Nested Fork-Join Queuing Networks and Their Application to Mobility Airfield Operations Analysis

A single-chain nested fork-join queuing network (FJQN) model of mobility airfield ground processing is proposed. In order to analyze the queuing network model, advances on two fronts are made. First, a general technique for decomposing nested FJQNs with probabilistic forks is proposed, which consists of incorporating feedback loops into the embedded Markov chain of the synchronization station, then using Marie\u27s Method to decompose the network. Numerical studies show this strategy to be effective, with less than two percent relative error in the approximate performance measures in most realistic cases. The second contribution is the identification of a quick, efficient method for solving for the stationary probabilities of the λn/Ck/r/N queue. Unpreconditioned Conjugate Gradient Squared is shown to be the method of choice in the context of decomposition using Marie\u27s Method, thus broadening the class of networks where the method is of practical use. The mobility airfield model is analyzed using the strategies described above, and accurate approximations of airfield performance measures are obtained in a fraction of the time needed for a simulation study. The proposed airfield modeling approach is especially effective for quick-look studies and sensitivity analysis

Coupled queues with customer impatience

Motivated by assembly processes, we consider a Markovian queueing system with multiple coupled queues and customer impatience. Coupling means that departures from all constituent queues are synchronised and that service is interrupted whenever any of the queues is empty and only resumes when all queues are non-empty again. Even under Markovian assumptions, the state space grows exponentially with the number of queues involved. To cope with this inherent state space explosion problem, we investigate performance by means of two numerical approximation techniques based on series expansions, as well as by deriving the fluid limit. In addition, we provide closed-form expressions for the first terms in the series expansion of the mean queue content for the symmetric coupled queueing system. By an extensive set of numerical experiments, we show that the approximation methods complement each other, each one being accurate in a particular subset of the parameter space. (C) 2017 Elsevier B.V. All rights reserved

A Simple, Practical Prioritization Scheme for a Job Shop Processing Multiple Job Types

The maintenance, repair, and overhaul (MRO) process is used to recondition equipment in the railroad, off-shore drilling, aircraft, and shipping industries. In the typical MRO process, the equipment is disassembled into component parts and these parts are routed to back-shops for repair. Repaired parts are returned for reassembling the equipment. Scheduling the back-shop for smooth flow often requires prioritizing the repair of component parts from different original assemblies at different machines. To enable such prioritization, we model the back-shop as a multi-class queueing network with a ConWIP execution system and introduce a new priority scheme to maximize the system performance. In this scheme, we identify the bottleneck machine based on overall workload and classify machines into two categories: the bottleneck machine and the non-bottleneck machine(s). Assemblies with the lowest cycle time receive the highest priority on the bottleneck machine and the lowest priority on non-bottleneck machine(s). Our experimental results show that this priority scheme increases the system performance by lowering the average cycle times without adversely impacting the total throughput. The contribution of this thesis consists primarily of three parts. First, we develop a simple priority scheme for multi-class, multi-server, ConWIP queueing systems with the disassembly/reassembly feature so that schedulers for a job-shop environment would be able to know which part should be given priority, in what order and where. Next, we provide an exact analytical solution to a two-class, two-server closed queueing model with mixed non-preemptive priority scheme. The queueing network model we study has not been analyzed in the literature, and there are no existing models that address the underlying problem of deciding prioritization by job types to maximize the system performance. Finally, we explore conditions under which the non-preemptive priority discipline can be approximated by a preemptive priority discipline

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

Modelling parallel database management systems for performance prediction

Abstract unavailable please refer to PD

Methodology for modeling high performance distributed and parallel systems

Performance modeling of distributed and parallel systems is of considerable importance to the high performance computing community. To achieve high performance, proper task or process assignment and data or file allocation among processing sites is essential. This dissertation describes an elegant approach to model distributed and parallel systems, which combines the optimal static solutions for data allocation with dynamic policies for task assignment. A performance-efficient system model is developed using analytical tools and techniques. The system model is accomplished in three steps. First, the basic client-server model which allows only data transfer is evaluated. A prediction and evaluation method is developed to examine the system behavior and estimate performance measures. The method is based on known product form queueing networks. The next step extends the model so that each site of the system behaves as both client and server. A data-allocation strategy is designed at this stage which optimally assigns the data to the processing sites. The strategy is based on flow deviation technique in queueing models. The third stage considers process-migration policies. A novel on-line adaptive load-balancing algorithm is proposed which dynamically migrates processes and transfers data among different sites to minimize the job execution cost. The gradient-descent rule is used to optimize the cost function, which expresses the cost of process execution at different processing sites. The accuracy of the prediction method and the effectiveness of the analytical techniques is established by the simulations. The modeling procedure described here is general and applicable to any message-passing distributed and parallel system. The proposed techniques and tools can be easily utilized in other related areas such as networking and operating systems. This work contributes significantly towards the design of distributed and parallel systems where performance is critical

Dynamical Modeling of Cloud Applications for Runtime Performance Management

Cloud computing has quickly grown to become an essential component in many modern-day software applications. It allows consumers, such as a provider of some web service, to quickly and on demand obtain the necessary computational resources to run their applications. It is desirable for these service providers to keep the running cost of their cloud application low while adhering to various performance constraints. This is made difficult due to the dynamics imposed by, e.g., resource contentions or changing arrival rate of users, and the fact that there exist multiple ways of influencing the performance of a running cloud application. To facilitate decision making in this environment, performance models can be introduced that relate the workload and different actions to important performance metrics.In this thesis, such performance models of cloud applications are studied. In particular, we focus on modeling using queueing theory and on the fluid model for approximating the often intractable dynamics of the queue lengths. First, existing results on how the fluid model can be obtained from the mean-field approximation of a closed queueing network are simplified and extended to allow for mixed networks. The queues are allowed to follow the processor sharing or delay disciplines, and can have multiple classes with phase-type service times. An improvement to this fluid model is then presented to increase accuracy when the \emph{system size}, i.e., number of servers, initial population, and arrival rate, is small. Furthermore, a closed-form approximation of the response time CDF is presented. The methods are tested in a series of simulation experiments and shown to be accurate. This mean-field fluid model is then used to derive a general fluid model for microservices with interservice delays. The model is shown to be completely extractable at runtime in a distributed fashion. It is further evaluated on a simple microservice application and found to accurately predict important performance metrics in most cases. Furthermore, a method is devised to reduce the cost of a running application by tuning load balancing parameters between replicas. The method is built on gradient stepping by applying automatic differentiation to the fluid model. This allows for arbitrarily defined cost functions and constraints, most notably including different response time percentiles. The method is tested on a simple application distributed over multiple computing clusters and is shown to reduce costs while adhering to percentile constraints. Finally, modeling of request cloning is studied using the novel concept of synchronized service. This allows certain forms of cloning over servers, each modeled with a single queue, to be equivalently expressed as one single queue. The concept is very general regarding the involved queueing discipline and distributions, but instead introduces new, less realistic assumptions. How the equivalent queue model is affected by relaxing these assumptions is studied considering the processor sharing discipline, and an extension to enable modeling of speculative execution is made. In a simulation campaign, it is shown that these relaxations only has a minor effect in certain cases