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The model is a "generalized switch", serving multiple traffic flows in discrete time. The switch uses MaxWeight algorithm to make a service decision (scheduling choice) at each time step, which determines the probability distribution of the…

Probability · Mathematics 2015-02-13 Rahul Singh , Alexander Stolyar

We study stochastic tree fluid networks driven by a multidimensional Levy process. We are interested in (the joint distribution of) the steady-state content in each of the buffers, the busy periods, and the idle periods. To investigate…

Probability · Mathematics 2007-12-06 K. Debicki , A. B. Dieker , T. Rolski

Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we…

Physics and Society · Physics 2015-06-26 Bosiljka Tadic , G. J. Rodgers , Stefan Thurner

We study the load balancing system operating under Join the Shortest Queue (JSQ) in the many-server heavy-traffic regime. If $N$ is the number of servers, we let the difference between the total service rate and the total arrival rate be…

Probability · Mathematics 2022-08-25 Daniela Hurtado-Lange , Siva Theja Maguluri

In this paper, we analyze a two-queue random time-limited Markov modulated polling model. In the first part of the paper, we investigate the fluid version: Fluid arrives at the two queues as two independent flows with deterministic rate.…

Probability · Mathematics 2021-12-10 Stella Kapodistria , Mayank Saxena , Onno Boxma , Offer Kella

We study a single server FIFO queue that offers general service. Each of n customers enter the queue at random time epochs that are inde- pendent and identically distributed. We call this the random scattering traffic model, and the…

Probability · Mathematics 2017-08-21 Peter W. Glynn , Harsha Honnappa

Platooning of connected and autonomous vehicles (CAVs) has a significant potential for throughput improvement. However, the interaction between CAVs and non-CAVs may limit the practically attainable improvement due to platooning. To better…

Optimization and Control · Mathematics 2020-11-16 Li Jin , Mladen Cicic , Karl H. Johansson , Saurabh Amin

In this note, we apply Stein's method to analyze the steady-state distribution of queueing systems in the traditional heavy-traffic regime. Compared to previous methods (e.g., drift method and transform method), Stein's method allows us to…

Probability · Mathematics 2020-10-08 Xingyu Zhou , Ness Shroff

Atar and Miyazawa recently introduced a single server queue with queue length dependent arrival and service processes, and name it a multi-level queue. They prove that the heavy traffic limit of its queue length process weakly converges to…

Probability · Mathematics 2025-05-07 Masahiro Kobayashi , Masakiyo Miyazawa , Yutaka Sakuma

Fundamental to many transportation network studies, traffic flow models can be used to describe traffic dynamics determined by drivers' car-following, lane-changing, merging, and diverging behaviors. In this study, we develop a…

Dynamical Systems · Mathematics 2013-07-31 Wen-Long Jin

We consider GI/Ph/n+M parallel-server systems with a renewal arrival process, a phase-type service time distribution, n homogenous servers, and an exponential patience time distribution with positive rate. We show that in the Halfin-Whitt…

Probability · Mathematics 2014-01-14 J. G. Dai , A. B. Dieker , Xuefeng Gao

The emergence of congestion is a critical phenomenon in transport systems. Transport is organized along pathways abstracted by links, which connect different nodes as regions to form the network. The modeling of traffic has so far mainly…

Physics and Society · Physics 2023-03-23 Zhidong He

We consider a queueing system with $n$ parallel queues operating according to the so-called "supermarket model" in which arriving customers join the shortest of $d$ randomly selected queues. Assuming rate $n\lambda_{n}$ Poisson arrivals and…

Probability · Mathematics 2017-01-19 Patrick Eschenfeldt , David Gamarnik

In this note, we apply Stein's method to analyze the performance of general load balancing schemes in the many-server heavy-traffic regime. In particular, consider a load balancing system of $N$ servers and the distance of arrival rate to…

Probability · Mathematics 2020-04-28 Xingyu Zhou , Ness Shroff

We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise. In view of the L\'{e}vy noise sensitivity to the confining "potential landscape" where jumps take place (in other words, to environmental…

Statistical Mechanics · Physics 2015-06-11 M. Zaba , P. Garbaczewski , V. Stephanovich

Writing data in parallel is a common operation in some computing environments and a good proxy for a number of other parallel processing patterns. The duration of time taken to write data in large-scale compute environments can vary…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-01-12 R. Henwood , N. W. Watkins , S. C. Chapman , R. McLay

In traffic signal control, flow-based (optimizing the overall flow) and pressure-based methods (equalizing and alleviating congestion) are commonly used but often considered separately. This study introduces a unified framework using…

Systems and Control · Electrical Eng. & Systems 2024-01-18 Chaolun Ma , Bruce Wang , Zihao Li , Ahmadreza Mahmoudzadeh , Yunlong Zhang

The residual queue during a given study period (e.g., peak hour) is an important feature that should be considered when solving a traffic assignment problem under equilibrium for strategic traffic planning. Although studies have focused…

Systems and Control · Electrical Eng. & Systems 2025-01-14 Hao Fu , William H. K. Lam , Wei Ma , Yuxin Shi , Rui Jiang , Huijun Sun , Ziyou Gao

Heavy-traffic limit theory deals with queues that operate close to criticality and face severe queueing times. Let $W$ denote the steady-state waiting time in the ${\rm GI}/{\rm G}/1$ queue. Kingman (1961) showed that $W$, when…

Probability · Mathematics 2022-06-22 M. A. A. Boon , A. J. E. M. Janssen , J. S. H. van Leeuwaarden

Macroscopic link-based flow models are efficient for simulating flow propagation in urban road networks. Existing link-based flow models described traffic states of a link with two state variables of link inflow and outflow and assumed…

Systems and Control · Electrical Eng. & Systems 2024-11-14 Lei Wei , S. Travis Waller , Yu Mei , Peng Chen , Yunpeng Wang , Meng Wang