SimQPN—A tool and methodology for analyzing queueing Petri net models by means of simulation

Abstract

The queueing Petri net (QPN) paradigm provides a number of benefits over conventional modeling paradigms such as queueing networks and generalized stochastic Petri nets. Using queueing Petri nets (QPNs), one can integrate both hardware and software aspects of system behavior into the same model. This lends itself very well to modeling distributed component-based systems, such as modern e-business applications. However, currently available tools and techniques for QPN analysis suffer the state space explosion problem, imposing a limit on the size of the models that are tractable. In this paper, we present SimQPN—a simulation tool for QPNs that provides an alternative approach to analyze QPN models, circumventing the state space explosion problem. In doing this, we propose a methodology for analyzing QPN models by means of discrete event simulation. The methodology shows how to simulate QPN models and analyze the output data from simulation runs. We validate our approach by applying it to study several different QPN models, ranging from simple models to models of realistic systems. The performance of point and interval estimators implemented in SimQPN is subjected to a rigorous experimental analysis.

Introduction

The queueing Petri net (QPN) modeling formalism was introduced in 1993 by Bause [5]. It allows queues (queueing stations) to be integrated into the places of Petri nets (more specifically colored generalized stochastic Petri nets) and thus brings the benefits of queueing networks into the world of Petri nets. In [4] it is shown that QPNs have greater expressive power than queueing networks, extended queueing networks and stochastic Petri nets. In addition to hardware contention and scheduling strategies, using QPNs one can easily model simultaneous resource possession, synchronization, blocking and software contention. This enables the integration of both hardware and software aspects of system behavior into the same model [8], [22]. While the above could also be achieved by using layered queueing networks (LQNs) (or stochastic rendezvous networks) [45], [38], [29], the latter are defined at a higher-level of abstraction and are usually less detailed and accurate. Another benefit of QPNs is that, since they are based on Petri nets, one can exploit a number of efficient techniques from Petri net theory to verify some important qualitative properties of QPNs, such as ergodicity, boundedness, liveness or existence of home states. The latter not only help to gain insight into the behavior of QPNs, but are also essential preconditions for a successful quantitative analysis [5].

In [22], we showed that QPNs lend themselves very well to modeling distributed e-business applications with software contention and demonstrated how this can be exploited for performance prediction in the capacity planning process. However, we also showed that modeling a realistic e-business application using QPNs often leads to a model that is way too large to be analyzable using currently available tools and techniques. This is the reason why QPNs have hardly been exploited in the past decade and very few, if any, practical applications have been reported. The problem is that, until now, available tools and solution techniques for QPN models have all been based on Markov chain analysis, which suffers the well known state space explosion problem and limits the size of the models that can be analyzed.

This paper shows how the above problem can be approached by exploiting discrete event simulation for model analysis. We present SimQPN—a Java-based simulation tool for QPNs that can be used to analyze QPN models of realistic size and complexity. While doing this, we propose a methodology for simulating QPN models and analyzing the output data from simulation runs. SimQPN can be seen as an implementation of this methodology. We validate our approach by studying several different QPN models by means of SimQPN. Models of different size and complexity are considered, including models of realistic e-business applications such as the SPECjAppServer¹ set of benchmarks. We evaluate the quality of data provided by SimQPN, conducting an exhaustive experimental analysis of the variation of point estimates and coverage of confidence intervals reported.

An alternative approach to simulate QPN models would be to use a general purpose simulation package. However, this approach has some disadvantages. First, general purpose simulation packages do not provide means to represent QPN constructs directly. Instead, they require that simulation models are described using a general purpose simulation language. Mapping a QPN model to a description in the terms of a general purpose simulation language is a complex, time-consuming and error-prone task. Moreover, not all simulation languages provide the expressiveness needed to describe complex QPN models. Some simplifications might be required, which could lead to less accurate results. Another disadvantage is that general purpose simulators are generally not as fast and efficient as specialized simulators, since they are usually not optimized for any particular type of models. Being specialized for QPNs, SimQPN simulates QPN models directly and has been designed to exploit the knowledge of the structure and behavior of QPNs to improve the efficiency of the simulation. Therefore, SimQPN is expected to provide much better performance than a general purpose simulator, both in terms of the speed of simulation and the quality of output data provided. Last but not least, SimQPN has the advantage that it is extremely light-weight and being implemented in Java it is platform independent.

The rest of the paper is organized as follows. We start with a brief introduction to queueing Petri nets in Section 2. In Section 3, we present SimQPN—our simulation tool for QPNs, and discuss its features, design and architecture. In parallel to this, we discuss our methodology for simulating QPN models, based on which SimQPN was developed. We look at the methods for output data analysis employed, and discuss the specifics of their implementation. Following this, in Section 4, we study several different QPN models using SimQPN and validate the results with respect to correctness and accuracy. We evaluate the performance of point and interval estimators implemented in SimQPN. Finally, we discuss our ongoing/future work and present some concluding remarks.