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...

The 95 percentile billing mechanism has been an industry de facto standard for transit providers for well over a decade. While the simplicity of the scheme makes it attractive as a billing mechanism, dramatic evolution in traffic patterns, associated interconnection practices and industry structure over the last two decades motivates an obvious question: is it still appropriate? In this paper, ...

In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. Let Q X ≡ {Q X (t) : t ≥ 0} denote a stationary buffer content process for a fluid queue fed by the centered Gaussian process X ≡ {X(t) : t ∈ R} with stationary increments, X(0) = 0, continuous sample paths and variance function σ 2(·). The system is drained at a constant rate c > 0, so that for a...

Unlimited access to a motorway network can, in overloaded conditions, cause a loss of capacity. Ramp metering (signals on slip roads to control access to the motorway) can help avoid this loss of capacity. The design of ramp metering strategies has several features in common with the design of access control mechanisms in communication networks. Inspired by models and rate control mechanisms de...

We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue.

We establish heavy-traffic stochastic-process limits for queue-length, waiting-time and overflow stochastic processes in a class of G/GI/n/m queueing models with n servers and m extra waiting spaces. We let the arrival process be general, only requiring that it satisfy a functional central limit theorem. In order to capture the impact of the service-time distribution beyond its mean within a Ma...

The purpose of this write-up is to compare multistage filters [3] and sketches with respect to their ability to identify heavy hitters. In a nutshell, the conclusion is that multistage filters as I use them identify heavy hitters with less memory than sketches, but some sketches support important other operations, more specifically they can be added and subtracted without any need to re-read th...

Exposure to traffic and traffic-related air pollution is associated with a wide array of health effects. Time spent in a vehicle, in active transportation, along roadsides, and in close proximity to traffic can substantially contribute to daily exposure to air pollutants. For this study, we evaluated daily time spent in transportation and traffic-influenced microenvironments by urban Canadians ...