Limits for Cumulative Input Processes to Queues

Whitt, Ward

We establish functional central limit theorems (FCLTs) for a cumulative input process to a fluid queue from the superposition of independent on—off sources, where the on periods and off periods may have heavy-tailed probability distributions. Variants of these FCLTs hold for cumulative busy-time and idle-time processes associated with standard queueing models. The heavy-tailed on-period and off-period distributions can cause the limit process to have discontinuous sample paths (e.g., to be a non-Brownian stable process or more general Lévy process) even though the converging processes have continuous sample paths. Consequently, we exploit the Skorohod M1 topology on the function space D of right-continuous functions with left limits. The limits here combined with the previously established continuity of the reflection map in the M1 topology imply both heavy-traffic and non-heavy-traffic FCLTs for buffer-content processes in stochastic fluid networks.


Also Published In

Probability in the Engineering and Information Sciences

More About This Work

Academic Units
Industrial Engineering and Operations Research
Published Here
September 19, 2017