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Analyzing a Two-Stage Queueing System with Many Point Process Arrivals at Upstream Queue
Queueing Systems, 2004A two-stage queueing network is considered where 1st (upstream) queue can be treated as one of the core routers with large capacity, and the downstream queues represent the periphery routers with a much smaller capacity. It is assumed that after being served at the upstream queues, the \(N\) different flows are routed to many different downstream ...
Do Young Eun, Ness B. Shroff
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Point Processes and Queues: Martingale Dynamics.
Journal of the American Statistical Association, 1983I Martingales.- 1. Histories and Stopping Times.- 2. Martingales.- 3. Predictability.- 4. Square-Integrable Martingales.- References.- Solutions to Exercises, Chapter I.- II Point Processes, Queues, and Intensities.- 1. Counting Processes and Queues.- 2. Watanabe's Characterization.- 3. Stochastic Intensity, General Case.- 4.
D. Vere-Jones, Pierre Bremaud
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Spiking Point Transformer for Point Cloud Classification
AAAI Conference on Artificial IntelligenceSpiking Neural Networks (SNNs) offer an attractive and energy-efficient alternative to conventional Artificial Neural Networks (ANNs) due to their sparse binary activation.
Peixi Wu +8 more
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The System Point Method in Exponential Queues: A Level Crossing Approach
Mathematics of Operations Research, 1981The purpose of this paper is to describe the new System Point method for analyzing queues. It considers the stationary probability distribution of the waiting time in variations of the M/M/R queue with first come first served discipline for a large class of service mechanisms. It is shown that the stationary probability density function of the waiting
P. H. Brill, Morton J. M. Posner
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Beyond Heavy-Traffic Regimes: Universal Bounds and Controls for the Single-Server Queue
Operational Research, 2016Brownian approximations are widely studied because of their tractability relative to the original queueing models. Their stationary distributions are used as proxies for those of the original queues that they model and the convergence of suitably scaled ...
Jun-fei Huang, I. Gurvich
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Large-scale join-idle-queue system with general service times
Journal of Applied Probability, 2016A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/\mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival.
S. Foss, A. Stolyar
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Poisson's equation for queues driven by a Markovian marked point process
Queueing Systems, 1994Let \(\{J_ t\}_{t>0}\) be a finite Markov process, generating a marked point process input, and denote by \(V_ t\) the virtual waiting time at time \(t\) in the queue. This paper dals with Poisson's equation which in the setting \(\{(V_ t, J_ t)\}\) has the form \((*)\) \({\mathcal A}_ g = - f\), where \({\mathcal A}\) is the infinitesimal generator of
Asmussen, Søren, Bladt, Mogens
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Revisiting queueing output processes: a point process viewpoint
Queueing Systems, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Level Crossings in Point Processes Applied to Queues: Single-Server Case
Operations Research, 1977This paper introduces a new methodology for obtaining the stationary waiting time distribution in single-server queues with Poisson arrivals. The basis of the method is the observation that the stationary density of the virtual waiting time can be interpreted as the long-run average rate of downcrossings of a level in a stochastic point process ...
P. H. Brill, Morton J. M. Posner
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