{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T05:03:15Z","timestamp":1755925395926},"publisher-location":"Berlin, Heidelberg","reference-count":38,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540442523"},{"type":"electronic","value":"9783540457985"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2002]]},"DOI":"10.1007\/3-540-45798-4_4","type":"book-chapter","created":{"date-parts":[[2007,7,3]],"date-time":"2007-07-03T01:42:40Z","timestamp":1183426960000},"page":"64-88","source":"Crossref","is-referenced-by-count":38,"title":["An Algorithmic Approach to Stochastic Bounds"],"prefix":"10.1007","author":[{"given":"J. M.","family":"Fourneau","sequence":"first","affiliation":[]},{"given":"N.","family":"Pekergin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2002,9,5]]},"reference":[{"key":"4_CR1","unstructured":"Abu-Amsha O., Vincent J.-M.: An algorithm to bound functionals of Markov chains with large state space. Int: 4th INFORMS Conference on Telecommunications, Boca Raton, Florida, (1998)"},{"key":"4_CR2","unstructured":"Benmammoun M.: Encadrement stochastiques et \u00e9valuation de performances des r\u00e9seaux, PHD, Universit\u00e9 de Versailles St-Quentin en Yvelines, (2002)"},{"key":"4_CR3","unstructured":"Benmammoun M., Fourneau J.M., Pekergin N., Troubniko. A.: An algorithmic and numerical approach to bound the performance of high speed networks, Submitted, (2002)"},{"key":"4_CR4","doi-asserted-by":"crossref","unstructured":"Benmammoun M., Pekergin N.: Closed form stochastic bounds on the stationary distribution of Markov chains. To appear in Probability in the Engineering and Informational Sciences, (2002)","DOI":"10.1017\/S0269964802164023"},{"key":"4_CR5","unstructured":"Boujdaine F., Dayar T., Fourneau J.M., Pekergin N., Saadi S., Vincent J.M.: A new proof of st-comparison for polynomials of a stochastic matrix, Submitted, (2002)"},{"key":"4_CR6","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1017\/S0269964800004782","volume":"11","author":"P. Buchholz","year":"1997","unstructured":"Buchholz P.: An aggregation\u29c0saggregation algorithm for stochastic automata networks. In: Probability in the Engineering and Informational Sciences, V 11, (1997) 229\u2013253","journal-title":"Probability in the Engineering and Informational Sciences"},{"key":"4_CR7","unstructured":"Buchholz P.: Projection methods for the analysis of stochastic automata networks. In: Proc. of the 3rd International Workshop on the Numerical Solution of Markov Chains, B. Plateau, W. J. Stewart, M. Silva, (Eds.), Prensas Universitarias de Zaragoza, Spain, (1999) pp. 149\u2013168."},{"key":"4_CR8","doi-asserted-by":"publisher","first-page":"804","DOI":"10.1145\/1634.1637","volume":"31","author":"P.J. Courtois","year":"1984","unstructured":"Courtois P.J., Semal P.: Bounds for the positive eigenvectors of nonnegative matrices and for their approximations by decomposition. In: Journal of ACM, V 31 (1984) 804\u2013825","journal-title":"Journal of ACM"},{"key":"4_CR9","doi-asserted-by":"crossref","unstructured":"Courtois P.J., Semal P.: Computable bounds for conditional steady-state probabilities in large Markov chains and queueing models. In: IEEE JSAC, V4, N6, (1986)","DOI":"10.1109\/JSAC.1986.1146398"},{"key":"4_CR10","doi-asserted-by":"crossref","unstructured":"Dayar T., Fourneau J.M., Pekergin N.: Transforming stochastic matrices for stochastic comparison with the st-order, Submitted, (2002)","DOI":"10.1051\/ro:2003015"},{"key":"4_CR11","unstructured":"Dayar T., Pekergin, N.: Stochastic comparison, reorderings, and nearly completely decomposable Markov chains. In: Proceedings of the International Conference on the Numerical Solution of Markov Chains (NSMC\u201999), (Ed. Plateau, B. Stewart, W.), Prensas universitarias de Zaragoza. (1999) 228\u2013246"},{"key":"4_CR12","doi-asserted-by":"publisher","first-page":"1691","DOI":"10.1137\/S1064827598338159","volume":"21","author":"T. Dayar","year":"2000","unstructured":"Dayar T., Stewart W. J.: Comparison of partitioning techniques for two-level iterative solvers on large sparse Markov chains. In: SIAM Journal on Scientific Computing V21 (2000) 1691\u20131705.","journal-title":"SIAM Journal on Scientific Computing"},{"key":"4_CR13","doi-asserted-by":"crossref","unstructured":"Donatelli S.: Superposed generalized stochastic Petri nets: definition and efficient solution. In: Proc. 15th Int. Conf. on Application and Theory of Petri Nets, Zaragoza, Spain, (1994)","DOI":"10.1007\/3-540-58152-9_15"},{"key":"4_CR14","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1287\/opre.35.2.282","volume":"35","author":"B.N. Feinberg","year":"1987","unstructured":"Feinberg B.N., Chiu S.S.: A method to calculate steady-state distributions of large Markov chains by aggregating states. In: Oper. Res, V 35 (1987) 282\u2013290","journal-title":"Oper. Res"},{"key":"4_CR15","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1145\/278298.278303","volume":"45","author":"P. Fernandes","year":"1998","unstructured":"Fernandes P., Plateau B., Stewart W.J.: Efficient descriptor-vector multiplications in stochastic automata networks. In: Journal of the ACM, V45 (1998) 381\u2013414.","journal-title":"Journal of the ACM"},{"key":"4_CR16","doi-asserted-by":"crossref","unstructured":"Fourneau J.M., Pekergin N., Taleb H.: An Application of Stochastic Ordering to the Analysis of the PushOut Mechanism. In Performance Modelling and Evaluation of ATM Networks, Chapman and Hall, (1995) 227\u2013244","DOI":"10.1007\/978-0-387-34881-0_12"},{"key":"4_CR17","doi-asserted-by":"crossref","unstructured":"Fourneau J.M., Quessette F.: Graphs and Stochastic Automata Networks. In: Proceedings of the 2nd Int. Workshop on the Numerical Solution of Markov Chains, Raleigh, USA, (1995)","DOI":"10.1007\/978-1-4615-2241-6_14"},{"key":"4_CR18","doi-asserted-by":"crossref","unstructured":"H\u00e9buterne G., Gravey A.: A space priority queueing mechanism for multiplexing ATM channels. In: ITC Specialist Seminar, Computer Network and ISDN Systems, V20 (1990) 37\u201343","DOI":"10.1016\/0169-7552(90)90007-F"},{"key":"4_CR19","unstructured":"Golubchik, L. and Lui, J.: Bounding of performance measures for a threshold-based queuing systems with hysteresis. In: Proceeding of ACM SIGMETRICS\u201997, (1997) 147\u2013157"},{"key":"4_CR20","doi-asserted-by":"crossref","unstructured":"Hillston J., Kloul L.: An Efficient Kronecker Representation for PEPA Models. In: PAPM\u20192001, Aachen Germany, (2001)","DOI":"10.1007\/3-540-44804-7_8"},{"key":"4_CR21","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/0304-4149(77)90033-3","volume":"5","author":"J. Keilson","year":"1977","unstructured":"Keilson J., Kester A.: Monotone matrices and monotone Markov processes. In: Stochastic Processes and Their Applications, V5 (1977) 231\u2013241","journal-title":"Stochastic Processes and Their Applications"},{"key":"4_CR22","doi-asserted-by":"crossref","unstructured":"Kijima M.: Markov Processes for stochastic modeling. Chapman & Hall (1997)","DOI":"10.1007\/978-1-4899-3132-0"},{"key":"4_CR23","doi-asserted-by":"crossref","unstructured":"Latouche G., Ramaswami V.: Introduction to Matrix Analytic Methods in Stochastic Modeling. SIAM, (1999)","DOI":"10.1137\/1.9780898719734"},{"issue":"12","key":"4_CR24","doi-asserted-by":"publisher","first-page":"1371","DOI":"10.1109\/12.477243","volume":"44","author":"J. Lui","year":"1995","unstructured":"Lui, J. Muntz, R. and Towsley, D.: Bounding the mean response time of the minimum expected delay routing policy: an algorithmic approach. In: IEEE Transactions on Computers. V44 N12 (1995) 1371\u20131382","journal-title":"IEEE Transactions on Computers"},{"issue":"3","key":"4_CR25","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1109\/71.674321","volume":"9","author":"J. Lui","year":"1998","unstructured":"Lui, J. Muntz, R. and Towsley, D.: Computing performance bounds of Fork-Join parallel programs under a multiprocessing environment. In: IEEE Transactions on Parallel and Distributed Systems. V9 N3 (1998) 295\u2013311","journal-title":"IEEE Transactions on Parallel and Distributed Systems"},{"key":"4_CR26","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1137\/1031050","volume":"31","author":"C.D. Meyer","year":"1989","unstructured":"Meyer C.D.: Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems. In: SIAM Review. V31 (1989) 240\u2013272.","journal-title":"SIAM Review"},{"key":"4_CR27","doi-asserted-by":"crossref","unstructured":"Pekergin N.: Stochastic delay bounds on fair queueing algorithms. In: Proceedings of INFOCOM\u201999 New York (1999) 1212\u20131220","DOI":"10.1109\/INFCOM.1999.751678"},{"key":"4_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0166-5316(99)00026-7","volume":"36","author":"N. Pekergin","year":"1999","unstructured":"Pekergin N.: Stochastic performance bounds by state reduction. In: Performance Evaluation V36\u201337 (1999) 1\u201317","journal-title":"Performance Evaluation"},{"key":"4_CR29","doi-asserted-by":"crossref","unstructured":"Plateau B.: On the stochastic structure of parallelism and synchronization models for distributed algorithms. In: Proceedings of the SIGMETRICS Conference on Measurement and Modeling of Computer Systems, Texas (1985) 147\u2013154","DOI":"10.1145\/317795.317819"},{"key":"4_CR30","unstructured":"Plateau B., Fourneau J.-M., Lee K.-H.: PEPS: A package for solving complex Markov models of parallel systems. In: Modeling Techniques and Tools for Computer Performance Evaluation, R. Puigjaner, D. Potier (Eds.), Spain (1988) 291\u2013305"},{"key":"4_CR31","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1016\/0743-7315(91)90007-V","volume":"12","author":"B. Plateau","year":"1991","unstructured":"Plateau B., Fourneau J.-M.: A methodology for solving Markov models of parallel systems. In: Journal of Parallel and Distributed Computing. V12 (1991) 370\u2013387.","journal-title":"Journal of Parallel and Distributed Computing"},{"key":"4_CR32","volume-title":"Stochastic Orders and Their Applications","author":"M. Shaked","year":"1994","unstructured":"Shaked M., Shantikumar J.G.: Stochastic Orders and Their Applications. In: Academic Press, California (1994)"},{"key":"4_CR33","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1016\/0377-2217(94)00075-N","volume":"86","author":"W.J. Stewart","year":"1995","unstructured":"Stewart W.J., Atif K., Plateau B.: The numerical solution of stochastic automata networks. In: European Journal of Operational Research V86 (1995) 503\u2013525","journal-title":"European Journal of Operational Research"},{"key":"4_CR34","doi-asserted-by":"crossref","unstructured":"Stewart W. J.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, (1994)","DOI":"10.1515\/9780691223384"},{"key":"4_CR35","volume-title":"Comparison Methods for Queues and Other Stochastic Models","author":"D. Stoyan","year":"1983","unstructured":"Stoyan D.: Comparison Methods for Queues and Other Stochastic Models. John Wiley & Sons, Berlin, Germany, (1983)"},{"key":"4_CR36","doi-asserted-by":"crossref","unstructured":"Truffet L.: Reduction Technique For Discrete Time Markov Chains on Totally Ordered State Space Using Stochastic Comparisons. In: Journal of Applied Probability, V37 N3 (2000)","DOI":"10.1017\/S0021900200016004"},{"key":"4_CR37","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1016\/S0377-2217(97)00215-4","volume":"110","author":"E. Uysal","year":"1998","unstructured":"Uysal E., Dayar T.: Iterative methods based on splittings for stochastic automata networks. In: European Journal of Operational Research, V 110 (1998) 166\u2013186","journal-title":"European Journal of Operational Research"},{"key":"4_CR38","unstructured":"Van Dijk N.: \u201cError bound analysis for queueing networks\u201d In: Performane 96 Tutorials, Lausanne, (1996)"}],"container-title":["Lecture Notes in Computer Science","Performance Evaluation of Complex Systems: Techniques and Tools"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-45798-4_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T20:45:51Z","timestamp":1683924351000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-45798-4_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002]]},"ISBN":["9783540442523","9783540457985"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/3-540-45798-4_4","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2002]]}}}