Explain the single-server and multi-server waiting line models. Launch Classic WoW Server Queue Times (EU) - Wowhead News

Introduction At the beginning of the 21st century computers are omnipresent and widely accepted in both professional and private sectors. The importance and complexity of modern IT systems grew in the last decades. For example, factors such as globalization and outsourcing have led to an increased demand of companies for an effectual IT system and environment.

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In this context it is significant to ensure resource efficiency and Quality-of-Service demands. A main goal of computer system designers, administrators and users is to obtain or provide a high performance at a low cost.

To reach that goal, performance evaluation is useful at every stage in the life cycle of a computer system, e. The more complex the systems and relations are, the more difficult but also the more important is the analyze. Besides constructing models of IT systems performance prediction analysis is very valuable to finally evaluate these models.

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To represent IT systems with a large number of resources, Queueing Network models have been extensively applied. A lot of research has shown that these models are robust and versatile for performance evaluation and prediction. Basic queueing systems were first introduced to study congestion in telephonic system by one service center and then it was extended to analyze congestion in computer and communication systems cf.

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Queueing Network models consist of basic queueing systems. To get performance predictions, several assumptions for Queueing Networks e.

explain the single-server and multi-server waiting line models

The analysis of performance models such as Queueing Networks can either be simulation-based or analytical-based. Both approaches share differences, advantages as well as disadvantages.

In simulations as well as in analytical processes the input parameters are measured or invented. Simulations are general and have a wide application, while analytical methods, which are based on mathematical relationships, have a set of assumptions and limitations. On the other hand computational costs of simulations grow the more complex the system of interest gets.

Operations Research Tutorial #31: Queuing Theory #7_Multiple Channel Problem

The big advantage of analytical approaches however is the significantly lower computational costs. Analytical methods have a relatively high accuracy in the performance measures and in efficiency. In cases where computer system designers or administrators want to find the best design or system, they have to compare a number of alternatives, so an analytical tool may be more suitable.

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This explain the single-server and multi-server waiting line models focuses on an analytical solution of performance metrics. Basic queueing theory formulas are considered because performance results can be computed very fast by them. Possibilities and limitations of mapping the basic formulas on Queueing Network models are presented by using theoretical knowledge and practical comparison of a self-developed analysis tool with an existing simulation tool. Deviations in performance metrics and savings on computational costs of the analytical solver in contrast to a simulation tool are shown and by this the usefulness of analytical procedures will be underlined exemplarily.

The remainder of this paper is divided into six sections. Chapter 2 describes the foundation of this thesis, where queues, Queueing Networks and the solution possibility for system-level performance models are shown.

Chapter 3 gives an overview of the main goals and the approach of this paper. In chapter 4 basic queueing formulas are derived and a self-developed tool for solving performance measures of queueing models by analytical formulas is presented. The possibility and the way of mapping basic performance formulas on Queueing Networks is discussed in chapter 5 on a theoretical level. The evaluation of the self-developed solving tool in chapter 6 has a practical aspect.

Performance results of the analytical tool and explain the single-server and multi-server waiting line models simulation tool as well as time explain the single-server and multi-server waiting line models of the analytical procedure are illustrated there.

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Chapter 7 provides some conclusions and directions for future work. Foundation This Chapter introduces fundamental concepts and models. Queueing models are described in section 2.

Solving system-level performance models is discussed in section 2.


The waiting line is a buffer space for waiting elements such as database transactions, batch jobs and different requests called customers. When a server is free, the next customer according to the scheduling discipline will be processed.

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The scheduling discipline orders which customers are served next at the service station. There are several types, only typical ones will be explained below cf. Customers are served in the same order they arrived in.

Customers are served in the reverse order they arrived in. Customers are served in a random order independent of the order they arrived in. Customers with the highest priority are served next. FCFS is used, when the priority is equal. Many variations are possible: Customers get equal time slices of a defined length and are explain the single-server and multi-server waiting line models according to FCFS.

All customers are served simultaneously and the server speed is divided similarly among them. This discipline is like RR but with infinitesimally small time slices. Service rate of the resource is constant independent of the load i.

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Resources such as CPUs and disks are usually load-independent. Service rate is dependant of the load and can be represented by explain the single-server and multi-server waiting line models number of customers in the queue. The service rate can both increase or decrease depending on the resource as the number of requests grows. Customers are served immediately so there is no waiting line.

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The number can be limited finite queue size but also unlimited infinite queue size. In the latter case no argument is needed. The population size can be limited finite population size as well as unlimited infinite population size. For FCFS no argument is needed. Some possible distributions for the arrival and service processes are: Moreover the queue has a single server, no limitations in capacity and population size and the scheduling discipline is FCF.

Customers move between the queues on a path until they complete their execution. According to their different behaviours, they are often grouped into customer classes, which can either be open or closed.

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Example of a Explain the single-server and multi-server waiting line models Network Customers of an singletrails zwickau class arrive from an external source, get served in the QN and depart.

The main characteristic is the unbounded population size. The workload is described by an arrival rate. Customers of a closed class do not arrive from an external source and do not depart from the QN but they circulate in the network. Closed classes have a bounded and known number of customers in the system finite population and their workload is described by the population size and a think time.

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In an open QN all customer classes are open, in a closed QN all customer classes are closed and in a mixed QN there are closed and open customer classes. The network topology describes how the queues are interconnected and how the customers move between them.

In figure 2. In c the QN is also closed and the network topology is central server, where p is the probability that a customer moves to the displayed queue after getting served by the central server queue. The sum of all probabilities have to be one. See [Bal00] for more details. Example of explain the single-server and multi-server waiting line models network topologies QNs are often distinguished in product-form and non-product-form, since product-form QNs are easier to analyse.

Solving performance models based on basic queueing theory formulas

To calculate performance measures of QNs, system steady-state probabilities are to be considered. If the solution of the steady-state probabilities can be expressed as a product of factors describing the state of each queue of a Queueing Network, it is called to be product-form.

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In other words, product-form Queueing Networks have a simple expression of the stationary state distribution. These QNs have a special structure.

explain the single-server and multi-server waiting line models