Anup Biswas

Control of the multiclass

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, the analysis of the problem is closely related to the much studied area of control in heavy traffic at the diffusion scale.

{G/G/1}

ABSTRACT We study stochastic differential equations with jumps with no diffusion part, governed by a large class of stable-like operators, which may contain a drift term. For this class of operators, we establish the regularity of solutions to the Dirichlet problem up to the boundary as well as the usual stochastic characterization of these solutions. We also establish key connections between the recurrence properties of the jump process and the associated nonlocal partial differential operator. Provided that the process is positive (Harris) recurrent, we also show that the mean hitting time of a ball is a viscosity solution of an exterior Dirichlet problem.

queue in the moderate deviation regime

We study a dynamic scheduling problem for a multi-class queueing network with a large pool of statistically identical servers. The arrival processes are Poisson, and service times and patience times are assumed to be exponentially distributed and class dependent. The optimization criterion is the expected long time average (ergodic) of a general (nonlinear) running cost function of the queue lengths. We consider this control problem in the Halfin-Whitt (QED) regime, that is, the number of servers

The Dirichlet problem for stable-like operators and related probabilistic representations

n

Ergodic control of multi-class

and the total offered load

M/M/N+M

\mathbf{r}

queues in the Halfin–Whitt regime

scale like

An eigenvalue approach to the risk sensitive control problem in near monotone case

n\approx\mathbf{r}+\hat{\rho}\sqrt{\mathbf{r}}

Fluid Limits of G/G/1+G Queues Under the Nonpreemptive Earliest-Deadline-First Discipline

for some constant

On Scaling Limits of Power Law Shot-Noise Fields

\hat{\rho}