GUARDS Project - PDCC Technical Note, Report GUARDS/I3A4/AO/6016 version a, 11 June 1998.

** Dept. of Information Engineering, Via Diotisalvi 2, 56100 Pisa, Italy mura@iet.unipi.it

Due to their intrinsic complexity and dynamic structure, modelling of PMS is a challenging activity that the GUARDS consortium decided to address. Therefore part of the effort devoted in GUARDS to dependability modelling has been spent dealing with modelling methodologies for Phased-Mission Systems. Two different methodologies, based on two different approaches, have been proposed by PDCC in GUARDS for the dependability modelling and analysis of PMS, described in details in [1-4].

The first methodology, called here Approach A [4], is based on a separate modelling of the different phases, which are combined in a global model of the mission through a hierarchy of models, whose upper level represents the profile of the mission. For the modelling of each phase a Generalised Stochastic Petri Net (GSPN) representation can be conveniently used, while the upper level is modelled as a Discrete-Time (DT) Markov chain.

Then, PDCC introduced a new modelling approach, hereafter Approach B [3], based on Deterministic and Stochastic Petri Nets (DSPN), which provides a single model of the overall phased-mission system. Still, the analytic solution of the DSPN model can be partitioned and reduced to the sequential solution of each phase, thus requiring the same computational cost as needed by the former approach.

Both approaches basically require for the evaluation the transient solution of a set of Markov chains, either Continuous-Time or Discrete-Time, and therefore no specific tools for this purpose are required and have been foreseen. Rather, the solution is intended to be carried out by taking advantage of the existing tools for the automated evaluation of systems dependability. Many of these tools are indeed based on Petri-Nets and/or Markov-chain modelling, and thus they include both the editing facilities to build the models, and also implement the solution algorithms for the transient analysis of Markov-chain. Among the off-the-shelf tools commercially available, we choose three examples, namely SURF-2 [5], UltraSAN [6], and SPNP [7], to show the modelling and evaluation of Phased-Mission Systems dependability according with the methodologies proposed by PDCC.

The purpose of this guide is to introduce a user to a practical application the proposed methodologies, with the aid of the selected automated tools. Therefore, this guide is organised as follows. In Section 2 we give a general algorithm that highlights the steps needed for the definition and solution of a PMS model with Approach A. Then, for each of the considered tools, the basic algorithm is specified to take into account the support they can provide. In particular, we clarify which parts of the modelling and of the solution procedure of can be supported by the tools, and which ones require some user-assistance instead. Section 3 has the same organisation of the previous one dealing with Approach B.

**References**

[1] A. Bondavalli, I. Mura and M. Nelli, "Analytical Modelling and Evaluation of Phased-Mission Systems for Space Applications," in Proc. IEEE High Assurance System Engineering Workshop (HASE'97), Washington D.C. USA, 1997, pp. to appear.

[2] A. Bondavalli, I. Mura and M. Nelli, "Analytical modelling and evaluation of the GUARDS instances: example for space applications," GUARDS Project - PDCC Activity Output (D3A4/AO/6001/C) (also GUARDS First Year Deliverable), Mar 18 1997.

[3] A. Bondavalli, I. Mura, X. Zang and K. S. Trivedi, "Dependability Modelling and Evaluation of Phased Mission Systems: a DSPN Approach," GUARDS Project - PDCC Activity Output (I3A4/AO/6010/a), 20 January 1998 1998.

[4] I. Mura and A. Bondavalli, "Hierarchical Modelling and Evaluation of Phased-Mission Systems," CNUCE-CNR Internal Report (C97-016) also GUARDS Project - PDCC Activity Output, (I3A4/AO/6007/A), November 1997.

[5] WEB address: http://www.crhc.uiuc.edu/UltraSAN/UltraSAN.html

[6] WEB address: http://www.laas.fr/surf/surf.html

[7] WEB address: http://www.ee.duke.edu/~kst/kst.html