Ananda Weerasinghe

Controlling a Process to a Goal in Finite Time

A player starts at x in 0, 1 and seeks to reach 1 by time t0. The process {Xt, 0 ≤ t ≤ t0} of the players positions is a diffusion process or an Ito process whose infinitesimal parameters μ, σ are chosen by the player at each instant of time from a set depending on the current position. The probability of reaching 1 by time t0 is maximized if the player can and does choose the parameters so that σ and μ/σ2 are maximized, at least when these maxima are sufficiently regular. This result implies that bold play is optimal for subfair, continuous-time red-and-black and roulette when there is a limit on playing time.

Optimal buffer size for a stochastic processing network in heavy traffic

Abstract We consider a one-dimensional stochastic control problem that arises from queueing network applications. The state process corresponding to the queue-length process is given by a stochastic differential equation which reflects at the origin. The controller can choose the drift coefficient which represents the service rate and the buffer size b>0. When the queue length reaches b, the new customers are rejected and this incurs a penalty. There are three types of costs involved: A “control cost” related to the dynamically controlled service rate, a “congestion cost” which depends on the queue length and a “rejection penalty” for the rejection of the customers. We consider the problem of minimizing long-term average cost, which is also known as the ergodic cost criterion. We obtain an optimal drift rate (i.e. an optimal service rate) as well as the optimal buffer size b*>0. When the buffer size b>0 is fixed and where there is no congestion cost, this problem is similar to the work in Ata, Harrison and Shepp (Ann. Appl. Probab. 15, 1145–1160, 2005). Our method is quite different from that of (Ata, Harrison and Shepp (Ann. Appl. Probab. 15, 1145–1160, 2005)). To obtain a solution to the corresponding Hamilton–Jacobi–Bellman (HJB) equation, we analyze a family of ordinary differential equations. We make use of some specific characteristics of this family of solutions to obtain the optimal buffer size b*>0.

Abandonment versus blocking in many-server queues: asymptotic optimality in the QED regime

We consider a controlled queueing system of the

Stationary stochastic control for Itô processes

G/M/n/B+GI

An Abelian Limit Approach to a Singular Ergodic Control Problem

G/M/n/B+GI type, with many servers and impatient customers. The queue-capacity

Stochastic non-linear oscillators

B