**5. References**


<sup>\*</sup> Corresponding Author

[8] Hoffmann KA, Chiang ST (1993) Computational Fluid Dynamics for Engineers: Volume I & II. Engineering Education System.

254 Petri Nets – Manufacturing and Computer Science

potential under different scenarios.

and Zoran Kotevski

**Author details** 

Pece Mitrevski\*

**5. References** 

Wisconsin - Madison.

Performance Models. Zaragoza.

Theory of Petri Nets. 691: 24-31.

Berlin: TR 1996-13.

Verlag.

Corresponding Author

 \*

Discrete Event Dynamic Systems. 11(1/2): 97-117.

presented performance evaluation results in order to illustrate its usage in deriving measures of interest. Since the equations characterizing the evolution of FSPNs are a coupled system of partial differential equations, the numerical transient analysis poses some interesting challenges. Because of a mixed, discrete and continuous state space, another important avenue for the solution is the discrete-event simulation of the FSPN model. We believe that our stochastic modeling framework reveals considerable potential for further research in this area, needed to better understand speculation techniques in ILP processors and their performance

In the second part of this chapter, we have shown how the FSPN formalism can be used to model P2P live video streaming systems. We have also presented a simulation solution method using process-based discrete-event simulation language whenever analytic/numeric solution becomes infeasible, that is usually a result of state space explosion. We managed to create a model that accounts for numerous features of such complex systems including: network topology, peer churn, scalability, average size of peers' neighborhoods, peer upload bandwidth heterogeneity and video buffering, among which control traffic overhead

and admission control for lesser contributing peers are introduced for the first time.

*Faculty of Technical Sciences, University of St. Clement Ohridski, Bitola, Republic of Macedonia* 

[1] Rajan R (1995) General Fluid Models for Queuing Networks. PhD Thesis. University of

[2] Gribaudo M, Sereno M, Bobbio A (1999) Fluid Stochastic Petri Nets: An extended Formalism to Include non-Markovian Models. Proc. 8th Int. Workshop on Petri Nets and

[3] Gribaudo M, Sereno M, Horvath A, Bobbio A (2001) Fluid Stochastic Petri Nets Augmented with Flush-out Arcs: Modeling and Analysis. Kluwer Academic Publishers:

[4] Horton G, Kulkarni V, Nicol D, Trivedi K (1998) Fluid Stochastic Petri Nets: Theory, Applications, and Solution. European Journal of Operations Research. 105(1): 184-201. [5] Trivedi K, Kulkarni V (1993) FSPNs: Fluid Stochastic Petri Nets. In: M. Ajmone Marsan, editor. Lecture Notes in Computer Science: Proc. 14th Int. Conf. on Applications and

[6] Wolter K, Horton G, German R (1996) Non-Markovian Fluid Stochastic Petri Nets. TU

[7] Ferziger JH, Perić M (1997) Computational Methods for Fluid Dynamics. Springer-

	- [25] Lu Z, Li Y, Wu J, Zhang SY, Zhong YP (2008) MultiPeerCast: A Tree-mesh-hybrid P2P Live Streaming Scheme Design and Implementation based on PeerCast. 10th IEEE Int. Conf. on High Performance Computing and Communications. pp. 714-719.

**Chapter 11** 

© 2012 Khan et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Khan et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

to compose the services by means of collaboration and role bindings [12].

Considering system execution architecture to specify the deployment of the service components is realized by the UML deployment diagram. Abstract view of the system

**Performance Evaluation** 

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/48813

**1. Introduction** 

**of Distributed System Using SPN** 

Razib Hayat Khan, Poul E. Heegaard and Kazi Wali Ullah

Distributed system poses one of the main streams of information and communication technology arena with immense complexity. Designing and implementation of such complex systems are always an intricate endeavour. Likewise, performance evaluation is also a great concern of such complex system to evaluate whether the system meets the performance related system requirements. Hence, modeling plays an important role in the whole design process of the system for qualitative and quantitative analysis. However, in a distributed system, system functional behavior is normally distributed among several objects. The overall behavior of the system is composed of the partial behavior of the distributed objects of the system. So it is indispensable to capture the functional behavior of the distributed objects for appropriate analysis to evaluate the performance related factors of the overall system. We therefore adopt UML collaboration and activity oriented approach as UML is the most widely used modeling language which models both the system requirements and qualitative behavior through different notations. Collaboration and activity diagram are utilized to demonstrate the overall system behavior by defining both the structure of the partial object behavior as well as the interaction between them as reusable specification building blocks and later on, this UML specification style is applied to generate the SPN model by our performance modeling framework. UML collaboration and activity provides a tremendous modeling framework containing several interesting properties. Firstly, collaborations and activity model the concept of service provided by the system very nicely. They define structure of partial object behavior, the collaboration roles and enable a precise definition of the overall system behavior. They also delineate the way

