On many-server queues in heavy traffic

Abstract

We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue when the number of servers tends to infinity. No critical loading condition is assumed. Generally, the limit process does not have trajectories in the Skorohod space. We give conditions for the convergence to hold in the topology of compact convergence. Some new results for an infinite server are also provided.

Published in at http://dx.doi.org/10.1214/09-AAP604 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Martingale proofs of many-server heavy-traffic limits for Markovian queues
• The $G/GI/N$ queue in the Halfin--Whitt regime

Cited by in corpus (11)

• Many-server diffusion limits for $G/Ph/n+GI$ queues
• Steady-state $GI/GI/n$ queue in the Halfin-Whitt regime
• Fluid Models of Many-server Queues with Abandonment
• A queueing model with independent arrivals, and its fluid and diffusion limits
• On Universal Scaling of Distributed Queues under Load Balancing
• On Transitory Queueing
• Distribution-valued heavy-traffic limits for the $G/GI/\infty$ queue
• On the steady-state probability of delay and large negative deviations for the $GI/GI/n$ queue in the Halfin-Whitt regime
• Economies-of-scale in resource sharing systems: tutorial and partial review of the QED heavy-traffic regime
• Stein's method, Gaussian processes and Palm measures, with applications to queueing
• Asymptotic dimensioning of stochastic service systems