Scale Service Systems with Heterogeneous Servers
Queueing Systems: Theory and Applications
Reliability by design in distributed power transmission networks
Automatica (Journal of IFAC)
Dynamic Control of a Multiclass Queue with Thin Arrival Streams
Operations Research
Contact Centers with a Call-Back Option and Real-Time Delay Information
Operations Research
Optimal scheduling and routing for maximum network throughput
IEEE/ACM Transactions on Networking (TON)
Queueing Systems: Theory and Applications
Proceedings of the tenth ACM international symposium on Mobile ad hoc networking and computing
Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems
Manufacturing & Service Operations Management
Queue-and-Idleness-Ratio Controls in Many-Server Service Systems
Mathematics of Operations Research
On the flow-level dynamics of a packet-switched network
Proceedings of the ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Queueing Systems: Theory and Applications
On the power of (even a little) centralization in distributed processing
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems
Mathematics of Operations Research
On the power of (even a little) centralization in distributed processing
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
A Fluid Approximation for Service Systems Responding to Unexpected Overloads
Operations Research
Queueing Systems: Theory and Applications
Optimal queue-size scaling in switched networks
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems
A simple proof of diffusion approximations for LBFS re-entrant lines
Operations Research Letters
Analysis and control of correlated web server queues
Computer Communications
Log-weight scheduling in switched networks
Queueing Systems: Theory and Applications
Asymptotic Optimality of Balanced Routing
Operations Research
Model Predictive Control for Dynamic Resource Allocation
Mathematics of 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
Separation of timescales in a two-layered network
Proceedings of the 24th International Teletraffic Congress
Stability analysis of N-model systems under a static priority rule
Queueing Systems: Theory and Applications
Heavy-traffic-optimal scheduling with regular service guarantees in wireless networks
Proceedings of the fourteenth ACM international symposium on Mobile ad hoc networking and computing
Interchange of limits in heavy traffic analysis under a moment condition
ACM SIGMETRICS Performance Evaluation Review
Stability of multi-class queueing networks with infinite virtual queues
Queueing Systems: Theory and Applications
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Heavy traffic limits for multiclass queueing networks are a topic of continuing interest. Presently, the class of networks for which these limits have been rigorously derived is restricted. An important ingredient in such work is the demonstration of state space collapse. Here, we demonstrate state space collapse for two families of networks, first-in first-out (FIFO) queueing networks of Kelly type and head-of-the-line proportional processor sharing (HLPPS) queueing networks. We then apply our techniques to more general networks. To demonstrate state space collapse for FIFO networks of Kelly type and HLPPS networks, we employ law of large number estimates to show a form of compactness for appropriately scaled solutions. The limits of these solutions are next shown to satisfy fluid model equations corresponding to the above queueing networks. Results from Bramson [4,5] on the asymptotic behavior of these limits then imply state space collapse. The desired heavy traffic limits for FIFO networks of Kelly type and HLPPS networks follow from this and the general criteria set forth in the companion paper Williams [41]. State space collapse and the ensuing heavy traffic limits also hold for more general queueing networks, provided the solutions of their fluid model equations converge. Partial results are given for such networks, which include the static priority disciplines.