A Closed Queueing Maintenance Network with Two Repair Centres

In this paper we introduce a model to determine the maintenance float needed to maximize the availability of an operating system with N number of circulating units. An implicit enumeration algorithm is used as a solution technique to the closed queueing maintenance network with two types of repairs: minor and major repairs. It is shown that when there is no differentiation of repair type, this special case is obtained as a by-product of the two-repair-centre model. This paper assumes exponential failure times and exponential repair times with load-independent servers. The approach followed in this paper provides an approximate and simple way to solve the maintenance-float problem of this complex closed-network system.     

Implementation of Markovian Queueing Network Model with Multiple Closed Chains

Mathematical strategy portrays the performance evaluation of computer and communication system and it deals with the stochastic properties of the multiclass Markovian queueing system with class-dependent and server-dependent service times. An algorithm is designed where the job transitions are characterized by more than one closed Markov chain. Generating functions are implemented to derive closed form of solutions and product form solution with the parameters such as stability, normalizations constant and marginal distributions. For such a system with N servers and L chains, the solutions are considerably more complicated than those for the systems with one sub-chain only. In Multi-class queueing network, a job moves from a queue to another queue with some probability after getting a service. A multiple class of customer could be open or closed where each class has its own set of queueing parameters. These parameters are obtained by analyzing each station in isolation under the assumption that the arrival process of each class is a state-dependent Markovian process along with different service time distributions. An algorithmic approach is implemented from the generating function representation for the general class of Networks. Based on the algorithmic approach it is proved that how open and closed sub-chain interact with each other in such system. Specifically, computation techniques are provided for the calculation of the Markovian model for multiple chains and it is shown that these algorithms converge exponentially fast.     

A Large Closed Queueing Network Containing Two Types of Node and Multiple Customer Classes: One Bottleneck Station

Queueing Systems - The paper studies a closed queueing network containing two types of node. The first type (server station) is an infinite server queueing system, and the second type (client...     

Comments on: Queueing models for the analysis of communication systems

The paper under discussion is a well-written exposition on the performance modeling of communication systems by discrete-time queueing systems, and their analysis. It basically consists of two parts: a review of the literature, focusing on the modelling of information streams and on scheduling disciplines (Sects. 2, 3), and a demonstration of some key methods for the analysis of discrete-time queueing systems, focusing on a particular two-class discrete-time queue with correlated arrivals and two priority classes (Sects. 4–6). In Sect. 1 of the present note, we make some introductory comments. In Sect. 2, realizing that the literature review in Bruneel et al. (TOP, 2014) is authoritative and extensive, we focus on a few adjacent topics which fall outside the scope of Bruneel et al. (TOP, 2014) but which in our view may also be of some interest. Finally, in Sect. 3, we discuss the analysis in Sects. 4–6 of Bruneel et al. (TOP, 2014).     

A Closed Queueing Network Model to Evaluate the Impact of Recovery Operations on the Performance of Database Servers

As database servers proliferate in modern information systems architectures in organizations, the issue of protecting and recovering the databases becomes of utmost importance. By developing an analytical model based on a closed network of queues, this paper analyses how different database recovery mechanisms impact on the normal transaction processing. Such a model enables one to capture intricate effects that are peculiar to complex, tightly coupled, multi-component systems, such as database recovery systems, and can be used to facilitate the design and the tuning of database recovery managers. The proposed model provides important performance measures in terms of average transaction processing time and overall systems throughput. Numerical experiments using actual recovery methods demonstrate the effectiveness of the modelling approach.     

一个基于多类顾客和多阶段排队模型的设备维修案例仿真

通过对一个设备维修案例进行研究,建立了顾客到达、服务时间、服务台故障间隔、故障修复均为负指数分布且相互独立的多类顾客和多阶段排队系统模型.然后,根据时钟推进法构建排队仿真流程,应用MATLAB仿真,结合VSM,对系统进行分析改进.仿真结果表明周期时间由26.06小时减少至4.05小时,增值比由1.82%上升至15.08%,为多类顾客和多阶段排队系统优化提供参考依据.     

具有位相型修理的离散时间可修排队系统

本文研究了具有一般独立输入，位相型修理的离散时间可修排队系统，假定服务台对顾客的服务时间和服务台寿命服从几何分布，运用矩阵解析方法我们给出系统嵌入在到达时刻的稳态队长分布和等待时间分布，并证明这些分布均为离散位相型分布．我们也得到在广义服务时间内服务台发生故障次数的分布，证明它服从一个修正的几何分布．我们对离散时间可修排队与连续时间可修排队进行了比较，说明这两种排队系统在一些性能指标方面的区别之处．最后我们通过一些数值例子说明在这类系统中顾客的到达过程、服务时间和服务台的故障率之间的关系．     

Some Results for Large Closed Queueing Networks with and without Bottleneck: Up- and Down-Crossings Approach

The paper provides the up- and down-crossing method to study the asymptotic behavior of queue-length and waiting time in closed Jackson-type queueing networks. These queueing networks consist of central node (hub) and k single-server satellite stations. The case of infinite server hub with exponentially distributed service times is considered in the first section to demonstrate the up- and down-crossing approach to such kind of problems and help to understand the readers the main idea of the method. The main results of the paper are related to the case of single-server hub with generally distributed service times depending on queue-length. Assuming that the first k–1 satellite nodes operate in light usage regime, we consider three cases concerning the kth satellite node. They are the light usage regime and limiting cases for the moderate usage regime and heavy usage regime. The results related to light usage regime show that, as the number of customers in network increases to infinity, the network is decomposed to independent single-server queueing systems. In the limiting cases of moderate usage regime, the diffusion approximations of queue-length and waiting time processes are obtained. In the case of heavy usage regime it is shown that the joint limiting non-stationary queue-lengths distribution at the first k–1 satellite nodes is represented in the product form and coincides with the product of stationary GI/M/1 queue-length distributions with parameters depending on time.     

A Multiclass Feedback Queueing Network with a Regular Skorokhod Problem

We consider a four-class two-station network with feedback, with fluid inputs and a head-of-the-line generalized processor sharing discipline at each station. We derive the Skorokhod Problem associated with the network and obtain algebraic sufficient conditions for Lipschitz continuity of the associated Skorokhod Map. This provides the first example of a multiclass network with feedback for which the associated Skorokhod Problem has been proved to be regular. As an elementary application, we show that under the conditions which guarantee Lipschitz continuity the network is stable if and only if the usual load conditions apply.     

Closed Submodules of Holomorphic Functions with Two Generators

Let I be a closed submodule over a polynomial ring in a space of holomorphic functions on a domain in the complex plane. We establish sufficient conditions under which I is generated by two functions or two special submodules. As a corollary, it follows from these results that if an invariant subspace W C (a,b) (with respect to the differentiation operator) admits spectral synthesis, then it is the solution space of a system of two homogeneous convolution equations.     

Closed Ideals of Holomorphic Functions with Two Generators

Mathematical Notes - For a wide class of algebras P of holomorphic functions on a domain in ?, sufficient conditions are obtained under which a closed ideal I ? P is 2-generated.     

Using Operational Analysis in Simulation: A Queueing Network Example

The calculation of certain performance measures in queueing network simulation using operational analysis is presented. A systematic approach to the gathering of output and calculation of performance measures for quantitative system-performance analysis is demonstrated. The assumptions used in operational analysis to derive performance-measure relationships are verifiable by examining the output generated by the simulation. Any errors in assumptions revealed by the output may be measured, and these error measures used to determine correction terms. The performance-measure relations may still be used, even when the assumptions upon which they are based are in error, by adding these correction terms to the performance-measure values obtained. The results will be exact values for the performance measures over the period of the simulation. Calculations of performance measures, error measures and correction terms are illustrated with an example queueing network simulation.     

Maximizing Queueing Network Utility Subject to Stability: Greedy Primal-Dual Algorithm

We study a model of controlled queueing network, which operates and makes control decisions in discrete time. An underlying random network mode determines the set of available controls in each time slot. Each control decision “produces” a certain vector of “commodities”; it also has associated “traditional” queueing control effect, i.e., it determines traffic (customer) arrival rates, service rates at the nodes, and random routing of processed customers among the nodes. The problem is to find a dynamic control strategy which maximizes a concave utility function H(X), where X is the average value of commodity vector, subject to the constraint that network queues remain stable.We introduce a dynamic control algorithm, which we call Greedy Primal-Dual (GPD) algorithm, and prove its asymptotic optimality. We show that our network model and GPD algorithm accommodate a wide range of applications. As one example, we consider the problem of congestion control of networks where both traffic sources and network processing nodes may be randomly time-varying and interdependent. We also discuss a variety of resource allocation problems in wireless networks, which in particular involve average power consumption constraints and/or optimization, as well as traffic rate constraints.     

基于排队的两类顾客易逝品库存控制策略研究

本文采用排队理论在面向两类顾客需求的环境下讨论易逝品库存排队系统控制策略问题。首先刻画面向两类顾客服务且具有马尔科夫结构的易逝品库存系统排队模型,获得库存水平状态的稳态概率分布以及作为库存成本控制的系统稳态性能指标。接下来,构建库存控制成本函数及考虑服务水平约束的库存控制优化模型,设计了改进的遗传算法。最后,数值算例揭示出系统参数的敏感性和相应的管理启示。     

带有启动的N级串联开排队网络系统模型

主要研究了带有启动策略的多级串联开排队模型,其中采用递推方式给出了马尔科夫过程的转移矩阵,并利用矩阵分析法进行求解,得到了系统的稳态解及忙期长度、逗留时间和其它相关指标.