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We study a multi-server queueing system with a periodic arrival rate and customers whose joining decision is based on their patience and a delay proxy. Specifically, each customer has a patience level sampled from a common distribution.…
Motivated by the growing interest in today's massive parallel computing capabilities we analyze a queueing network with many servers in parallel to which jobs arrive a according to a Poisson process. Each job, upon arrival, is split into…
We study a single server FIFO queue that offers general service. Each of n customers enter the queue at random time epochs that are inde- pendent and identically distributed. We call this the random scattering traffic model, and the…
This paper examines a continuous-time routing system with general interarrival and service time distributions, operating under the join-the-shortest-queue and power-of-two-choices policies. Under a weaker set of assumptions than those…
We consider a general queueing system with price-sensitive customers in which the service provider seeks to balance two objectives, maximizing the average revenue rate and minimizing the average queue length. Customers arrive according to a…
We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
We consider a queueing system with $n$ parallel queues operating according to the so-called "supermarket model" in which arriving customers join the shortest of $d$ randomly selected queues. Assuming rate $n\lambda_{n}$ Poisson arrivals and…
The non-stationary Erlang-A queue is a fundamental queueing model that is used to describe the dynamic behavior of large scale multi-server service systems that may experience customer abandonments, such as call centers, hospitals, and…
We study a diffusion approximation for a model of stochastic motion of a particle in one spatial dimension. The velocity of the particle is constant but the direction of the motion undergoes random changes with a Poisson clock. Moreover,…
The Join-the-Shortest-Queue (JSQ) policy is among the most widely used load balancing algorithms and has been extensively studied. However, an exact characterization of the system behavior remains challenging. Most prior research has…
We present methodology for estimating the stochastic intensity of a doubly stochastic Poisson process. Statistical and theoretical analyses of traffic traces show that these processes are appropriate models of high intensity traffic…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
We consider a multi-stage stochastic optimization problem originally introduced by Cygan et al. (2013), studying how a single server should prioritize stochastically departing customers. In this setting, our objective is to determine an…
This paper studies an infinite buffer single server queueing model with exponentially distributed service times and negative arrivals. The ordinary (positive) customers arrive in batches of random size according to renewal arrival process,…
Modeling the arrival process to an Emergency Department (ED) is the first step of all studies dealing with the patient flow within the ED. Many of them focus on the increasing phenomenon of ED overcrowding, which is afflicting hospitals all…
In this paper, we develop a novel argument, the non-autonomous approximation method, to seek the asymptotic limits of the fully coupled multi-scale McKean-Vlasov stochastic systems with irregular coefficients, which, as summarized in…
We prove the asymptotic functional Poisson laws in the total variation norm and obtain estimates of the corresponding convergence rates for a large class of hyperbolic dynamical systems. These results generalize the ones obtained before in…
In this paper, we consider asymptotic behaviors of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with…
We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in stochastic processes using lower dimensional projections. Our model combines the techniques…