ISPN: Modeling Stochastic with Input Uncertainties Using an Interval-Based Approach
Sérgio Mário Lins Galdino, Paulo Maciel · InTech eBooks · 2011
Analytic techniques are frequently used for performance analysis of discrete event systems.Conventional models have a set of single value input parameters (such as mean resource demands) and give single value results for each performance index of interest (such as mean system throughput).However, this single point characterization of parameters is insufficient when uncertainties and variabilities are related with system parameters.As an application domain, we may highlight software performance engineering, which accomplishes performance modelling in several phases design-cycle and throughout implementation (Girault & Valk, 2003;Smith, 1990).Even if uncertainties and variabilities may be associated with one or more parameters of the system in early stages of system design, the expert designer might have a suitable guess related to the interval of values associated with these parameters due to previous experience.The current availability of software tools for performance evaluation allows one to hide the technicalities from the end-user.Users specify their performance model using some high-level modeling language supported by tools such as PEPSY-QNS, TimeNET 4.0, SPNP 6.0, GreatSPN 2.0, or PEPA, in which the underlying mathematical model is automatically generated and analyzed.We propose the adoption of intervals to represent the uncertainties in the parameters of ISPN (Interval Stochastic Petri Net) models (Galdino & Maciel, 2006; Galdino et al., 2007a;b).Therefore, the set of methods considered for Markov chain steady-state analysis have to be adapted for taking into account interval arithmetic.In ISPN the exponential transition rates and immediate transition weights are represented by intervals.This chapter focuses on ISPN using MATLAB with INTLAB toolbox.We briefly introduce the interval arithmetic.Afterwards, we describe the ISPN and outline the approach adopted to the respective interval steady state analysis.We present two ISPN system models and the respective results of analysis.Further possibilities of the method are also suggested. BackgroundPrior to present the ISPN, this section introduces some basic concepts needed to understand how interval arithmetics may be used for evaluating system's metrics.Hence, we initially introduce some concepts on interval arithmetics.