Abstract
The Available Bit Rate protocol (ABR) for ATM networks is well adapted to data traffic by providing minimum rate guarantees and low cell loss to the ABR source end system. An ABR conformance algorithm for controlling the source rates through an interface has been defined by ATM Forum, and a more efficient version of it has been designed by Rabadan and Klay. We present in this work the first complete mechanical verification of the equivalence between these two algorithms. The proof is involved and has been supported by the PVS theorem prover. It has required many lemmas, case analysis, and induction reasoning for the manipulation of unbounded scheduling lists. Some ABR conformance protocols have been verified in previous works. However, these protocols are approximations of the one we consider here. In particular, the algorithms assume a bound on the number of rates to be scheduled.
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References
Arnold, A.: MEC: A system for constructing and analysing transition systems, in J. Sifakis (ed.), Proceedings of the International Workshop on Automatic Verification Methods for Finite State Systems, Lecture Notes in Comput. Sci. 407, Springer-Verlag, 1990, pp. 117-132.
Barras, B., Boutin, S., Cornes, C., Courant, J., Filliatre, J. C., Giménez, E., Herbelin, H., Huet, G., Muñoz, C., Murthy, C., Parent, C., Paulin, C., Saïbi, A. and Werner, B.: The Coq proof assistant reference manual - version V6.1, Technical Report 0203, INRIA, August 1997.
Bengtsson, J., Larsen, K. G., Larsson, F., Pettersson, P. and Yi, W.: UPPAAL: A tool suite for the automatic verification of real-time systems, in R. Alur, T. A. Henzinger and E. D. Sontag (eds), Hybrid Systems III, Lecture Notes in Comput. Sci. 1066, 1996, pp. 232-243.
Berger, A., Bonomi, F. and Fendick, K.: Proposed TM baseline text on an ABR conformance definition, Technical Report 95-0212R1, ATM Forum Traffic Management Group, 1995.
Bouhoula, A. and Rusinowitch, M.: SPIKE-User Manual, December 1995.
Bérard, B. and Fribourg, L.: Automated verification of a parametric real-time program: The ABR conformance protocol, in Proc. 11th Int. Conf. Computer Aided Verification (CAV’99), Lecture Notes in Comput. Sci. 1633, July 1999, pp. 96-107.
Dijkstra, E. W.: A Discipline of Programming, Prentice-Hall, Englewood Cliffs, 1976.
Fribourg, L.: A closed-form evaluation for extended timed automata, Technical Report LSV-98-2, Lab. Specification and Verification, ENS de Cachan, March 1998. 17 pages.
Henzinger, T. A., Ho, P. H. and Wong-Toi, H.: HYTECH: A model checker for hybrid systems, in CAV’97, Lecture Notes in Comput. Sci. 1254, Springer-Verlag, 1997, pp. 460-463.
Jain, R.: Congestion control and traffic management in ATM networks: Recent advances and a survey, Computer Networks and ISDN Systems 28 (1996), 1723-1738. ftp://ftp.netlab.ohio-state.edu/pub/jain/papers/cnis/index.html.
Monin, J. F. and Klay, F.: Correctness proof of the standardized algorithm for ABR conformance, in J. Wing, J. Woodcock and J. Davies (eds), Formal Methods (FM)’ 99, Lecture Notes in Comput. Sci. 1709, Springer-Verlag, 1999, pp. 662-681.
Owre, S. and Shankar, N.: PVS semantics document, March 1999. http://www.csl.sri.com/papers/csl-97-2/
Rabadan, C.: L’ABR et sa conformité, Technical Report NT DAC/ARP/034, CNET, 1997.
Rabadan, C. and Klay, F.: Un nouvel algorithme de contrôle de conformité pour la capacité de transfert “Available Bit Rate”, Technical Report NT/CNET/5476, CNET, 1997.
Rusinowitch, M., Stratulat, S. and Klay, F.: Mechanical verification of an ideal incremental ABR conformance algorithm, in E. A. Emerson and A. P. Sistla (eds), Proceedings of 12th International Conference on Computer Aided Verification (CAV’2000), Lecture Notes in Comput. Sci. 1855, Springer-Verlag, July 2000, pp. 344-357.
Shankar, N., Owre, S., Rushby, J. M. and Stringer-Calvert, D. W. J.: PVS: Prover Guide. Version 2.3, 1999.
Rushby, J., Owre, S. and Shankar, N.: Subtypes for specifications: Predicate subtyping in PVS, IEEE Trans. on Software Engrg. 24(9) (1998), 709-720.
Shankar, N. and Owre, S.: Principles and pragmatics of subtyping in PVS, in D. Bert, C. Choppy and P. Mosses (eds), Recent Trends in Algebraic Development Techniques, WADT’99, Lecture Notes in Comput. Sci. 1827, Toulouse, France, September 1999, pp. 37-52.
Stratulat, S.: Preuves par récurrence avec ensembles couvrants contextuels: Applications à la vérification de logiciels de télécommunications. Ph.D. thesis, Université Henri Poincaré, Nancy I, 2000.
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Rusinowitch, M., Stratulat, S. & Klay, F. Mechanical Verification of an Ideal Incremental ABR Conformance Algorithm. Journal of Automated Reasoning 30, 153–177 (2003). https://doi.org/10.1023/A:1023251327012
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DOI: https://doi.org/10.1023/A:1023251327012