We consider the waiting time distribution of the Gl/Gl /1 queue where customers are served in random order; inter-arrival and service times may have finite or infinite variance. Our main result shows that the waiting time in heavy traffic can be written as a product of two random variables. Our proof is based on the intuitively appealing fact that in heavy traffic, the queue length stays consta...

We consider the problem of minimizing queue-length costs in a system with heterogenous parallel servers, operating in a many-server heavy-traffic regime with nondegenerate slowdown. This regime is distinct from the wellstudied heavy traffic diffusion regimes, namely the (single server) conventional regime and the (many-server) Halfin–Whitt regime. It has the distinguishing property that waiting...

A multi-class single-server system with general service time distributions is studied in a moderate deviation heavy traffic regime. In the scaling limit, an optimal control problem associated with the model is shown to be governed by a differential game that can be explicitly solved. While the characterization of the limit by a differential game is akin to results at the large deviation scale, ...

air quality inside commuting vehicles has seldom been evaluated in iran. accordingly, this study investigates the levels of benzene, toluene, ethylbenzene and xylene (btex) during workdays characterized by heavy traffic inside taxis in tehran- iran between may 2009 and october 2010. the totals of 35 personal samples were collected onto solid sorbent tubes and the concentration of volatile organ...

Modern service systems, like cloud computing platforms or data center environments, commonly face a high degree of heterogeneity. This heterogeneity is not only caused by different server speeds but also, binding task-server relations that must be taken into account when assigning incoming tasks. Unfortunately, there are hardly any theoretical performance guarantees as these systems do fall wit...

Metals such as antimony, cadmium, chromium, copper, lead, nickel, and zinc can be highly relevant pollutants in stormwater runoff from traffic areas because of their occurrence, toxicity, and non-degradability. Long-term measurements of their concentrations, the corresponding water volumes, the catchment areas, and the traffic volumes can be used to calculate specific emission loads and annual ...