Related papers: Asymptotically Optimal Idling in the GI/GI/N+GI Qu…
We consider optimal control problems governed by systems describing the flow of an incompressible second grade fluid with Dirichlet boundary conditions. We prove the existence of an optimal solution, derive the corresponding necessary…
Problem of damping of an arbitrary number of linear oscillators under common bounded control is considered. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the…
In this paper, we study the $G/\mathit{GI}/N$ queue in the Halfin--Whitt regime. Our first result is to obtain a deterministic fluid limit for the properly centered and scaled number of customers in the system which may be used to provide a…
Motivated by various distributed control applications, we consider a linear system with Gaussian noise observed by multiple sensors which transmit measurements over a dynamic lossy network. We characterize the stationary optimal sensor…
In this study, we consider multi-class multi-server asymmetric queueing systems consisting of $N$ queues on one side and $K$ servers on the other side, where jobs randomly arrive in queues at each time. The service rate of each job-server…
Motivated by the work of Whitt, who studied stabilization of the mean virtual waiting time (excluding service time) in a $GI_t/GI_t/1/FCFS$ queue, this paper investigates the stabilization of the mean virtual response time in a…
A many-server heavy-traffic FCLT is proved for the $G_t/M/s_t+\mathit {GI}$ queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment…
We consider an inventory system whose state is modeled by a L\'{e}vy process. There are two types of costs--the running costs and the inventory control costs. The running costs (also known as the holding/penalty costs) are incurred…
A fundamental challenge in large-scale cloud networks and data centers is to achieve highly efficient server utilization and limit energy consumption, while providing excellent user-perceived performance in the presence of uncertain and…
We consider a system consisting of a server alternating between two service points. At both service points there is an infinite queue of customers that have to undergo a preparation phase before being served. We are interested in the…
We propose a model uncertainty approach to heavy traffic asymptotics that allows for a high level of uncertainty. That is, the uncertainty classes of underlying distributions accommodate disturbances that are of order 1 at the usual…
Motivated by applications in online marketplaces such as ride-hailing platforms and payment channel networks, we study a single-server queue with state-dependent arrival control. The service operator dynamically chooses the arrival rate as…
The subject of this paper is the problem of estimating service time distribution of the $M/G/\infty$ queue from incomplete data on the queue. The goal is to estimate $G$ from observations of the queue--length process at the points of the…
We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals…
We analyze an M/M/1 queue with a service discipline in which customers, upon arriving when the server is busy, search a sequence of stations for a vacant station at which to wait, and in which the server, upon becoming free when one or more…
We consider the scheduling control problem for a family of unitary networks under heavy traffic, with general interarrival and service times, probabilistic routing and infinite horizon discounted linear holding cost. A natural…
We propose an optimal control framework for persistent monitoring problems where the objective is to control the movement of mobile agents to minimize an uncertainty metric in a given mission space. For a single agent in a one-dimensional…
We consider a class of open stochastic processing networks, with feedback routing and overlapping server capabilities, in heavy traffic. The networks we consider satisfy the so-called complete resource pooling condition and therefore have…
In many-server systems it is crucial to staff the right number of servers so that targeted service levels are met. These staffing problems typically lead to constraint satisfaction problems that are hard to solve. During the last decade, a…
In this paper, we consider the infinite horizon optimal control problem for nonlinear systems. Under the conditions of controllability of the linearized system around the origin, and nonlinear controllability of the system to a terminal set…