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.

Multi-step ahead response time prediction for single server queuing systems

Multi-step ahead response time prediction of CPU constrained computing systems is vital for admission control, overload protection and optimization of resource allocation in these systems. CPU constrained computing systems such as web servers can be modeled as single server queuing systems. These systems are stochastic and nonlinear. Thus, a well-designed nonlinear prediction scheme would be able to represent the dynamics of such a system much better than a linear scheme. A nonlinear autoregressive neural network with exogenous inputs based multi-step ahead response time predictor has been developed. The proposed estimator has many promising characteristics that make it a viable candidate for being implemented in admission control products for computing systems. It has a simple structure, is nonlinear, supports multi-step ahead prediction, and works very well under time variant and non-stationary scenarios such as single server queuing systems under time varying mean arrival rate. Performance of the proposed predictor is evaluated through simulation. Simulations show that the proposed predictor is able to predict the response times of single server queuing systems in multi-step ahead with very good precision represented by very small mean absolute and mean squared prediction errors

Bootstrap approximations for Bayesian analysis of Geo/G/1 discrete-time queueing models

In this paper we consider a Bayesian nonparametric approach to the analysis of discrete-time queueing models. The main motivation consists in applications to telecommunications, and in particular to asynchronous transfer mode (ATM) systems. Attention is focused on the posterior distribution of the overflow rate. Since the exact distribution of such a quantity is not available in a closed form, an approximation based on "proper" Bayesian bootstrap is proposed, and its properties are studied. Some possible alternatives to proper Bayesian bootstrap are also discussed. Finally, an application to real data is provided. (C) 2002 Elsevier B.V. All rights reserved

Resource Management in Computing Systems

Resource management is an essential building block of any modern computer and communication network. In this thesis, the results of our research in the following two tracks are summarized in four papers. The first track includes three papers and covers modeling, prediction and control for multi-tier computing systems. In the first paper, a NARX-based multi-step-ahead response time predictor for single server queuing systems is presented which can be applied to CPU-constrained computing systems. The second paper introduces a NARX-based multi-step-ahead query response time predictor for database servers. Both mentioned predictors can predict the dynamics of response times in the whole operation range particularly in high load scenarios without changes having to be applied to the current protocols and operating systems. In the third paper, queuing theory is used to model the dynamics of a database server. Several heuristics are presented to tune the parameters of the proposed model to the measured data from the database. Furthermore, an admission controller is presented, and its parameters are tuned to control the response time of queries which are sent to the database to stay below a predefined reference value.The second track includes one paper, covering a problem formulation and optimal solution for a content replication problem in Telecom operator's content delivery networks (Telco-CDNs). The problem is formulated in the form of an integer programming problem trying to minimize the communication delay and cost according to several constraints such as limited content replication budget, limited storage size and limited downlink bandwidth of each regional content server. The solution of this problem is a performance bound for any distributed content replication algorithm which addresses the same problem

Large sample Bayesian analysis for Geo/G/1{\rm Geo}/G/1 discrete-time queueing models

statistical inference for the probability generating function p.g.f. of the equilibrium waiting time distribution is considered. The consistency of the posterior distribution for such a p.g.f., as well as the weak convergence to a Gaussian process of a suitable rescaling, are proved. As by-products, results on statistical inference for queueing characteristics are also ob- tained. Finally, the problem of estimating the probability of a long delay is considered. 1. Introduction and preliminaries. Discrete-time queueing models have recently received considerable attention, mainly because of their appli- cations to telecommunication systems based on asynchronous transfer mode Ž. ATM , which is the standard transport vehicle of the broadband integrated Let T be the r.v. ''number of time slots between i 1 th and ith batches i Ž. Ž ith interarrival time , and let S be the r.v. ith service time i.e., the size of i . the ith batch . The hypotheses on r.v.'s T 's and S 's are: i