Related papers: Staffing under Taylor's Law: A Unifying Framework …
This paper introduces a new asymptotic regime for simplifying stochastic models having non-stationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the…
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…
We present a limited empirical study of scaling laws for transfer learning in transformer models. More specifically, we examine a scaling law that incorporates a "transfer gap" term, indicating the effectiveness of pre-training on one…
In random access protocols, the service rate depends on the number of stations with a packet buffered for transmission. We demonstrate via numerical analysis that this state-dependent rate along with the consideration of Poisson traffic and…
In a family of random variables, Taylor's law or Taylor's power law offluctuation scaling is a variance function that gives the variance $\sigma^{2}>0$ of a random variable (rv) $X$ with expectation $\mu >0$ as a powerof $\mu$: $\sigma…
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…
The performance of learning models often deteriorates when deployed in out-of-sample environments. To ensure reliable deployment, we propose a stability evaluation criterion based on distributional perturbations. Conceptually, our stability…
The paper considers a queueing system with limited processor sharing. No more than n jobs may be served simultaneously. This system may be used for modeling bandwidth sharing in wireless communication systems and processes of service in…
We consider a system of $N$ parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any,…
The Tweedie generalized linear models are commonly applied in the insurance industry to analyze semicontinuous claim data. For better prediction of the aggregated claim size, the mean and dispersion of the Tweedie model are often estimated…
We consider large-scale service systems with multiple customer classes and multiple server pools; interarrival and service times are exponentially distributed, and mean service times depend both on the customer class and server pool. It is…
Task replication has recently been advocated as a practical solution to reduce latencies in parallel systems. In addition to several convincing empirical studies, some others provide analytical results, yet under some strong assumptions…
Limit theorems are presented for the rescaled occupation time fluctuation process of a critical finite variance branching particle system in $\mathbb{R}^{d}$ with symmetric $\alpha$-stable motion starting off from either a standard Poisson…
We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness…
While scaling laws provide a reliable methodology for predicting train loss across compute scales for a single data distribution, less is known about how these predictions should change as we change the distribution. In this paper, we…
We describe how to solve the problem of Taylor dispersion in the presence of absorbing boundaries using an exact stochastic formulation. In addition to providing a clear stochastic picture of Taylor dispersion, our method leads to…
In this paper, we study the asymptotic behavior of a fully-coupled slow-fast McKean-Vlasov stochastic system. Using the non-linear Poisson equation on Wasserstein space, we first establish the strong convergence in the averaging principle…
Taylor's fluctuation scaling (FS) has been observed in many natural and man-made systems revealing an amazing universality of the law. Here we give strong theoretical foundations for the origins and abundance of Taylor's FS in different…
We introduce $p$-uniformity to characterize the scaling of density fluctuations in spatial random systems in $\mathbb{R}^d$, ranging from hyperfluctuation to stealthy hyperuniformity. Our central theorem establishes sufficient conditions to…
The queue system,with Poisson arrivals,constant service time and infinite servers, busy period distribution is intensively studied because, due to its probability density function quite easy interpretation, it may serve as a clue to…