28,258 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.
Proportional fairness and its relationship with multi-class queueing networks
We consider multi-class single-server queueing networks that have a product
form stationary distribution. A new limit result proves a sequence of such
networks converges weakly to a stochastic flow level model. The stochastic flow
level model found is insensitive. A large deviation principle for the
stationary distribution of these multi-class queueing networks is also found.
Its rate function has a dual form that coincides with proportional fairness. We
then give the first rigorous proof that the stationary throughput of a
multi-class single-server queueing network converges to a proportionally fair
allocation. This work combines classical queueing networks with more recent
work on stochastic flow level models and proportional fairness. One could view
these seemingly different models as the same system described at different
levels of granularity: a microscopic, queueing level description; a
macroscopic, flow level description and a teleological, optimization
description.Comment: Published in at http://dx.doi.org/10.1214/09-AAP612 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On deciding stability of multiclass queueing networks under buffer priority scheduling policies
One of the basic properties of a queueing network is stability. Roughly
speaking, it is the property that the total number of jobs in the network
remains bounded as a function of time. One of the key questions related to the
stability issue is how to determine the exact conditions under which a given
queueing network operating under a given scheduling policy remains stable.
While there was much initial progress in addressing this question, most of the
results obtained were partial at best and so the complete characterization of
stable queueing networks is still lacking. In this paper, we resolve this open
problem, albeit in a somewhat unexpected way. We show that characterizing
stable queueing networks is an algorithmically undecidable problem for the case
of nonpreemptive static buffer priority scheduling policies and deterministic
interarrival and service times. Thus, no constructive characterization of
stable queueing networks operating under this class of policies is possible.
The result is established for queueing networks with finite and infinite buffer
sizes and possibly zero service times, although we conjecture that it also
holds in the case of models with only infinite buffers and nonzero service
times. Our approach extends an earlier related work [Math. Oper. Res. 27 (2002)
272--293] and uses the so-called counter machine device as a reduction tool.Comment: Published in at http://dx.doi.org/10.1214/09-AAP597 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Sample path large deviations for multiclass feedforward queueing networks in critical loading
We consider multiclass feedforward queueing networks with first in first out
and priority service disciplines at the nodes, and class dependent
deterministic routing between nodes. The random behavior of the network is
constructed from cumulative arrival and service time processes which are
assumed to satisfy an appropriate sample path large deviation principle. We
establish logarithmic asymptotics of large deviations for waiting time, idle
time, queue length, departure and sojourn-time processes in critical loading.
This transfers similar results from Puhalskii about single class queueing
networks with feedback to multiclass feedforward queueing networks, and
complements diffusion approximation results from Peterson. An example with
renewal inter arrival and service time processes yields the rate function of a
reflected Brownian motion. The model directly captures stationary situations.Comment: Published at http://dx.doi.org/10.1214/105051606000000439 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Maximum Likelihood Estimation of Closed Queueing Network Demands from Queue Length Data
Resource demand estimation is essential for the application of analyical models, such as queueing networks, to real-world systems. In this paper, we investigate maximum likelihood (ML) estimators for service demands in closed queueing networks with load-independent and load-dependent service times. Stemming from a characterization of necessary conditions for ML estimation, we propose new estimators that infer demands from queue-length measurements, which are inexpensive metrics to collect in real systems. One advantage of focusing on queue-length data compared to response times or utilizations is that confidence intervals can be rigorously derived from the equilibrium distribution of the queueing network model. Our estimators and their confidence intervals are validated against simulation and real system measurements for a multi-tier application
Modelling multi-tier enterprise applications behaviour with design of experiments technique
Queueing network models are commonly used for performance modelling. However, through application development stage analytical models might not be able to continuously reflect performance, for example due to performance bugs or minor changes in the application code that cannot be readily reflected in the queueing model. To cope with this problem, a measurement-based approach adopting Design of Experiments (DoE) technique is proposed. The applicability of the proposed method is demonstrated on a complex 3-tier e-commerce application that is difficult to model with queueing networks
Energy-delay tradeoff in wireless network coding
A queueing model for wireless communication network in which network coding is employed is introduced. It is shown that networks with coding are closely related to queueing networks with positive and negative customers. Analytical upper and lower bounds on the energy consumption and the delay are obtained using a Markov reward approach. The tradeoff between minimizing energy consumption and minimizing delay is investigated. Exact expressions are given for the minimum energy consumption and the minimum delay attainable in a network
Decomposition-based analysis of queueing networks
Model-based numerical analysis is an important branch of the model-based performance evaluation. Especially state-oriented formalisms and methods based on Markovian processes, like stochastic Petri nets and Markov chains, have been successfully adopted because they are mathematically well understood and allow the intuitive modeling of many processes of the real world. However, these methods are sensitive to the well-known phenomenon called state space explosion. One way to handle this problem is the decomposition approach.\ud
In this thesis, we present a decomposition framework for the analysis of a fairly general class of open and closed queueing networks. The decomposition is done at queueing station level, i.e., the queueing stations are independently analyzed. During the analysis, traffic descriptors are exchanged between the stations, representing the streams of jobs flowing between them. Networks with feedback are analyzed using a fixed-point iteration
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