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We propose a unified approach to establishing diffusion approximations for queues with impatient customers within a general framework of scaling customer patience time. The approach consists of two steps. The first step is to show that the…

Probability · Mathematics 2015-10-06 Junfei Huang , Hanqin Zhang , Jiheng Zhang

This paper concerns the recurrence structure of the infinite server queue, as viewed through the prism of the maximum dater sequence, namely the time to drain the current work in the system as seen at arrival epochs. Despite the importance…

Probability · Mathematics 2026-01-12 Sergey Foss , Peter Glynn

We consider a polling system with two queues, where a single server is attending the queues in a cyclic order and requires non-zero switching times to switch between the queues. Our aim is to identify a fairly general and comprehensive…

Optimization and Control · Mathematics 2025-10-20 Konstantin Avrachenkov , Kousik Das , Veeraruna Kavitha , Vartika Singh

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…

Optimization and Control · Mathematics 2022-07-19 Rami Atar , Eyal Castiel , Marty Reiman

Stability with respect to a given scheduling policy has become an important issue for wireless communication systems, but it is hard to prove in particular scenarios. In this paper two simple conditions for stability in broadcast channels…

Networking and Internet Architecture · Computer Science 2009-04-16 Chan Zhou , Gerhard Wunder

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…

Probability · Mathematics 2022-04-13 Rami Atar , Eyal Castiel , Yonatan Shadmi

We investigate the stability condition for redundancy-d systems where each of the servers follows a processor-sharing (PS) discipline. We allow for generally distributed job sizes, with possible dependence among the d replica sizes being…

Probability · Mathematics 2020-03-09 Youri Raaijmakers , Sem Borst , Onno Boxma

In this paper continuity theorems are established for the number of losses during a busy period of the $M/M/1/n$ queue. We consider an $M/GI/1/n$ queueing system where the service time probability distribution, slightly different in a…

Probability · Mathematics 2008-08-01 Vyacheslav M. Abramov

This note studies (practical) asymptotic stability of nonlinear networked control systems whose protocols are not necessarily uniformly globally exponentially stable. In particular, we propose a Lyapunov-based approach to establish…

Systems and Control · Computer Science 2018-10-10 Seyed Hossein Mousavi , Navid Noroozi , Anton H. J. de Ruiter , Roman Geiselhart

We study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the $n$-intertwined Markov model, over arbitrary directed network topologies. As in the majority of the work on infection spread…

Systems and Control · Computer Science 2015-02-23 Ali Khanafer , Tamer Başar , Bahman Gharesifard

Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent…

Probability · Mathematics 2017-10-13 Reza Aghajani , Kavita Ramanan

We study a robust control problem for dynamical flow networks. In the considered dynamical models, traffic flows along the links of a transportation network --modeled as a capacited multigraph-- and queues up at the nodes, whereby control…

Systems and Control · Electrical Eng. & Systems 2020-12-24 Gustav Nilsson , Giacomo Como

This study investigates the trade-off between system stability and offloading cost in collaborative edge computing. While collaborative offloading among multiple edge servers enhances resource utilization, existing methods often overlook…

Networking and Internet Architecture · Computer Science 2025-09-16 Peiyan Yuan , Ming Li , Chenyang Wang , Ledong An , Xiaoyan Zhao , Junna Zhang , Xiangyang Li , Huadong Ma

We study the phenomenon of entrainment in processor sharing networks, whereby, while individual network resources have sufficient capacity to met demand, the requirement for simultaneous availability of resources means that a network may…

Probability · Mathematics 2007-08-01 Jennie Hansen , Cian Reynolds , Stan Zachary

Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove,…

Probability · Mathematics 2014-09-12 Itai Gurvich

This paper studies a class of load balancing algorithms for many-server ($N$ servers) systems assuming finite buffer with size $b-1$ (i.e. a server can have at most one job in service and $b-1$ jobs in queue). We focus on steady-state…

Probability · Mathematics 2018-04-10 Xin Liu , Lei Ying

The problem of reliability of a large distributed system is analyzed via a new mathematical model. A typical framework is a system where a set of files are duplicated on several data servers. When one of these servers breaks down, all…

Probability · Mathematics 2017-06-05 Reza Aghajani , Philippe Robert , Wen Sun

In this study, we consider multi-class multi-server asymmetric queueing systems consisting of $N$ queues on one side and $K$ servers on the other side, where jobs randomly arrive in queues at each time. The service rate of each job-server…

Machine Learning · Statistics 2025-05-07 Jung-hun Kim , Min-hwan Oh

This paper studies a scheduling control problem for a single-server multiclass queueing network in heavy traffic, operating in a changing environment. The changing environment is modeled as a finite state Markov process that modulates the…

Probability · Mathematics 2012-11-30 Amarjit Budhiraja , Arka Ghosh , Xin Liu

We consider the so-called GI/GI/N queue, in which a stream of jobs with independent and identically distributed service times arrive as a renewal process to a common queue that is served by $N$ identical parallel servers in a…

Probability · Mathematics 2017-12-06 Reza Aghajani , Kavita Ramanan