Abstract Interpretation of PEPA Models

This paper relates the fluid-flow semantics of the stochastic process algebra PEPA Performance Evaluation Process Algebra to the static analysis technique of abstract interpretation. The explanation in the paper is illustrated through the example of a distributed denial of service DDoS attack which is being launched against a server. DDoS attacks are mounted by a large population of attackers, who are coordinating and working together in attacking a specific server. The scale of the attack is crucial to its success, but the resulting large number of states in the system makes it difficult to model and analyse using the conventional discrete-state interpretation of PEPA.

[1]  S. Gilmore,et al.  The PEPA Eclipse Plug-in , 2008 .

[2]  Adam Duguid.  Coping with the Parallelism of BitTorrent: Conversion of PEPA to ODEs in Dealing with State Space Explosion , 2006, FORMATS.

[3]  Flemming Nielson,et al.  Denial-of-Service Security Attack in the Continuous-Time World , 2014, FORTE.

[4]  Vincent Danos,et al.  Abstract Interpretation of Cellular Signalling Networks , 2008, VMCAI.

[5]  Jane Hillston,et al.  Fluid flow approximation of PEPA models , 2005, Second International Conference on the Quantitative Evaluation of Systems (QEST'05).

[6]  Stephen Gilmore,et al.  An Efficient Algorithm for Aggregating PEPA Models , 2001, IEEE Trans. Software Eng..

[7]  Fan Yang,et al.  Static Analysis of Stochastic Process Algebras , 2007 .

[8]  Stephen Gilmore,et al.  Automatic Translation of UML Sequence Diagrams into PEPA Models , 2008, 2008 Fifth International Conference on Quantitative Evaluation of Systems.

[9]  Adam Duguid,et al.  The PEPA eclipse plugin , 2009, PERV.

[10]  Flemming Nielson,et al.  Securing Statically-verified Communications Protocols Against Timing Attacks , 2005, PASM.

[11]  Stephen Gilmore,et al.  Scalable Differential Analysis of Process Algebra Models , 2012, IEEE Transactions on Software Engineering.

[12]  Stephen Gilmore,et al.  Evaluating the Scalability of a Web Service-Based Distributed e-Learning and Course Management System , 2006, WS-FM.

[13]  Flemming Nielson,et al.  The Stochastic Quality Calculus , 2014, COORDINATION.

[14]  Flemming Nielson,et al.  A Calculus for Quality , 2012, FACS.

[15]  Diego Latella,et al.  Quantitative Analysis of Services , 2011, Results of the SENSORIA Project.

[16]  Patrick Cousot,et al.  Abstract Interpretation Based Formal Methods and Future Challenges , 2001, Informatics.

[17]  Jane Hillston,et al.  The Benefits of Sometimes Not Being Discrete , 2014, CONCUR.

[18]  Flemming Nielson,et al.  A Framework for Hybrid Systems with Denial-of-Service Security Attack , 2014, ArXiv.

[19]  Allan Clark,et al.  Stochastic Process Algebras , 2007, SFM.

[20]  Stephen Gilmore,et al.  Fluid Rewards for a Stochastic Process Algebra , 2012, IEEE Transactions on Software Engineering.

[21]  Stephen Gilmore,et al.  Replicating Web Services for Scalability , 2007, TGC.

[22]  Stephen Gilmore,et al.  Analysing distributed Internet worm attacks using continuous state-space approximation of process algebra models , 2008, J. Comput. Syst. Sci..

[23]  Jane Hillston,et al.  Automated Capacity Planning for PEPA Models , 2014, EPEW.

[24]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[25]  T. Kurtz.  Solutions of ordinary differential equations as limits of pure jump markov processes , 1970, Journal of Applied Probability.

[26]  Stephen Gilmore,et al.  Automatic extraction of PEPA performance models from UML activity diagrams annotated with the MARTE profile , 2008, WOSP '08.

[27]  Flemming Nielson,et al.  Stochastic Model Checking of the Stochastic Quality Calculus , 2015, Software, Services, and Systems.

[28]  Nigel Thomas,et al.  Approximate Solution of a PEPA Model of a Key Distribution Centre , 2008, SIPEW.

[29]  Jane Hillston,et al.  A compositional approach to performance modelling , 1996 .

[30]  Flemming Nielson,et al.  Key Update Assistant for resource-constrained networks , 2012, 2012 IEEE Symposium on Computers and Communications (ISCC).

[31]  Flemming Nielson,et al.  Broadcast, Denial-of-Service, and Secure Communication , 2013, IFM.

[32]  Allan Clark,et al.  Formal Methods for Performance Evaluation , 2007 .