We consider the maximum waiting time among the first n customers in the GI/G/1 queue. We use strong approximations to prove, under regularity conditions, convergence of the normalized maximum wait to the Gumbel extreme-value distribution when the traffic intensity p approaches 1 from below and n approaches infinity at a suitable rate. The normalization depends on the interarrival-time and servi...

Using a slight modification of the framework in Bramson [7] and Williams [52], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single station systems operating under first-in first-out (FIFO), generalized headof-the-line proportional processor sharing (GHLPPS) and static buffer priority (SBP) service disciplines. The next two ...

Energy consumption in optical access networks costs carriers substantial operational expense (OPEX) every year and is one of contributing factors for the global warming. To reduce energy consumption in the 10-gigabit Ethernet passive optical network (10G-EPON), a hybrid intracycle and cyclic sleep mechanism is proposed in this paper. Under heavy traffic load, optical network units (ONUs) can ut...

Heavy-Traffic Limits via an Averaging Principle for Service Systems Responding to Unexpected Overloads

For the GI0GI01 queue we show that the scaled queue size converges to reflected Brownian motion in a critical queue and converges to reflected Brownian motion with drift for a sequence of subcritical queuing models that approach a critical model+ Instead of invoking the topological argument of the usual continuousmapping approach, we give a probabilistic argument using Skorokhod embeddings in B...

Background: The primary objective of this prospective study was to measure the change from baseline in visual function – Best-Corrected Visual Acuity (BCVA) via the Early Treatment Diabetic Retinopathy Study (ETDRS) chart, contrast sensitivity, central 10 degree visual fields and retinal imaging (angiograms and photographs) at 6 months in subjects with atrophic (dry) age-related macular degener...

We study heavy traffic asymptotics of many Additive Increase Multiplicative Decrease (AIMD) connections sharing a common router in the presence of other uncontrolled traffic, called ”mice”. The system is scaled by speed and average number of sources. With appropriate scalings of the packet rate and buffer content, an approximating delayed diffusion model is derived. By heavy traffic we mean tha...

We consider a queue fed by a mixture of light-tailed and heavytailed traffic. The two traffic classes are served in accordance with the Generalized Processor Sharing (GPS) discipline. GPS-based scheduling algorithms, such as Weighted Fair Queueing (WFQ), have emerged as an important mechanism for achieving service differentiation in integrated networks. We derive the asymptotic workload behavio...

The Negative Binomial modeling technique was used to model the frequency of accident occurrence and involvement. Accident data over a period of 3 years, accounting for 1,606 accidents on a principal arterial in Central Florida, were used to estimate the model. The model illustrated the significance of the Annual Average Daily Traffic (AADT), degree of horizontal curvature, lane, shoulder and me...