Stochastic timed Petri nets are a useful tool in performance analysis of concurrent systems such as parallel computers, communication networks and flexible manufacturing systems. In general, performance measures of stochastic timed Petri nets are difficult to obtain for problems of practical sizes. In this paper, we provide a method to compute efficiently upper and lower bounds for the throughputs and mean token numbers in general Markovian timed Petri nets. Our approach is based on uniformization technique and linear programming.

A new algorithm called the tree convolution algorithm for the computation of normalization constants and performance measures of product-form queueing algorithms, in the solution of networks with many service centers and many sparse routing chains. (A network is said to have sparse routing chains if the chains visit, on the average, only a small fraction of all centers in the net- work.) In such a network, substantial time and space savings can be achieved by exploiting the network's routing information. The time and space reductions are made possible by two features of the algorithm: (1) the sequence of array convolutions to compute a normalization constant is determined according to the traversal of a tree; and (2) the convolutions are performed between arrays that are smaller than arrays used by existing algorithms. The routing information of a given network is used to configure the tree to reduce the algorithms time and space requirements; some effective heuristics for optimization are de- scribed herein. An exact solution of a communication network model with 64 queues and 32 routing chains is illustrated.

We introduce an efficient algorithm for the exact analysis of closed multiclass product-form queueing network models with large population sizes. We adopt a novel approach, based on linear systems of equations, which significantly reduces the cost of computing normalizing constants. With the proposed algorithm, the analysis of a model with N circulating jobs of multiple classes requires essentially the solution of N linear systems with order independent of population sizes. A distinguishing feature of our approach is that we can immediately apply theorems, solution techniques, and decompositions for linear systems to queueing network analysis. Following this idea, we propose a block triangular form of the linear system that further reduces the requirements, in terms of both time and storage, of an exact analysis. An example illustrates the efficiency of the resulting algorithm in presence of large populations.

Queueing networks are important as Performance models of computer and communication systems because the performance of these systems is usually principally affected by contention for resources. Exact numerical solution of a queueing network is usually only feasible ifthe network has a product form solution in the sense of Jackson. An important network characteristic which apparently precludes a product form solution is simultaneous resource possession, e.g., a job holds memory and processor simultaneously. This paper extends previous methods for approximate numerical solution of queueing networks with homogeneous jobs and simultaneous resource possession to networks with heterogeneous jobs and simultaneous resource possession. 1.

As distributed systems such as Internet and Integrated Services Digital Networks (ISDN) become increasingly complex, the interactions among numerous components and workloads make system performance difficult to predict reliably. It is increasingly important to apply suitable performance evaluation tools to aid system analysis and design, system configuration and capacity planning, and resource management. Queueing network models are widely adopted for the performance evaluation of computer systems and communication networks. Approximate Mean Value Analysis (MVA) is a popular technique for analyzing queueing networks because of the efficiency and accuracy that it affords. In this thesis, all of the existing approximate MVA algorithms for separable queueing networks are surveyed. New numerical and complexity analysis results for existing approximate MVA algorithms are presented. The relative merits and tradeoffs of different implementations of the existing approximate MVA algorithms are ...

Queueing network models have been extensively applied to represent and analyze resource sharing systems such as communication and computer systems and they have proved to be a powerful and versatile tool for system performance evaluation and prediction. Product form queueing networks have a simple closed form expression of the stationary state distribution that allow to define efficient algorithms to evaluate average performance measures. We introduce product form queueing networks and some interesting properties including the arrival theorem, exact aggregation and insensitivity. Various special models of product form queueing networks allow to represent particular system features such as state-dependent routing, negative customers, batch arrivals and departures and finite capacity queues. 1 Introduction and Short History System performance evaluation is often based on the development and analysis of appropriate models. Queueing network models have been extensively applied to represent and analyze resource sharing systems, such as production, communication and computer systems. They have proved to be a powerful and versatile tool for system performance

Open, mixed and closed queueing networks with multiple job classes, reversible routing and rejection blocking are investigated in this paper. Jobs may change class membership and general service requirement distributions that depend on the job class are allowed. We prove that the equilibrium state probabilities have product form if at all stations either the scheduling discipline is symmetric or all service requirements at the station have the same exponential distribution. The solution implies insensitivity in this kind of blocking networks, i.e. the distribution of the jobs in equilibrium, irrespective of their remaining service requirements, depends only on their mean service requirement.

We introduce the Class-oriented Method of Moments (CoMoM), a new exact algorithm to compute performance indexes in closed multiclass queueing networks. Closed models are important for performance evaluation of multi-tier applications, but when the number of service classes is large they become too expensive to solve with exact methods such as Mean Value Analysis (MVA). CoMoM addresses this limitation by a new recursion that scales efficiently with the number of classes. Compared to the MVA algorithm, which recursively computes mean queue-lengths, CoMoM carries on in the recursion also information on higher-order moments of queue-lengths. We show that this additional information greatly reduces the number of operations needed to solve the model and makes CoMoM the best-available algorithm for networks with several classes. We conclude the paper by generalizing CoMoM to the efficient computation of marginal queue-length probabilities, which finds application in the evaluation of state-dependent attributes such as energy consumption or quality-of-service metrics.

We introduce the Class-oriented Method of Moments (CoMoM), a new exact algorithm to compute performance indexes in closed multiclass queueing networks. Closed models are important for performance evaluation of multi-tier applications, but when the number of service classes is large they become too expensive to solve with exact methods such as Mean Value Analysis (MVA). CoMoM addresses this limitation by a new recursion that scales efficiently with the number of classes. Compared to the MVA algorithm, which recursively computes mean queue-lengths, CoMoM carries on in the recursion also information on higher-order moments of queue-lengths. We show that this additional information greatly reduces the number of recursive steps needed to solve the model and makes CoMoM the best-available algorithm for networks with several classes. We conclude the paper by generalizing CoMoM to the efficient computation of marginal queue-length probabilities, which finds application in the evaluation of state-dependent attributes such as energy consumption or quality-of-service metrics.

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