2,047 research outputs found
Computationally Efficient Simulation of Queues: The R Package queuecomputer
Large networks of queueing systems model important real-world systems such as
MapReduce clusters, web-servers, hospitals, call centers and airport passenger
terminals. To model such systems accurately, we must infer queueing parameters
from data. Unfortunately, for many queueing networks there is no clear way to
proceed with parameter inference from data. Approximate Bayesian computation
could offer a straightforward way to infer parameters for such networks if we
could simulate data quickly enough.
We present a computationally efficient method for simulating from a very
general set of queueing networks with the R package queuecomputer. Remarkable
speedups of more than 2 orders of magnitude are observed relative to the
popular DES packages simmer and simpy. We replicate output from these packages
to validate the package.
The package is modular and integrates well with the popular R package dplyr.
Complex queueing networks with tandem, parallel and fork/join topologies can
easily be built with these two packages together. We show how to use this
package with two examples: a call center and an airport terminal.Comment: Updated for queuecomputer_0.8.
A Fixed-Point Algorithm for Closed Queueing Networks
In this paper we propose a new efficient iterative scheme for solving closed queueing networks with phase-type service time distributions. The method is especially efficient and accurate in case of large numbers of nodes and large customer populations. We present the method, put it in perspective, and validate it through a large number of test scenarios. In most cases, the method provides accuracies within 5% relative error (in comparison to discrete-event simulation)
On closed queueing networks with mixed preemptive resume priority servers.
This paper discusses a typical closed queueing network model in which multiple preemptive resume servers are present with different priority structures at each priority node. An algorithm is developed that is applicable for the three-node two-class model and results are compared to point estimates obtained from simulation. The algorithm is partly based on the Delay/MVA algorithm developed by Bondi and Chuang, because of the accuracy with which instant arrival queue lengths at fcfs servers are calculated. Results are also compared with results obtained from the Shadow Approximation.Networks;
The MVA Priority Approximation
A Mean Value Analysis (MVA) approximation is presented for computing the average performance measures of closed-, open-, and mixed-type multiclass queuing networks containing Preemptive Resume (PR) and nonpreemptive Head-Of-Line (HOL) priority service centers. The approximation has essentially the same storage and computational requirements as MVA, thus allowing computationally efficient solutions of large priority queuing networks. The accuracy of the MVA approximation is systematically investigated and presented. It is shown that the approximation can compute the average performance measures of priority networks to within an accuracy of 5 percent for a large range of network parameter values. Accuracy of the method is shown to be superior to that of Sevcik's shadow approximation
Super-Exponential Solution in Markovian Supermarket Models: Framework and Challenge
Marcel F. Neuts opened a key door in numerical computation of stochastic
models by means of phase-type (PH) distributions and Markovian arrival
processes (MAPs). To celebrate his 75th birthday, this paper reports a more
general framework of Markovian supermarket models, including a system of
differential equations for the fraction measure and a system of nonlinear
equations for the fixed point. To understand this framework heuristically, this
paper gives a detailed analysis for three important supermarket examples: M/G/1
type, GI/M/1 type and multiple choices, explains how to derive the system of
differential equations by means of density-dependent jump Markov processes, and
shows that the fixed point may be simply super-exponential through solving the
system of nonlinear equations. Note that supermarket models are a class of
complicated queueing systems and their analysis can not apply popular queueing
theory, it is necessary in the study of supermarket models to summarize such a
more general framework which enables us to focus on important research issues.
On this line, this paper develops matrix-analytical methods of Markovian
supermarket models. We hope this will be able to open a new avenue in
performance evaluation of supermarket models by means of matrix-analytical
methods.Comment: Randomized load balancing, supermarket model, matrix-analytic method,
super-exponential solution, density-dependent jump Markov process, Batch
Markovian Arrival Process (BMAP), phase-type (PH) distribution, fixed poin
Bayesian inference for queueing networks and modeling of internet services
Modern Internet services, such as those at Google, Yahoo!, and Amazon, handle
billions of requests per day on clusters of thousands of computers. Because
these services operate under strict performance requirements, a statistical
understanding of their performance is of great practical interest. Such
services are modeled by networks of queues, where each queue models one of the
computers in the system. A key challenge is that the data are incomplete,
because recording detailed information about every request to a heavily used
system can require unacceptable overhead. In this paper we develop a Bayesian
perspective on queueing models in which the arrival and departure times that
are not observed are treated as latent variables. Underlying this viewpoint is
the observation that a queueing model defines a deterministic transformation
between the data and a set of independent variables called the service times.
With this viewpoint in hand, we sample from the posterior distribution over
missing data and model parameters using Markov chain Monte Carlo. We evaluate
our framework on data from a benchmark Web application. We also present a
simple technique for selection among nested queueing models. We are unaware of
any previous work that considers inference in networks of queues in the
presence of missing data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS392 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Queueing networks: solutions and applications
During the pasttwo decades queueing network models have proven to be a versatile tool for computer system and computer communication system performance evaluation. This chapter provides a survey of th field with a particular emphasis on applications. We start with a brief historical retrospective which also servesto introduce the majr issues and application areas. Formal results for product form queuenig networks are reviewed with particular emphasis on the implications for computer systems modeling. Computation algorithms, sensitivity analysis and optimization techniques are among the topics covered. Many of the important applicationsof queueing networks are not amenableto exact analysis and an (often confusing) array of approximation methods have been developed over the years. A taxonomy of approximation methods is given and used as the basis for for surveing the major approximation methods that have been studied. The application of queueing network to a number of areas is surveyed, including computer system cpacity planning, packet switching networks, parallel processing, database systems and availability modeling.Durante as últimas duas décadas modelos de redes de filas provaram ser uma ferramenta versátil para avaliação de desempenho de sistemas de computação e sistemas de comunicação. Este capítulo faz um apanhado geral da área, com ênfase em aplicações. Começamos com uma breve retrospectiva histórica que serve também para introduzir os pontos mais importantes e as áreas de aplicação. Resultados formais para redes de filas em forma de produto são revisados com ênfase na modelagem de sistemas de computação. Algoritmos de computação, análise de sensibilidade e técnicas de otimização estão entre os tópicos revistos. Muitas dentre importantes aplicações de redes de filas não são tratáveis por análise exata e uma série (frequentemente confusa) de métodos de aproximação tem sido desenvolvida. Uma taxonomia de métodos de aproximação é dada e usada como base para revisão dos mais importantes métodos de aproximação propostos. Uma revisão das aplicações de redes de filas em um número de áreas é feita, incluindo planejamento de capacidade de sistemas de computação, redes de comunicação por chaveamento de pacotes, processamento paralelo, sistemas de bancos de dados e modelagem de confiabilidade
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