Related papers: Diffusion limits for shortest remaining processing…
We address the problem of giving robust performance bounds based on the study of the asymptotic behavior of the insensitive load balancing schemes when the number of servers and the load scales jointly. These schemes have the desirable…
We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic…
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…
We investigate the scaling limit of the seed bank diffusion when reproduction and migration (to and from the seed bank) happen on different time-scales. More precisely, we consider the case when migration is `slow' and reproduction is…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
In this paper, we analyze a discrete-time queue that is motivated from studying hospital inpatient flow management, where the customer count process captures the midnight inpatient census. The stationary distribution of the customer count…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
In an earlier paper, a randomized load balancing model was studied in a heavy traffic asymptotic regime where the load balancing stream is thin compared to the total arrival stream. It was shown that the limit is given by a system of…
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…
The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW)is presented starting from its representation as an infinite series that points out the subordinated character of the CTRW…
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…
Continuous diffusion models have demonstrated remarkable performance in data generation across various domains, yet their efficiency remains constrained by two critical limitations: (1) the local adjacency structure of the forward Markov…
The scope of this paper is generative modeling through diffusion processes. An approach falling within this paradigm is the work of Song et al. (2021), which relies on a time-reversal argument to construct a diffusion process targeting the…
We study infinite server queues driven by Cox processes in a fast oscillatory random environment. While exact performance analysis is difficult, we establish diffusion approximations to the (re-scaled) number-in-system process by proving…
We study the conditional sojourn time distributions of processor sharing (PS), foreground background processor sharing (FBPS) and shortest remaining processing time first (SRPT) scheduling disciplines on an event where the job size of a…
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…
We consider the classical problem of particle diffusion in $d$-dimensional radially-symmetric systems with absorbing boundaries. A key quantity to characterise such diffusive transport is the evolution of the proportion of particles…
In cloud storage systems with a large number of servers, files are typically not stored in single servers. Instead, they are split, replicated (to ensure reliability in case of server malfunction) and stored in different servers. We analyze…
We consider the problem of online preemptive scheduling on a single machine to minimize the total flow time. In clairvoyant scheduling, where job processing times are revealed upon arrival, the Shortest Remaining Processing Time (SRPT)…
A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore…