Abstract.
In this paper we present a first approach to the definition of conformance testing relations for systems presenting stochastic timed behavior. By stochastic time we mean that the probability of performing an event may vary according to the elapsed time. In particular, we will consider delays specified by means of random variables.
In order to define our formal model, we will provide a stochastic extension of the notion of finite state machine. We will give a first implementation relation and we will discuss its practical drawbacks. That is, we will show that this relation cannot be appropriately checked under a black/grey-box testing methodology. We will also present other alternative implementation relations that can be checked up to a certain degree of confidence. We will define test cases and how they are applied to implementations. Finally, we will give a test generation algorithm providing complete, up to a degree of confidence, test suites.
Research supported in part by the Spanish MCYT projects AMEVA and MASTER and the Junta de Castilla-La Mancha project DISMEF.
Chapter PDF
Similar content being viewed by others
References
Ajmone Marsan, M., Bianco, A., Ciminiera, L., Sisto, R., Valenzano, A.: A LOTOS extension for the performance analysis of distributed systems. IEEE/ACM Transactions on Networking 2(2), 151–165 (1994)
Ajmone Marsan, M., Conte, G., Balbo, G.: A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Transactions on Computer Systems 5(2), 93–122 (1984)
Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)
Bernardo, M., Cleaveland, W.R.: A theory of testing for markovian processes. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 305–319. Springer, Heidelberg (2000)
Bernardo, M., Gorrieri, R.: A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time. Theoretical Computer Science 202, 1–54 (1998)
Bosik, B.S., Uyar, M.U.: Finite state machine based formal methods in protocol conformance testing. Computer Networks & ISDN Systems 22, 7–33 (1991)
Bravetti, M., Gorrieri, R.: The theory of interactive generalized semi-Markov processes. Theoretical Computer Science 282(1), 5–32 (2002)
Clarke, D., Lee, I.: Automatic generation of tests for timing constraints from requirements. In: 3rd Workshop on Object-Oriented Real-Time Dependable Systems (1997)
de Nicola, R., Hennessy, M.C.B.: Testing equivalences for processes. Theoretical Computer Science 34, 83–133 (1984)
En-Nouaary, A., Dssouli, R., Khendek, F.: Timed Wp-method: Testing real time systems. IEEE Transactions on Software Engineering 28(11), 1024–1039 (2002)
Götz, N., Herzog, U., Rettelbach, M.: Multiprocessor and distributed system design: The integration of functional specification and performance analysis using stochastic process algebras. In: Donatiello, L., Nelson, R. (eds.) SIGMETRICS 1993 and Performance 1993. LNCS, vol. 729, pp. 121–146. Springer, Heidelberg (1993)
Harrison, P.G., Strulo, B.: SPADES – a process algebra for discrete event simulation. Journal of Logic Computation 10(1), 3–42 (2000)
Hennessy, M.: Algebraic Theory of Processes. MIT Press, Cambridge (1988)
Hermanns, H., Herzog, U., Katoen, J.-P.: Process algebra for performance evaluation. Theoretical Computer Science 274(1-2), 43–87 (2002)
Higashino, T., Nakata, A., Taniguchi, K., Cavalli, A.: Generating test cases for a timed I/O automaton model. In: 12th Workshop on Testing of Communicating Systems, pp. 197–214. Kluwer Academic Publishers, Dordrecht (1999)
Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, Cambridge (1996)
Lai, R.: A survey of communication protocol testing. Journal of Systems and Software 62, 21–46 (2002)
Lee, D., Yannakakis, M.: Principles and methods of testing finite state machines: A survey. Proceedings of the IEEE 84(8), 1090–1123 (1996)
López, N., Núñez, M.: A testing theory for generally distributed stochastic processes. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 321–335. Springer, Heidelberg (2001)
López, N., Núñez, M., Rubio, F.: Stochastic process algebras meet Eden. In: Butler, M., Petre, L., Sere, K. (eds.) IFM 2002. LNCS, vol. 2335, pp. 29–48. Springer, Heidelberg (2002)
Mandrioli, D., Morasca, S., Morzenti, A.: Generating test cases for real time systems from logic specifications. ACM Transactions on Computer Systems 13(4), 356–398 (1995)
M. Núñez and I. Rodríguez. Encoding PAMR into (timed) EFSMs. In FORTE 2002, LNCS 2529, pages 1–16. Springer, 2002.
Springintveld, J., Vaandrager, F., D’Argenio, P.R.: Testing timed automata. Theoretical Computer Science 254(1-2), 225–257 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 IFIP International Federation for Information Processing
About this paper
Cite this paper
Núñez, M., Rodríguez, I. (2003). Towards Testing Stochastic Timed Systems. In: König, H., Heiner, M., Wolisz, A. (eds) Formal Techniques for Networked and Distributed Systems - FORTE 2003. FORTE 2003. Lecture Notes in Computer Science, vol 2767. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39979-7_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-39979-7_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20175-5
Online ISBN: 978-3-540-39979-7
eBook Packages: Springer Book Archive