We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy traffic assumptions, we prove a diffusion limit theorem for a measure-valued state descriptor, from which we conclude a similar theorem for the queue length proces...

We show how to write the solution to the generalized drift Skorokhod problem in one-dimension in terms of the supremum of the solution of a tractable unrestricted integral equation (that is, an integral equation with no boundaries). As an application of our result, we equate the transient distribution of a reflected Ornstein-Uhlenbeck (O-U) process to the first hitting time distribution of an O...

We show how to write the solution to the generalized drift Skorokhod problem in onedimension in terms of the supremum of the solution of an unrestricted integral equation (that is, an integral equation with no boundaries). As an application of our result, we equate the transient distribution of a reflected Ornstein-Uhlenbeck (O-U) process to the first hitting time distribution of an O-U process...

This paper studies the classical polling model under the exhaustive-service assumption; such models continue to be very useful in performance studies of computer/communication systems. The analysis here extends earlier work of the authors to the general case of nonzero switchover times. It shows that, under the standard heavy-traffic scaling, the total unfinished work in the system tends to a B...

This paper studies a multiple-server queueing model under the assumptions of renewal arrival processes and limited buffer size. An approximation for the loss probability and the asymptotic behavior are studied under the heavy traffic conditions. We present an asymptotic analysis of the loss probabilitywhen both the arrival rate and number of servers approach infinity. In illustrative examples, ...

We consider two tandem single-server stations in heavy traffic. There are two job types and they visit both stations in order. The first station processes jobs in an exhaustive service or gated service fashion and the second station uses an arbitrary nonidling service discipline. The stations have zero switch-over times. We prove heavy traffic limit theorems for the two-dimensional total worklo...

Effective approximations are developed for the blocking probability in a general stationary loss model with dependence among successive service times as well as among successive interarrival times by exploiting heavy-traffic limits for the steady-state number of busy servers in the associated infinite-server model with the same arrival and service processes. In addition, a new heavy-traffic app...

Under fairly general assumptions on the arrival and service time processes, we prove fluid and heavy traffic limit theorems for the unfinished work, queue length, sojourn time and waiting time processes associated with a single station multiclass generalized processor sharing model. The fluid limit of the unfinished work process is characterized by the Skorokhod map associated with a Skorokhod ...

Recent works by Newell [13] and Coffman et al. [2] have studied a queuing or storage model which is most easily visualized as the process of parking cars in a parking lot where customers park as close as they can to some fixed point. This paper describes several space-time processes which arise as heavy-traffic limits in this model, and which seem interesting in their own right. M/M/a queue * d...

BACKGROUND An association between traffic air pollution and respiratory symptoms among children has been reported. However, the effects of traffic air pollution on asthma and wheeze have been very sparsely studied in areas with low traffic intensity in cold climate with poor dispersion. We evaluated the impact of vehicle traffic on childhood asthma and wheeze by objective exposure assessment. ...