Ergodic control of multidimensional diffusions 1: the existence results
SIAM Journal on Control and Optimization
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Ordinary Differential Equations
Ordinary Differential Equations
Degenerate Variance Control of a One-Dimensional Diffusion
SIAM Journal on Control and Optimization
Heavy traffic analysis of controlled multiplexing systems
Queueing Systems: Theory and Applications
Dynamic Control of a Queue with Adjustable Service Rate
Operations Research
A Bounded Variation Control Problem for Diffusion Processes
SIAM Journal on Control and Optimization
Dynamic Control of a Multiclass Queue with Thin Arrival Streams
Operations Research
A Numerical Method for Solving Singular Stochastic Control Problems
Operations Research
Admission control for a multi-server queue with abandonment
Queueing Systems: Theory and Applications
Drift Control with Changeover Costs
Operations Research
Dynamic scheduling of a GI/GI/1+GI queue with multiple customer classes
Queueing Systems: Theory and Applications
Abandonment versus blocking in many-server queues: asymptotic optimality in the QED regime
Queueing Systems: Theory and Applications
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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 b0. 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 b0 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.