Heavy-traffic limits for Polling Models with Exhaustive Service and non-FCFS Service Order Policies

We study cyclic polling models with exhaustive service at each queue under a variety of non-FCFS local service orders, namely Last-Come-First-Served (LCFS) with and without preemption, Random-Order-of-Service (ROS), Processor Sharing (PS), the multi-class priority scheduling with and without preemption, Shortest-Job-First (SJF) and the Shortest Remaining Processing Time (SRPT) policy. For each of these policies, we rst express the waiting-time distributions in terms of intervisit-time distributions. Next, we use these expressions to derive the asymptotic waiting-time distributions under heavy-trac assumptions, i.e., when the system tends to saturate. The results show that in all cases the asymptotic wait

The impact of scheduling policies on the waiting-time distributions in polling systems

We consider polling models consisting of a single server that visits the queues in a cyclic order. In the vast majority of papers that have appeared on polling models, it is assumed that at each of the individual queues, the customers are served on a first-come-first-served (FCFS) basis. In this paper, we study polling models where the local scheduling policy is not FCFS but instead is varied as last-come-first-served (LCFS), random order of service (ROS), processor sharing (PS), and shortest-job-first (SJF). The service policies are assumed to be either gated or globally gated. The main result of the paper is the derivation of asymptotic closed-form expressions for the Laplace–Stieltjes transform of the scaled waiting-time and sojourn-time distributions under heavy-traffic assumptions. For FCFS service, the asymptotic sojourn-time distribution is known to be of the form UG , where U and G are uniformly and gamma distributed with known parameters. In this paper, we show that the asymptotic sojourn-time distribution (1) for LCFS is also of the form UG , (2) for ROS is of the form U~G , where U~ has a trapezoidal distribution, and (3) for PS and SJF is of the form U~*G , where U~* has a generalized trapezoidal distribution. These results are rather intriguing and lead to new fundamental insight into the impact of the local scheduling policy on the performance of polling models. As a by-product, the heavy-traffic results suggest simple closed-form approximations for the complete waiting-time and sojourn-time distributions for stable systems with arbitrary load values. The accuracy of the approximations is evaluated by simulations. Keywords: Polling systems; Local scheduling policies; Waiting times; Heavy traffic; Approximation

Melhoria do desempenho em sistemas de escalonamento-Híbrido SJF/FIFO através da gestão do tamanho de jobs

Orientadores: Michel Daoud Yacoub, Edson Luiz UrsiniTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Esta tese propõe um método de simulação discreta para planejar e gerenciar o desempenho de sistemas de filas M/G/1 de relativa complexidade. O sistema é formado por servidores em paralelo submetidos a mudanças dinâmicas entre as políticas de escalonamento SJF e FIFO. O tráfego de entrada de entidades é aleatório com oscilações até a sobrecarga do sistema. As entidades são formadas por multiplas classes de jobs e cada servidor processa uma única classe desses jobs. O método gerencia o desempenho das classes de jobs que provocam perda no desempenho do sistema por atrasos no tempo médio de residência. O modelo de simulação obtém o tempo médio de residência relativo de cada classe de job para calcular o atraso relativo dessas classes no atraso total do sistema. Os jobs que ultrapassam os limites dos requisitos podem ser gerenciados, e.g., direcionados para outros servidores, ou serem bloqueados temporária ou definitivamente. Como exemplo de um problema complexo, apresentamos um estudo de caso logístico de carregamento e movimentação de cargas dentro da área de produção industrial. As cargas são formadas por múltiplas classes de produtos simultaneamente carregados em diferentes servidores. A implementação desse modelo logístico é iniciada com um modelo reconhecido e validado e prossegue com pequenos incrementos validados até a representação de um modelo o mais próximo possível da realidade. A técnica de Escalonamento Híbrido de Sistemas com Gestão do Tamanho de Jobs permite a mudança dinâmica de políticas de escalonamento do sistema entre SJF e FIFO, ainda que sujeita a variações abruptas de tráfego de entrada. Essa técnica é efetiva para reduzir os tempos médios, conter os tempos máximos e habilitar a identificação dos jobs que provocam atrasos, permitindo dessa forma, ações de gestão para mitigar resultados indesejadosAbstract: This thesis proposes a discrete-event simulation method to plan and manage the performance of M/G/1 queuing systems of relative complexity. The system has parallel servers undergoing dynamic changes under system instabilities (e.g., spontaneous oscillations of the incoming traffic to the system overload). Entities have multi classes of jobs and each server performs a single class of this jobs. The method manages the size of jobs that may cause loss of performance, e.g. the delays in average residence time. Performance management is carried out via the monitoring of the impact of classes of job sizes on the total system delay. Jobs that exceed a certain threshold value may then be managed accordingly, e.g. by moving them to different servers or by (temporarily or permanently) blocking them. We present a case study of loading and moving cargoes within an industrial production area. Each cargo consists of multiple product classes which are simultaneously loaded on different servers. This logistic-model implementation begins with a well-known validated model extended by small validated increments to better be able to represent the real-world. The technique of Improving the Performance of SJF/FIFO Hybrid-Scheduling Systems through the Management of Job Size under dynamic conditions, i.e. when subject to toggling SJF and FIFO policies and fluctuations of inbound traffic, has shown to be effective in the reduction of the time average, in the decrease of the mean time maximum, and in the identification of jobs that cause delays to the system, and thus enable the management of these jobs to mitigate unwanted system performanceDoutoradoTelecomunicações e TelemáticaDoutor em Engenharia Elétrica138.553/2014CAPE