Related papers: An ergodic control problem for many-server multicl…
In this paper we study the uniform stability properties of two classes of parallel server networks with multiple classes of jobs and multiple server pools of a tree topology. These include a class of networks with a single non-leaf server…
We consider a control problem for a heterogeneous population composed of agents able to switch at any time between different options. The controller aims to maximize an average gain per time unit, supposing that the population is of…
We study the ergodic control problem for a class of controlled jump diffusions driven by a compound Poisson process. This extends the results of [SIAM J. Control Optim. 57 (2019), no. 2, 1516-1540] to running costs that are not…
We study the ergodic control problem for a class of jump diffusions in $\mathbb{R}^d$, which are controlled through the drift with bounded controls. The Levy measure is finite, but has no particular structure; it can be anisotropic and…
We consider Markovian many-server systems with admission control operating in a QED regime, where the relative utilization approaches unity while the number of servers grows large, providing natural Economies-of-Scale. In order to determine…
We consider a controlled double-ended queue consisting of two classes of customers, labeled sellers and buyers. The sellers and buyers arrive in a trading market according to two independent renewal processes. Whenever there is a seller and…
We formulate a control problem for a GI/GI/N+GI queue, whose objective is to trade off the long-run average operational costs (i.e., abandonment costs and holding costs) with server utilization costs. To solve the control problem, we…
We present a decentralized ergodic control policy for time-varying area coverage problems for multiple agents with nonlinear dynamics. Ergodic control allows us to specify distributions as objectives for area coverage problems for nonlinear…
We analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the…
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…
Motivated by applications in queueing theory, we consider a stochastic control problem whose state space is the $d$-dimensional positive orthant. The controlled process $Z$ evolves as a reflected Brownian motion whose covariance matrix is…
Dynamic capacity allocation control for resource sharing networks (RSN) is studied when the networks are in heavy traffic. The goal is to minimize an ergodic cost with a linear holding cost function. Our main result shows that the optimal…
We address a single server queue control problem (QCP) in heavy traffic originating from Lee and Weerasinghe (2011). The state process represents the offered waiting time, the customer arrival has a state-dependent intensity, and the…
A key operational challenge for call centers is to decide, in real time, which waiting customer should be served by which available agent. This is known as skill-based routing, and the decision becomes especially difficult in large systems…
In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost…
We characterize heavy-traffic process and steady-state limits for systems staffed according to the square-root safety rule, when the service requirements of the customers are perfectly correlated with their individual patience for waiting…
A G/M/N queue is considered in the moderate deviation heavy traffic regime. The rate function for the customers-in-system process is obtained for the single class model. A risk-sensitive type control problem is considered for multi-class…
We develop many-server asymptotics in the QED regime for models with admission control. The admission control, designed to reduce the incoming traffic in periods of congestion, scales with the size of the system. For a class of Markovian…
We study a G/GI/1 single-server queuing model with i.i.d.\ service times that are independent of a stationary process of inter-arrival times. We show that the distribution of the waiting time converges to a stationary law as time tends to…
The model is motivated by the problem of load distribution in large-scale cloud-based data processing systems. We consider a heterogeneous service system, consisting of multiple large server pools. The pools are different in that their…