A Fixed-Point Algorithm for Closed Queueing Networks

In this paper we propose a new efficient iterative scheme for solving closed queueing networks with phase-type service time distributions. The method is especially efficient and accurate in case of large numbers of nodes and large customer populations. We present the method, put it in perspective, and validate it through a large number of test scenarios. In most cases, the method provides accuracies within 5% relative error (in comparison to discrete-event simulation)

The MVA Priority Approximation

A Mean Value Analysis (MVA) approximation is presented for computing the average performance measures of closed-, open-, and mixed-type multiclass queuing networks containing Preemptive Resume (PR) and nonpreemptive Head-Of-Line (HOL) priority service centers. The approximation has essentially the same storage and computational requirements as MVA, thus allowing computationally efficient solutions of large priority queuing networks. The accuracy of the MVA approximation is systematically investigated and presented. It is shown that the approximation can compute the average performance measures of priority networks to within an accuracy of 5 percent for a large range of network parameter values. Accuracy of the method is shown to be superior to that of Sevcik's shadow approximation

Integrated performance evaluation of extended queueing network models with line

Despite the large literature on queueing theory and its applications, tool support to analyze these models ismostly focused on discrete-event simulation and mean-value analysis (MVA). This circumstance diminishesthe applicability of other types of advanced queueing analysis methods to practical engineering problems,for example analytical methods to extract probability measures useful in learning and inference. In this toolpaper, we present LINE 2.0, an integrated software package to specify and analyze extended queueingnetwork models. This new version of the tool is underpinned by an object-oriented language to declarea fairly broad class of extended queueing networks. These abstractions have been used to integrate in acoherent setting over 40 different simulation-based and analytical solution methods, facilitating their use inapplications

Closed queueing networks under congestion: non-bottleneck independence and bottleneck convergence

We analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the stationary distribution at non-bottleneck queues converges weakly to the stationary distribution of an ergodic, open product-form queueing network. This open network is obtained by replacing bottleneck queues with per-route Poissonian sources whose rates are determined by the solution of a strictly concave optimization problem. Then, we focus on the transient behavior of the network and use fluid limits to prove that the amount of fluid, or customers, on each route eventually concentrates on the bottleneck queues only, and that the long-term proportions of fluid in each route and in each queue solve the dual of the concave optimization problem that determines the throughputs of the previous open network.Comment: 22 page

Generalised analytic queueing network models. The need, creation, development and validation of mathematical and computational tools for the construction of analytic queueing network models capturing more critical system behaviour.

Modelling is an important technique in the comprehension and management of complex systems. Queueing network models capture most relevant information from computer system and network behaviour. The construction and resolution of these models is constrained by many factors. Approximations contain detail lost for exact solution and/or provide results at lower cost than simulation. Information at the resource and interactive command level is gathered with monitors under ULTRIX'. Validation studies indicate central processor service times are highly variable on the system. More pessimistic predictions assuming this variability are in part verified by observation. The utility of the Generalised Exponential (GE) as a distribution parameterised by mean and variance is explored. Small networks of GE service centres can be solved exactly using methods proposed for Generalised Stochastic Petri Nets. For two centre. systems of GE type a new technique simplifying the balance equations is developed. A very efficient "building bglloocbka"l. is presented for exactly solving two centre systems with service or transfer blocking, Bernoulli feedback and load dependent rate, multiple GE servers. In the tandem finite buffer algorithm the building block illustrates problems encountered modelling high variability in blocking networks. ': . _. A parametric validation study is made of approximations for single class closed networks of First-Come-First-Served (FCFS) centres with general service times. The multiserver extension using the building block is validated. Finally the Maximum Entropy approximation is extended to FCFS centres with multiple chains and implemented with computationally efficient convolution

JMT – Performance Engineering Tools for System Modeling

We present the Java Modelling Tools (JMT) suite, an integrated framework of Java tools for performance evaluation of computer systems using queueing models. The suite offers a rich user interface that simplifies the definition of performance models by means of wizard dialogs and of a graphical design workspace. The performance evaluation features of JMT span a wide range of state-of-the-art methodologies including discrete-event simulation, mean value analysis of product-form networks, analytical identification of bottleneck resources in multiclass environments, and workload characterization with fuzzy clustering. The discrete-event simulator supports several advanced modeling features such as finite capacity regions, load-dependent service times, bursty processes, fork-and-join nodes, and implements spectral estimation for analysis of simulative results. The suite is open-source, released under the GNU general public license (GPL), and it is available for free download at http://jmt.sourceforge.net