Limits for cumulative input processes to queues

We establish functional central limit theorems (FCLTs) for a cumulative inp ut process to a fluid queue from the superposition of independent on-off so urces, where the on periods and off periods may have heavy-tailed probabili ty distributions. Variants of these FCLTs hold for cumulative busy-time and idle-time processes associated with standard queueing models. The heavy-ta iled 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 Levy process) even though the converging processes have con tinuous sample paths. Consequently, we exploit the Skorohod M-1 topology on the function space D of right-continuous functions with left limits. The l imits here combined with the previously established continuity of the refle ction map in the M-1 topology imply both heavy-traffic and non-heavy-traffi c FCLTs for buffer-content processes in stochastic fluid networks.