A Novel Workload Allocation Strategy for Batch Jobs

The distribution of computational tasks across a diverse set of geographically distributed heterogeneous resources is a critical issue in the realisation of true computational grids. Conventionally, workload allocation algorithms are divided into static and dynamic approaches. Whilst dynamic approaches frequently outperform static schemes, they usually require the collection and processing of detailed system information at frequent intervals - a task that can be both time consuming and unreliable in the real-world. This paper introduces a novel workload allocation algorithm for optimally distributing the workload produced by the arrival of batches of jobs. Results show that, for the arrival of batches of jobs, this workload allocation algorithm outperforms other commonly used algorithms in the static case. A hybrid scheduling approach (using this workload allocation algorithm), where information about the speed of computational resources is inferred from previously completed jobs, is then introduced and the efficiency of this approach demonstrated using a real world computational grid. These results are compared to the same workload allocation algorithm used in the static case and it can be seen that this hybrid approach comprehensively outperforms the static approach

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.

Analysis of Multiserver Retrial Queueing System: A Martingale Approach and an Algorithm of Solution

The paper studies a multiserver retrial queueing system with $m$ servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon arrival all servers are busy, then the customer goes to the secondary queue, orbit, and after some random time retries more and more to occupy a server. A service time of each customer is exponentially distributed random variable with parameter $\mu_1$. A time between retrials is exponentially distributed with parameter $\mu_2$ for each customer. Using a martingale approach the paper provides an analysis of this system. The paper establishes the stability condition and studies a behavior of the limiting queue-length distributions as $\mu_2$ increases to infinity. As $\mu_2\to\infty$, the paper also proves the convergence of appropriate queue-length distributions to those of the associated `usual' multiserver queueing system without retrials. An algorithm for numerical solution of the equations, associated with the limiting queue-length distribution of retrial systems, is provided.Comment: To appear in "Annals of Operations Research" 141 (2006) 19-52. Replacement corrects a small number of misprint

A Maclaurin-series expansion approach to coupled queues with phase-type distributed service times

International audienc

Bayesian inference and prediction for the GI/M/1 queueing system

This article undertake Bayesian inference and prediction for GI/M/1 queueing systems. A semiparametric model based on mixtures of Erlang distributions is considered to model the general interarrival time distribution. Given arrival and service data, a Bayesian procedure based on birth-death Markov Chain Monte Carlo methods is proposed. An estimation of the system parameters and predictive distributions of measures such as the stationary system size and waiting time is give