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The passively Q-switched, self-pulsing all-solid-state laser is a device of widespread use in many applications. Depending on the condition of saturation, which is easy to adjust, different dynamical phenomena are observed: continuous wave…

We introduce the prioritising exclusion process, a stochastic scheduling mechanism for a priority queueing system in which high priority customers gain advantage by overtaking low priority customers. The model is analogous to a totally…

Statistical Mechanics · Physics 2014-07-23 Jan de Gier , Caley Finn

Rare events refer to qualitatively unlikely events whose realization can nevertheless have important consequences. Typically, the prediction of the kinetics of these events relies on Arrhenius laws, with exponentially distributed waiting…

Statistical Mechanics · Physics 2025-12-18 Apurba Biswas , Thomas Guérin

A service system with multiple types of customers, arriving as Poisson processes, is considered. The system has infinite number of servers, ranked by $1,2,3, \ldots$; a server rank is its ``location." Each customer has an independent…

Probability · Mathematics 2025-02-21 Alexander Stolyar

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 single-server GI/GI/1 queueing system with feedback. We assume the service times distribution to be (intermediate) regularly varying. We find the tail asymptotics for a customer's sojourn time in two regimes: the customer…

Probability · Mathematics 2018-08-01 Sergey Foss , Masakiyo Miyazawa

Mutually uncorrelated random discrete events, manifesting a common basic process, are examined often in terms of their occurrence rate as a function of one or more of their distinguishing attributes, such as measurements of photon spectrum…

Instrumentation and Methods for Astrophysics · Physics 2012-07-26 Avinash A. Deshpande , Harsha Raichur

We consider a set of flows passing through a set of servers. The injection rate into each flow is governed by a flow control that increases the injection rate when all the servers on the flow's path are empty and decreases the injection…

Networking and Internet Architecture · Computer Science 2008-12-09 Matthew Andrews , Aleksandrs Slivkins

Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the…

Computer Science and Game Theory · Computer Science 2020-01-07 Aris Filos-Ratsikas , Evi Micha , Alexandros A. Voudouris

Delay or queue length information has the potential to influence the decision of a customer to use a service system. Thus, it is imperative for service system managers to understand how the information that they provide will affect the…

Optimization and Control · Mathematics 2016-10-07 Jamol Pender , Richard H. Rand , Elizabeth Wesson

We consider a model for transitory queues in which only a finite number of customers can join. The queue thus operates over a finite time horizon. In this system, also known as the $\Delta_{(i)}/G/1$ queue, the customers decide…

Probability · Mathematics 2018-11-26 Gianmarco Bet

We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…

Statistical Mechanics · Physics 2007-05-23 Paolo Grigolini , Luigi Palatella , Giacomo Raffaelli

We study a system, where a random flow of customers is served by servers (called agents) invited on-demand. Each invited agent arrives into the system after a random time; after each service completion, an agent returns to the system or…

Probability · Mathematics 2017-11-28 Lam M. Nguyen , Alexander Stolyar

This paper addresses the analysis of the queue-length process of single-server queues under overdispersion, i.e., queues fed by an arrival process for which the variance of the number of arrivals in a given time window exceeds the…

Probability · Mathematics 2020-04-21 Onno Boxma , Mariska Heemskerk , Michel Mandjes

In this paper, we analyze a shared access network with a fixed primary node and randomly distributed secondary nodes whose distribution follows a Poisson point process (PPP). The secondaries use a random access protocol allowing them to…

Networking and Internet Architecture · Computer Science 2016-03-30 Zheng Chen , Nikolaos Pappas , Marios Kountouris , Vangelis Angelakis

In this work, we consider the case where a source with bursty traffic can adjust the transmission duration in order to increase the reliability. The source is equipped with a queue in order to store the arriving packets. We model the system…

Information Theory · Computer Science 2018-09-11 Nikolaos Pappas

Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…

Chaotic Dynamics · Physics 2020-08-26 Bruce N. Roth , Michael Wilkinson

We introduce the {\Delta}(i)/GI/1 queue, a new queueing model. In this model, customers from a given population independently sample a time to arrive from some given distribution F. Thus, the arrival times are an ordered statistics, and the…

Probability · Mathematics 2014-12-09 Harsha Honnappa , Rahul Jain , Amy R. Ward

We introduce a general methodology of update rules accounting for arbitrary interevent time distributions in simulations of interacting agents. In particular we consider update rules that depend on the state of the agent, so that the update…

Physics and Society · Physics 2011-07-19 Juan Fernández-Gracia , V. M. Eguíluz , M. San Miguel

In random access protocols, the service rate depends on the number of stations with a packet buffered for transmission. We demonstrate via numerical analysis that this state-dependent rate along with the consideration of Poisson traffic and…

Networking and Internet Architecture · Computer Science 2014-05-23 Cristina Cano , David Malone