Related papers: An ergodic control problem for many-server multicl…
This paper studies the steady-state properties of the Join the Shortest Queue model in the Halfin-Whitt regime. We focus on the process tracking the number of idle servers, and the number of servers with non-empty buffers. Recently,…
We consider a system of N queues with decentralized load balancing such as power-of-D strategies(where D may depend on N) and generic scheduling disciplines. To measure the dependence of the queues, we use the clan of ancestors, a technique…
We consider optimal control of a multi-class queue in the Halfin--Whitt regime, and revisit the notion of asymptotic optimality and the associated optimality gaps. The existing results in the literature for such systems provide…
Motivated by the design of fast reinforcement learning algorithms, we study the diffusive limit of a class of pure jump ergodic stochastic control problems. We show that, whenever the intensity of jumps is large enough, the approximation…
We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…
A large-scale service system with multiple customer classes and multiple server pools is considered, with the mean service time depending both on the customer class and server pool. The allowed activities (routing choices) form a tree (in…
In this paper we consider a single-server cyclic polling system. Between visits to successive queues, the server is delayed by a random switch-over time. The order in which customers are served in each queue is determined by a priority…
The focus of this paper is on the asymptotics of large-time numbers of customers in time-periodic Markovian many-server queues with customer abandonment in heavy traffic. Limit theorems are obtained for the periodic number-of-customers…
Heterogeneous diffusion processes can be well described by an overdamped Langevin equation with space-dependent diffusivity $D(x)$. We investigate the ergodic and non-ergodic behavior of these processes in an arbitrary potential well $U(x)$…
This paper introduces and analyzes the notion of throughput suboptimality for many-server queueing systems in heavy traffic. The queueing model under consideration has multiple customer classes, indexed by a finite set $\mathcal{I}$, and…
We consider an arbitrary network of $M/M/\infty$ queues with controlled transitions between queues. We consider optimal control problems where the costs are linear functions of the state and inputs over a finite or infinite horizon. We…
We consider a large-scale flexible service system with two large server pools and two types of customers. Servers in pool 1 can only serve type 1 customers, while server in pool 2 are flexible -- they can serve both types 1 and 2. (This is…
This paper studies maximisation of an average-cost-per-unit-time ergodic functional over impulse strategies controlling a Feller-Markov process. The uncontrolled process is assumed to be ergodic but, unlike the extant literature, the…
This paper studies a diffusion control problem motivated by challenges faced by public health agencies who run clinics to serve the public. A key challenge for these agencies is to motivate individuals to participate in the services…
In this paper we analyze an $M/M/1$ queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a…
We consider the heavy-traffic approximation to the $GI/M/s$ queueing system in the Halfin-Whitt regime, where both the number of servers $s$ and the arrival rate $\lambda$ grow large (taking the service rate as unity), with…
This self-contained discussion relates the long-run average holding cost per unit time to the long-run average response time per customer in a $G/G/1$ queue with no assumption made on the order of service. The only restriction established…
Given a random variable $N$ with values in ${\mathbb{N}}$, and $N$ i.i.d. positive random variables $\{\mu_k\}$, we consider a queue with renewal arrivals and $N$ exponential servers, where server $k$ serves at rate $\mu_k$, under two work…
This paper studies a 2-class, 2-server parallel server system under the recently introduced extended heavy traffic condition, which states that the underlying 'static allocation' linear program (LP) is critical, but does not require that it…
In this paper we revisit the Markovian queueing system with a single server, infinite capacity queue and the special queue skipping policy. Customers arrive in batches, but are served one by one according to any conservative discipline. The…