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Maglaras, Moallemi, and Zheng (2021) have introduced a flexible queueing model for fragmented limit-order markets, whose fluid limit remains remarkably tractable. In the present study we prove that, in the limit of small and frequent orders, the disc
Externí odkaz:
http://arxiv.org/abs/2407.04354
Autor:
Stolyar, Alexander
A service system with multiple types of customers, arriving as Poisson processes, is considered. The system has infinite number of servers, ranked by $1,2,3, \ldots$; a server rank is its ``location." Each customer has an independent exponentially di
Externí odkaz:
http://arxiv.org/abs/2407.01841
Consider a first-come, first-served single server queue with an initial workload $x>0$ and customers who arrive according to an inhomogeneous Poisson process with rate function $\lambda:[0,\infty)\rightarrow[0,\lambda_h ]$ for some $\lambda_h>0$. For
Externí odkaz:
http://arxiv.org/abs/2406.12745
Autor:
Popov, Serguei
We consider an $M/G/\infty$ queue with infinite expected service time. We then provide the transience/recurrence classification of the states (the system is said to be at state $n$ if there are $n$ customers being served), observing also that here (u
Externí odkaz:
http://arxiv.org/abs/2406.03517
Autor:
Miyazawa, Masakiyo
A semi-martingale reflecting Brownian motion is a popular process for diffusion approximations of queueing models including their networks. In this paper, we are concerned with the case that it lives on the nonnegative half-line, but the drift and va
Externí odkaz:
http://arxiv.org/abs/2405.16764
We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which suppre
Externí odkaz:
http://arxiv.org/abs/2405.05246
Autor:
Dimitriou, Ioannis
In this work, we study Markov-dependent reflected autoregressive processes. In queueing terms, such processes describe the workload just before a customer arrival, which makes obsolete a fraction of the work already present, and where the interarriva
Externí odkaz:
http://arxiv.org/abs/2404.10361
A large proportion of jobs submitted to modern computing clusters and data centers are parallelizable and capable of running on a flexible number of computing cores or servers. Although allocating more servers to such a job results in a higher speed-
Externí odkaz:
http://arxiv.org/abs/2406.09427
We consider a model inspired by compatibility constraints that arise between tasks and servers in data centers, cloud computing systems and content delivery networks. The constraints are represented by a bipartite graph or network that interconnects
Externí odkaz:
http://arxiv.org/abs/2404.06485
Autor:
Ernst, Philip, Stolyar, Alexander
We revisit a classical problem in dynamic storage allocation. Items arrive in a linear storage medium, modeled as a half-axis, at a Poisson rate $r$ and depart after an independent exponentially distributed unit mean service time. The arriving item s
Externí odkaz:
http://arxiv.org/abs/2404.03797