Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
Deciding which queue to join: Some counterexamples
Operations Research
Brownian networks with discretionary routing
Operations Research
The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
Dynamic scheduling in multiclass queueing networks: Stability under discrete-review policies
Queueing Systems: Theory and Applications
Heavy traffic resource pooling in parallel-server systems
Queueing Systems: Theory and Applications
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
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
Managing Response Time in a Call-Routing Problem with Service Failure
Operations Research
Dynamic routing of customers with general delay costs in a multiserver queuing system
Probability in the Engineering and Informational Sciences
Fair Dynamic Routing in Large-Scale Heterogeneous-Server Systems
Operations Research
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This paper studies dynamic routing in a parallel server queueing network with a single Poisson arrival process and two servers with exponential processing times of different rates. Each customer must be routed at the time of arrival to one of the two queues in the network. We establish that this system operating under a threshold policy can be well approximated by a one-dimensional reflected Brownian motion when the arrival rate to the network is close to the processing capacity of the two servers. As the heavy traffic limit is approached, thresholds which grow at a logarithmic rate are critical in determining the behavior of the limiting system. We provide necessary and sufficient conditions on the growth rate of the threshold for (i) approximation of the network by a reflected Brownian motion (ii) positive recurrence of the limiting Brownian diffusion and (iii) asymptotic optimality of the threshold policy.