Data networks
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
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
State space collapse with application to heavy traffic limits for multiclass queueing networks
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
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
State space collapse with application to heavy traffic limits for multiclass queueing networks
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
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Two Workload Properties for Brownian Networks
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Optimal Routing In Output-Queued Flexible Server Systems
Probability in the Engineering and Informational Sciences
Dynamic Control of a Multiclass Queue with Thin Arrival Streams
Operations Research
Stochastic Optimal Control Of Ato Systems With Batch Arrivals Via Diffusion Approximation
Probability in the Engineering and Informational Sciences
Queueing Systems: Theory and Applications
Queue-and-Idleness-Ratio Controls in Many-Server Service Systems
Mathematics of Operations Research
Queueing Systems: Theory and Applications
State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems
Mathematics of Operations Research
Mathematics of 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
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
Stability of Constrained Markov-Modulated Diffusions
Mathematics of Operations Research
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
Diffusion approximations for open Jackson networks with reneging
Queueing Systems: Theory and Applications
Stability of multi-class queueing networks with infinite virtual queues
Queueing Systems: Theory and Applications
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Certain diffusion processes known as semimartingale reflecting Brownian motions (SRBMs) have been shown to approximate many single class and some multiclass open queueing networks under conditions of heavy traffic. While it is known that not all multiclass networks with feedback can be approximated in heavy traffic by SRBMs, one of the outstanding challenges in contemporary research on queueing networks is to identify broad categories of networks that can be so approximated and to prove a heavy traffic limit theorem justifying the approximation. In this paper, general sufficient conditions are given under which a heavy traffic limit theorem holds for open multiclass queueing networks with head-of-the-line (HL) service disciplines, which, in particular, require that service within each class is on a first-in-first-out (FIFO) basis. The two main conditions that need to be verified are that (a) the reflection matrix for the SRBM is well defined and completely-\mathcal{S}, and (b) a form of state space collapse holds. A result of Dai and Harrison shows that condition (a) holds for FIFO networks of Kelly type and their proof is extended here to cover networks with the HLPPS (head-of-the-line proportional processor sharing) service discipline. In a companion work, Bramson shows that a multiplicative form of state space collapse holds for these two families of networks. These results, when combined with the main theorem of this paper, yield new heavy traffic limit theorems for FIFO networks of Kelly type and networks with the HLPPS service discipline.