In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold uid rather than discrete tokens. We de ne a class of uid stochastic Petri nets in such awaythat the discrete and continuous portions may a ect each other. Following this de nition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.

The purpose of this paper is to describe a method for simulation of recently introduced fluid stochastic Petri nets. Since such nets result in rather complex set of partial differential equations, numerical solution becomes a formidable task. Because of a mixed, discrete and continuous state space, simulative solution also poses some interesting challenges, which are addressed in the paper. 1

We address the suitability of a recently suggested approach for approximating self-similar traffic with a Markovian model. The phase-type nature of the proposed approach is identified and used to transform it from the discrete-time to the continuous-time domain. We then investigate the performance of a simple queueing system subject to self-similar arrival traffic, thereby comparing the results of trace-driven simulation with a measured self-similar trace to those derived from a numerical analysis of the suggested model. The numerical investigations are performed using a special class of stochastic Petri nets which is particularly suited for analyzing queueing-model like situations. Our results indicate that the suggested Markovian traffic model needs still to be improved, even though the properties of self-similarity per se are well approximated.

Introduction The Stochastic Petri Net Package (SPNP) is a versatile modeling tool for the solution of Stochastic Petri Nets (SPN) models. The SPN models are described in the input language for SPNP called CSPL (C-based SPN Language). The CSPL is an extension of the ANSI C programming language [16] with additional constructs to facilitate the easy description of SPN models. The full power and generality of C is available, but a working knowledge of C is sufficient to use SPNP effectively. The SPN models specified to SPNP are actually "SPN Reward Models" or Stochastic Reward Nets (SRNs) [9, 10] which are based on the "Markov Reward Model" paradigm [18, 37]. This provides a powerful modeling environment for the analysis of: ffl Dependability (Reliability, Availability, Safety). ffl Performance. ffl Performability. Several important Petri net constructs like marking dependency, variable cardinality arc and enabling functions [9] facil

this paper we present a numerical technique for steady state solution that makes use of known matrix geometric techniques

Continuous-time Markov chains are used extensively to analyze the performance of various computer networks. However, constructing and solving continuous-time Markov chain is a tedious and error-prone procedure, especially when the studied systems are complex. Stochastic Petri nets and the corresponding software packages provide automated generation and solution to continuous-time Markov chains. This paper gives an overview of stochastic Petri nets. Two examples in ATM networks are presented and studied to illustrate how to use stochastic Petri nets for performance analysis of computer networks. Index Terms: Stochastic Petri Nets, Stochastic Reward Nets, Computer Networks, ATM Networks This research was supported in part by the National Science Foundation under Grant No. EEC9418765. 1 Introduction From ARPAnet to Internet and to Internet 2, from Ethernet to fast Ethernet and to gigabit Ethernet, from packet switching to Asynchronous Transfer Mode (ATM) switching and to label switc...

In order to maximize system dependability improvements we need criteria for placement of component redundancy. One such criterion is based on quantitative measures provided by importance theory. Importance coefficients of components in mathematical models provide numerical ranks based on the contribution of the component to a system event occurrence (i.e., the one for which the model was constructed). If cost, size or weight are not objectives when maximizing system dependability, the importance ranks suggest components to which system upgrading effort should be directed first. Otherwise, the importance measures offer valid weighting factors to the optimization process. In this paper, we introduce novel techniques for computing importance measures in state space dependability models. Specifically, reward functions in a Markov reward model

Stochastic Petri Nets are well suited for the model-based performance and dependability evaluation of complex systems. In the past few years, many papers have been published dealing with the transient and steady-state analysis of all kinds of SPNs. However, because of the use of analytical methods, there are at least two limits: in most work related to Markov theory, including DTMCs and CTMCs, the researchers had to restrict the transitions to geometric or exponential distributions to ensure the memoryless property; another potential problem comes from the model size, since the state space will become too large to be stored in the computer main memory when the model size increases. Discrete event simulation can avoid these problems: simulation can deal with general distributions just as well as memoryless distributions and, for very large systems, simulation will simply take longer in terms of CPU time. However, in order to complete simulation experiments involving large model...