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Standard and retrial queueing systems: a comparative analysis.

Jesús Artalejo, Gennadi Falin (2002)

Revista Matemática Complutense

We describe main models and results of a new branch of the queueing theory, theory of retrial queues, which is characterized by the following basic assumption: a customer who cannot get service (due to finite capacity of the system, balking, impatience, etc.) leaves the service area, but after some random delay returns to the system again. Emphasis is done on comparison with standard queues with waiting line and queues with losses. We give a survey of main results for both single server M/G/1 type...

State space collapse for queueing networks.

Bramson, Maury (1998)

Documenta Mathematica

Statistical inference on the traffic intensity for the M/M/ $s$ queueing system.

Leahu, Alexei (2003)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Steady state and scaling limit for a traffic congestion model

Ilie Grigorescu, Min Kang (2010)

ESAIM: Probability and Statistics

In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t)+a with probability 1-ζi(x) on a unit scale or down to γxi(t), 0 < γ < 1 with probability ζi(x) on a logarithmic scale, where ζi depends on the joint state of the system x. We investigate the long time behavior, mean field...

Steady-state distributions of queue length in the GI/G/s queue

I. Kopocińska, B. Kopociński (1977)

Applicationes Mathematicae

Stochastic analysis of the departure and quasi-input processes in a versatile single-server queue.

Artalejo, J.R., Gomez-Corral, A. (1996)

Journal of Applied Mathematics and Stochastic Analysis

Study of Queuing Systems with a Generalized Departure Process

Mirtchev, Seferin, Statev, Stanimir (2008)

Serdica Journal of Computing

This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.This paper deals with a full accessibility loss system and a single server delay system with a Poisson arrival process and state dependent exponentially distributed service time. We use the generalized service flow with nonlinear state dependence mean service time. The idea is based on the analytical continuation of the Binomial distribution and the classic M/M/n/0 and M/M/1/k system. We apply techniques based...