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Related papers: Excessive Backlog Probabilities of Two Parallel Qu…

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It's a situation everyone dreads. A road is down to one lane for repairs. Traffic is let through one way until the backlog clears and then traffic is let through the other way to clear that backlog and so on. When stuck in a very long queue…

Probability · Mathematics 2024-01-09 Robert D. Foley , David R. McDonald

We consider the load balancing system under Poisson arrivals, exponential services, and homogeneous servers. Upon arrival, a job is to be routed to one of the servers, where it is queued until service. We consider the Power-of-$d$ choices…

Probability · Mathematics 2025-03-26 Sushil Mahavir Varma , Francisco Castro , Siva Theja Maguluri

In this article a special case of an M/G/2-queue is considered, where the two servers are exposed to two types of jobs that are distributed among the servers via a random switch. In this model the asymptotic behaviour of the workload buffer…

Probability · Mathematics 2021-04-07 Anita Behme , Philipp Lukas Strietzel

We consider a random walk X_n in Z_+, starting at X_0=x>= 0, with transition probabilities P(X_{n+1}=X_n+1|X_n=y>=1)=1/2-\delta/(4y+2\delta) P(X_{n+1}=X_n+1|X_n=y>=1)=1/2+\delta/(4y+2\delta) and X_{n+1}=1 whenever X_n=0. We prove that the…

Probability · Mathematics 2009-11-13 Joël De Coninck , François Dunlop , Thierry Huillet

We study a random walk in a N dimensional hypercube and exhibit results about stopping times when N diverges. The first theorem discusses the time in which two coupling processes spend to meet. A corollary provides a majorant for the…

Probability · Mathematics 2018-05-30 Cláudia Peixoto

We provide a queueing-theoretic framework for job replication schemes based on the principle "\emph{replicate a job as soon as the system detects it as a \emph{straggler}}". This is called job \emph{speculation}. Recent works have analyzed…

Performance · Computer Science 2025-02-23 Jonatha Anselmi , Neil Walton

In this paper, we investigate overlap times in a two-dimensional infinite server tandem queue. Specifically, we analyze the amount of time that a pair of customers spend overlapping in any station of the two dimensional tandem network. We…

Probability · Mathematics 2024-03-13 Ruici Gao , Jamol Pender

We study a model of a polling system, that is, a collection of $d$ queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is…

Probability · Mathematics 2007-11-06 Iain MacPhee , Mikhail Menshikov , Dimitri Petritis , Serguei Popov

Motivated by the growing interest in today's massive parallel computing capabilities we analyze a queueing network with many servers in parallel to which jobs arrive a according to a Poisson process. Each job, upon arrival, is split into…

Probability · Mathematics 2015-07-20 Mariana Olvera-Cravioto , Octavio Ruiz-Lacedelli

In this paper, we analyze the effects of erroneous load comparisons on the performance of the Po2 scheme. Specifically, we consider load-dependent and load-independent errors. In the load-dependent error model, an incoming job is sent to…

Probability · Mathematics 2023-03-15 Sanidhay Bhambay , Arpan Mukhopadhyay , Thirupathaiah Vasantam

Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump)…

Methodology · Statistics 2019-06-28 Iker Perez , Giuliano Casale

This paper studies the asymptotic behavior of the steady-state waiting time, W_infty, of the M/G/1 queue with subexponenential processing times for different combinations of traffic intensities and overflow levels. In particular, we provide…

Probability · Mathematics 2011-03-22 Mariana Olvera-Cravioto , Peter W. Glynn

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…

Probability · Mathematics 2013-02-14 Brian H. Fralix , Charles Knessl , Johan S. H. van Leeuwaarden

Consider the following random process: we are given $n$ queues, into which elements of increasing labels are inserted uniformly at random. To remove an element, we pick two queues at random, and remove the element of lower label (higher…

Data Structures and Algorithms · Computer Science 2017-06-14 Dan Alistarh , Justin Kopinsky , Jerry Li , Giorgi Nadiradze

The presented study elaborates a multi-server priority queueing model considering the pre-emptive repeat policy and phase-type distribution (PH) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new…

Optimization and Control · Mathematics 2021-08-03 Raina Raj , Vidyottama Jain

We study the persistence exponent for the first passage time of a random walk below the trajectory of another random walk. More precisely, let $\{B_n\}$ and $\{W_n\}$ be two centered, weakly dependent random walks. We establish that…

Probability · Mathematics 2019-05-21 Bastien Mallein , Piotr Miłoś

We study the heavy-traffic limit of the generalized switch operating under MaxWeight, without assuming that the CRP condition is satisfied and allowing for correlated arrivals. The main contribution of this paper is the steady-state mean of…

Probability · Mathematics 2021-03-03 D. Hurtado-Lange , S. T. Maguluri

In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service…

Probability · Mathematics 2015-08-28 Wanyang Dai

We consider a horizontal traffic queue (HTQ) on a periodic road segment, where vehicles arrive according to a spatio-temporal Poisson process, and depart after traveling a distance that is sampled independently and identically from a…

Dynamical Systems · Mathematics 2016-05-25 Mohammad Motie , Ketan Savla

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