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In the Hammersley-Aldous-Diaconis process infinitely many particles sit in R and at most one particle is allowed at each position. A particle at x$ whose nearest neighbor to the right is at y, jumps at rate y-x to a position uniformly…

Probability · Mathematics 2007-07-31 Pablo A. Ferrari , James B. Martin

We consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…

Probability · Mathematics 2011-05-04 David Gamarnik , Alexander Stolyar

The fractional non-homogeneous Poisson process was introduced by a time-change of the non-homogeneous Poisson process with the inverse $\alpha$-stable subordinator. We propose a similar definition for the (non-homogeneous) fractional…

Probability · Mathematics 2017-11-27 Nikolai Leonenko , Enrico Scalas , Mailan Trinh

We consider an exhaustive polling system with three nodes in its transient regime under a switching rule of generalized greedy type. We show that, for the system with Poisson arrivals and service times with finite second moment, the…

Probability · Mathematics 2007-05-23 I. M. MacPhee , M. V. Menshikov , S. Popov , S. Volkov

We use multidimensional diffusion processes to approximate the dynamics of a queue served by many parallel servers. The queue is served in the first-in-first-out (FIFO) order and the customers waiting in queue may abandon the system without…

Probability · Mathematics 2015-03-19 Shuangchi He , J. G. Dai

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…

Data Structures and Algorithms · Computer Science 2025-12-09 Jacob Bergquist , Adam N. Elmachtoub

We study the information-theoretic limit of reliable information processing by a server with queue-length dependent quality of service. We define the capacity for such a system as the number of bits reliably processed per unit time, and…

Information Theory · Computer Science 2016-03-08 Avhishek Chatterjee , Daewon Seo , Lav R. Varshney

This paper studies a diffusion model that arises as the limit of a queueing system scheduling problem in the asymptotic heavy traffic regime of Halfin and Whitt. The queueing system consists of several customer classes and many servers…

Probability · Mathematics 2007-05-23 Rami Atar

This paper studies the joint moments of a compound discounted renewal process observed at different times with each arrival removed from the system after a random delay. This process can be used to describe the aggregate (discounted)…

Probability · Mathematics 2018-12-10 Eric Cheung , Landy Rabehasaina , Jae-Kyung Woo , Ran Xu

We consider a service system where agents are invited on-demand. Customers arrive exogenously as a Poisson process and join a customer queue upon arrival if no agent is available. Agents decide to accept or decline invitations after some…

Probability · Mathematics 2015-10-27 Guodong Pang , Alexander L. Stolyar

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…

Applications · Statistics 2022-02-24 M. S. Alencar , A. G. Tatashev , O. V. Seleznjev , M. V. Yashina

A $M/M/1$ queue with catastrophes is a modified $M/M/1$ queue model for which, according to the times of a Poisson process, catastrophes occur leaving the system empty. In this work, we study a fractional $M/M/1$ queue with catastrophes,…

Probability · Mathematics 2021-07-13 Matheus de Oliveira Souza , Pablo Martin Rodriguez

We consider a queueing system consisting of two non-identical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue…

Probability · Mathematics 2017-03-20 Jori Selen , Ivo J. B. F. Adan , Stella Kapodistria , Johan S. H. van Leeuwaarden

The problem of appropriately matching items subject to compatibility constraints arises in a number of important applications. While most of the literature on matching theory focuses on a static setting with a fixed number of items, several…

Probability · Mathematics 2022-01-04 Céline Comte

This paper considers a multiclass processor-sharing queue with feedback. Jobs arrive according to renewal processes, and service times follow general distributions. Upon service completion, jobs may either depart the system or re-enter as a…

Probability · Mathematics 2025-04-30 Mohamed Ghazali , Abdelghani Ben Tahar , Amal Ezzidani

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.…

Probability · Mathematics 2024-03-25 Shreehari Anand Bodas , Michel Mandjes , Liron Ravner

Discrete-time queueing system has widespread applications in packet switching networks, internet protocol, Broadband Integrated Services Digital Network (B-ISDN), circuit switched time-division multiple access etc. In this paper, we analyze…

Probability · Mathematics 2020-07-20 S Pradhan , N Nandy

We consider the processor sharing $M/M/1$-PS queue which also models balking. A customer that arrives and sees $n$ others in the system "balks" (i.e., decides not to enter) with probability $1-b_n$. If $b_n$ is inversely proportional to…

Probability · Mathematics 2011-04-26 Qiang Zhen , Johan S. H. van Leeuwaarden , Charles Knessl

We consider a single large language model (LLM) server that serves a heterogeneous stream of queries belonging to $N$ distinct task types. Queries arrive according to a Poisson process, and each type occurs with a known prior probability.…

Machine Learning · Computer Science 2026-01-16 Emre Ozbas , Melih Bastopcu

We consider forecasting the latent rate profiles of a time series of inhomogeneous Poisson processes. The work is motivated by operations management of queueing systems, in particular, telephone call centers, where accurate forecasting of…

Applications · Statistics 2008-07-28 Haipeng Shen , Jianhua Z. Huang