**4. Conclusion**

252 Petri Nets – Manufacturing and Computer Science

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Universal Streaming probability

**Figure 12.** Performance of small and medium systems with and without AC

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25

*rVIDEO* /*rAVERAGE*

0.875 0.925 0.975 1.025 1.075 1.125 1.175 1.225

*rVIDEO* /*rAVERAGE*

0.9 0.925 0.95 0.975 1 1.025 1.05 1.075 1.1 1.125

*rVIDEO* /*rAVERAGE*

Small system without AC Small system with AC Medium system without AC Medium system with AC

> Small system Medium system Large system

Buffer size = 0 sec Buffer size = 30 sec Buffer size = 60 sec Buffer size = 90 sec Buffer size = 120 sec

**Figure 13.** Performance in respect to system scaling

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Universal Streaming probability

Universal Streaming probability

**Figure 14.** Buffer analysis of medium system without admission control

In the first part of this chapter, we have introduced an implementation-independent analytical modeling approach to evaluate the performance impact of branch and value prediction in modern ILP processors, by varying several parameters of both the microarchitecture and the operational environment, like branch and value prediction accuracy, machine width, instruction window size and operational profile. The proposed analytical model is based on recently introduced Fluid Stochastic Petri Nets (FSPNs). We have also 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 potential under different scenarios.

Fluid Stochastic Petri Nets:

From Fluid Atoms in ILP Processor Pipelines to Fluid Atoms in P2P Streaming Networks 255

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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.
