Distribution-valued heavy-traffic limits for the $G/GI/\infty$ queue

Abstract

We study the $G/GI/\infty$ queue in heavy-traffic using tempered distribution-valued processes which track the age and residual service time of each customer in the system. In both cases, we use the continuous mapping theorem together with functional central limit theorem results in order to obtain fluid and diffusion limits for these processes in the space of tempered distribution-valued processes. We find that our diffusion limits are tempered distribution-valued Ornstein-Uhlenbeck processes.

Published at http://dx.doi.org/10.1214/14-AAP1027 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (6)

• Martingale proofs of many-server heavy-traffic limits for Markovian queues
• Proofs of the martingale FCLT
• Diffusion approximation for a processor sharing queue in heavy traffic
• On many-server queues in heavy traffic
• A functional central limit theorem for the M/GI/$\infty$ queue
• Fluid limit of a heavily loaded EDF queue with impatient customers

Cited by in corpus (1)

• Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues