English
Related papers

Related papers: First Order Differential Equations Induced by the …

200 papers

We study a single-server priority queue with a finite number of classes, in which the arrivals follow a fractional Poisson process of index $\alpha \in (0,1]$ and the service completions are triggered by an independent fractional Poisson…

Probability · Mathematics 2026-03-20 Nicos Georgiou , Enrico Scalas , Vladislav Vysotsky

Consider a first-come, first-served single server queue with an initial workload $x>0$ and customers who arrive according to an inhomogeneous Poisson process with rate function $\lambda:[0,\infty)\rightarrow[0,\lambda_h ]$ for some…

Probability · Mathematics 2025-03-18 Shreehari Anand Bodas , Royi Jacobovic

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

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

We study the sojourn time in a queueing system with a single exponential server, serving a Poisson stream of customers in order of arrival. Service is provided at low or high rate, which can be adapted at exponential inspection times. When…

Probability · Mathematics 2015-11-05 Ivo Adan , Bernardo D'Auria

We consider queueing models, where customers arrive according to a continuous-time binomial process on a finite interval. In this arrival process, a total of $K$ customers arrive in the finite time interval $[0,T]$, where arrival times of…

Probability · Mathematics 2024-12-10 Kaito Hayashi , Yoshiaki Inoue , Tetsuya Takine

A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this…

Probability · Mathematics 2017-03-07 Mariska Heemskerk , Julia Kuhn , Michel Mandjes

We consider a stochastic, dynamic job scheduling problem, formulated as a queueing control problem, in which a single server processes jobs of different types that arrive according to independent Poisson processes. The problem is defined on…

Optimization and Control · Mathematics 2025-09-09 Dongnuan Tian , Rob Shone

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

To perform a queuing analysis or design in a communications context, we need to estimate the values of the input parameters, specifically the mean of the arrival rate and service time. In this paper, we propose an approach for estimating…

Applications · Statistics 2008-02-26 Xinjia Chen

This paper considers a network of infinite-server queues with the special feature that, triggered by specific events, the network population vector may undergo a linear transformation (a `multiplicative transition'). For this model we…

Probability · Mathematics 2017-11-15 Dieter Fiems , Michel Mandjes , Brendan Patch

In this paper, we present a condition to obtain instability for a class of queueing networks where the arrival rates in each server are constant and the departure rate in each server is a decreasing function of the queue lengths of other…

Probability · Mathematics 2023-08-01 Pierre Popineau , Seva Shneer

We consider a load balancing model where a Poisson stream of jobs arrive at a system of many servers whose service time distribution possesses a finite second moment. A small fraction of arrivals pass through the so called power-of-choice…

Probability · Mathematics 2024-04-16 Rami Atar , Gershon Wolansky

Motivated by applications that involve setting proper staffing levels for multi-server queueing systems with batch arrivals, we present a thorough study of the queue-length process $\{Q(t); t \geq 0\}$, departure process $\{D(t); t \geq…

Probability · Mathematics 2022-06-20 Andrew Daw , Brian Fralix , Jamol Pender

We investigate Markovian queues that are examined by a controller at random times determined by a Poisson process. Upon examination, the controller sets the service speed to be equal to the minimum of the current number of customers in the…

Performance · Computer Science 2023-03-30 R. Núñez-Queija , B. J. Prabhu , J. A. C. Resing

The infinite-server queueing models with homogeneous and non-homogeneous arrivals of customers and catastrophes are considered. The probability generating functions of joint distributions of numbers of busy servers and served customers, as…

Optimization and Control · Mathematics 2018-07-24 Khanik Kerobyan

We analyze a tandem network of polling queues with two product types and two stations. We assume that external arrivals to the network follow a Poisson process, and service times at each station are exponentially distributed. For this…

Performance · Computer Science 2021-05-25 Ravi Suman , Ananth Krishnamurthy

We consider a queueing system consisting of two non-identical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue…

Probability · Mathematics 2017-03-20 Jori Selen , Ivo J. B. F. Adan , Stella Kapodistria , Johan S. H. van Leeuwaarden

We consider a service system where agents (or, servers) are invited on-demand. Customers arrive as a Poisson process and join a customer queue. Customer service times are i.i.d. exponential. Agents' behavior is random in two respects.…

Probability · Mathematics 2016-09-09 Lam Nguyen , Alexander Stolyar

We consider a Markovian single server queue in which customers are preemptively scheduled by exogenously assigned priority levels. The novelty in our model is that the priority levels are randomly assigned from a continuous probability…

Probability · Mathematics 2017-01-09 Neal Master , Zhengyuan Zhou , Nicholas Bambos