Performance Analysis of ARQ Protocols using a Theorem Prover

Automatic-repeat-request (ARQ) protocols are widely used in modern data communications to guarantee reliable transmission over imperfect physical links. The behavior of an ARQ protocol largely depends on a number of network parameters and traditionally simulation is used for their performance analysis. However, simulation provides less accurate results and usually requires enormous amount of CPU time in order to attain reasonable estimates. To overcome these limitations, we propose to conduct the performance analysis of ARQ protocols in the environment of a higher-order-logic theorem prover (HOL). We present an approach to formally model the delay characteristics of ARQ protocols as a function of geometric random variable in higher-order-logic. In particular, we develop higher-order-logic models that describe the delay behavior of three basic types of ARQ protocols, i.e., Stop-and-Wait, Go-Back-N and Selective-Repeat. The paper also includes the verification of the average message delay relations for these three protocols in HOL.

[1]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[2]  Bruce D. McCullough,et al.  Assessing the Reliability of Statistical Software: Part I , 1998 .

[3]  Jan J. M. M. Rutten,et al.  Mathematical techniques for analyzing concurrent and probabilistic systems , 2004, CRM monograph series.

[4]  Michael J. C. Gordon,et al.  Mechanizing programming logics in higher order logic , 1989 .

[5]  Sofiène Tahar,et al.  Verification of Tail Distribution Bounds in a Theorem Prover , 2007 .

[6]  Mahesh Viswanathan,et al.  VESTA: A statistical model-checker and analyzer for probabilistic systems , 2005, Second International Conference on the Quantitative Evaluation of Systems (QEST'05).

[7]  M. Easton.  Batch Throughput Efficiency of ADCCP/HDLC/SDLC Selective Reject Protocols , 1980, IEEE Trans. Commun..

[8]  Marta Z. Kwiatkowska,et al.  Quantitative Analysis With the Probabilistic Model Checker PRISM , 2006, QAPL.

[9]  Ramakant Khazanie.  Basic probability theory and applications , 1976 .

[10]  Don Towsley,et al.  On the Statistical Analysis of Queue Lengths and Waiting Times for Statistical Multiplexers with ARQ Retransmission Schemes , 1979, IEEE Trans. Commun..

[11]  Alberto Leon-Garcia,et al.  Communication Networks: Fundamental Concepts and Key Architectures , 1999 .

[12]  MA John Harrison PhD.  Theorem Proving with the Real Numbers , 1998, Distinguished Dissertations.

[13]  Sofiène Tahar,et al.  Verification of Expectation Properties for Discrete Random Variables in HOL , 2007, TPHOLs.

[14]  Christel Baier,et al.  Model-Checking Algorithms for Continuous-Time Markov Chains , 2002, IEEE Trans. Software Eng..

[15]  Alan Bundy,et al.  Constructing Induction Rules for Deductive Synthesis Proofs , 2006, CLASE.

[16]  Erik P. de Vink,et al.  Verification and Improvement of the Sliding Window Protocol , 2003, TACAS.

[17]  Freek Wiedijk,et al.  The Seventeen Provers of the World , 2006 .

[18]  Jamil Y. Khan,et al.  An ARQ enhancement with QoS support for the 802.11 MAC protocol , 2004, 2004 IEEE Wireless Communications and Networking Conference (IEEE Cat. No.04TH8733).

[19]  Erol Gelenbe,et al.  An Analytic Evaluation of the Performance of the "Send and Wait" Protocol , 1978, IEEE Trans. Commun..

[20]  David J. C. Mackay,et al.  Introduction to Monte Carlo Methods , 1998, Learning in Graphical Models.

[21]  Shu Lin,et al.  Automatic-repeat-request error-control schemes , 1984, IEEE Communications Magazine.

[22]  Sofiène Tahar,et al.  Formalization of Continuous Probability Distributions , 2007, CADE.

[23]  Stephan Merz,et al.  Model Checking , 2000 .

[24]  Robin Milner,et al.  A Theory of Type Polymorphism in Programming , 1978, J. Comput. Syst. Sci..

[25]  Rachel Cardell-Oliver.  The formal verification of hard real-time systems , 1992 .

[26]  Thomas Hérault,et al.  Probabilistic Model Checking of the CSMA/CD Protocol Using PRISM and APMC , 2005, AVoCS.

[27]  Paul Bratley,et al.  A guide to simulation , 1983 .

[28]  Pin-Han Ho,et al.  Performance analysis of differentiated ARQ scheme for video transmission over wireless networks , 2005, WMuNeP '05.

[29]  Joe Hurd,et al.  Formal verification of probabilistic algorithms , 2003 .

[30]  Linus Schrage,et al.  A guide to simulation , 1983 .