{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T17:18:59Z","timestamp":1771003139494,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1991,5,1]],"date-time":"1991-05-01T00:00:00Z","timestamp":673056000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Event Dyn Syst"],"published-print":{"date-parts":[[1991,5]]},"DOI":"10.1007\/bf01797141","type":"journal-article","created":{"date-parts":[[2005,6,20]],"date-time":"2005-06-20T23:20:37Z","timestamp":1119309637000},"page":"7-35","source":"Crossref","is-referenced-by-count":27,"title":["Algebraic structure of some stochastic discrete event systems, with applications"],"prefix":"10.1007","volume":"1","author":[{"given":"Paul","family":"Glasserman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David D.","family":"Yao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF01797141_CR1","doi-asserted-by":"crossref","unstructured":"F. Baccelli, \u201cErgodic theory of stochastic decision free Petri nets,\u201d inProc. 28th IEEE Conf. Decision and Control, 1989, pp. 1521\u20141527. (Extended version to appear inAnn. Probab.)","DOI":"10.1109\/CDC.1989.70402"},{"key":"BF01797141_CR2","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1109\/5.21076","volume":"77","author":"F. Baccelli","year":"1989","unstructured":"F. Baccelli and A. M. Makowski, \u201cQueueing models for systems with synchronization constraints,\u201dProc. IEEE, Vol. 77, pp. 138\u2013161, 1989.","journal-title":"Proc. IEEE"},{"key":"BF01797141_CR3","series-title":"Colloq. Math. Soc. J. Bolyai","first-page":"25","volume-title":"Matroid Theory and Its Applications","author":"A. Bj\u00f6rner","year":"1985","unstructured":"A. Bj\u00f6rner \u201cOn matroids, groups, and exchange languages,\u201d inMatroid Theory and Its Applications (eds. L. Lov\u00e1sz and A. Rechksi), Colloq. Math. Soc. J. Bolyai 40, North-Holland: Amsterdam, 1985; pp. 25\u201360."},{"key":"BF01797141_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-0167-7","volume-title":"A Guide to Simulation","author":"P. Bratley","year":"1983","unstructured":"P. Bratley, B. L. Fox, and L. E. Schrage,A Guide to Simulation, Springer-Verlag: New York, 1983."},{"key":"BF01797141_CR5","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1109\/5.21070","volume":"77","author":"C. G. Cassandras","year":"1989","unstructured":"C. G. Cassandras and S. G. Strickland, \u201cSample path properties of timed discrete event systems,\u201dProc. IEEE, Vol. 77, pp. 59\u201371, 1989.","journal-title":"Proc. IEEE"},{"key":"BF01797141_CR6","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.4153\/CJM-1974-126-1","volume":"26","author":"K. M. Chong","year":"1974","unstructured":"K. M. Chong, \u201cSome extensions of a theorem of Hardy, Littlewood and Polya and their applications,\u201dCanad. J. Math., Vol. 26, pp. 1321\u20131340, 1974.","journal-title":"Canad. J. Math."},{"key":"BF01797141_CR7","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/5.21069","volume":"77","author":"G. Cohen","year":"1989","unstructured":"G. Cohen, P. Moller, J.-P., Quadrat, and M. Viot, \u201cAlgebraic tools for the performance analysis of discrete event systems,Proc. IEEE, Vol. 77, pp. 39\u201358, 1989.","journal-title":"Proc. IEEE"},{"key":"BF01797141_CR8","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/S0019-9958(77)90558-7","volume":"33","author":"S. Crespi-Reghizzi","year":"1977","unstructured":"S. Crespi-Reghizzi, \u201cPetri nets and Szilard languages,\u201dInform. Control, Vol. 33, pp. 177\u2013192, 1977.","journal-title":"Inform. Control"},{"key":"BF01797141_CR9","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/0020-0190(75)90020-4","volume":"3","author":"S. Crespi-Reghizzi","year":"1975","unstructured":"S. Crespi-Reghizzi and D. Mandrioli, \u201cA decidability theorem for a class of vector-addition systems,\u201dInform. Process. Lett., Vol. 3, pp. 78\u201380, 1975.","journal-title":"Inform. Process. Lett."},{"key":"BF01797141_CR10","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/0012-365X(89)90180-5","volume":"78","author":"B. L. Dietrich","year":"1989","unstructured":"B. L. Dietrich, \u201cMatroids and antimatroids\u2014a survey,\u201dDiscrete Math., Vol. 78, pp. 223\u2013237, 1989.","journal-title":"Discrete Math."},{"key":"BF01797141_CR11","unstructured":"P. Glasserman, \u201cStructural conditions for perturbation analysis derivative estimation: Finite-time performance indices, 1989,Operations Research, Forthcoming."},{"key":"BF01797141_CR12","unstructured":"P. Glasserman and D. D. Yao, \u201cMonotonicity in generalized semi-Markov processes,\u201d 1989,Math. of Oper. Res., forthcoming."},{"key":"BF01797141_CR13","unstructured":"P. Glasserman and D. D. Yao, \u201cGeneralized semi-Markov processes: Antimatroid structure and second-order properties, 1990,Math. Oper. Res., forthcoming."},{"key":"BF01797141_CR14","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/5.21067","volume":"77","author":"P. W. Glynn","year":"1989","unstructured":"P. W. Glynn, \u201cA GSMP formalism for discrete event systems,\u201dProc. IEEE, Vol. 77, pp. 14\u201323, 1989.","journal-title":"Proc. IEEE"},{"key":"BF01797141_CR15","doi-asserted-by":"crossref","unstructured":"A. G. Greenberg, G. D. Lubachevsky, and I. Mitrani, \u201cUnboundedly parallel simulations via recurrence relations,\u201dSigmetrics '90, Boulder, CO, 1990.ACM Trans. Comput. Syst., forthcoming.","DOI":"10.1145\/98457.98492"},{"key":"BF01797141_CR16","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1017\/S0269964800000152","volume":"2","author":"P. J. Haas","year":"1988","unstructured":"P. J. Haas and G. S. Schedler, \u201cModeling power of stochastic Petri nets,\u201dProbab. Eng. Inform. Sci., Vol. 2, pp. 435\u2013459, 1988.","journal-title":"Probab. Eng. Inform. Sci."},{"key":"BF01797141_CR17","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1109\/TAC.1987.1104665","volume":"32","author":"Y. C. Ho","year":"1987","unstructured":"Y. C. Ho, \u201cPerformance evaluation and perturbation analysis of discrete event dynamic systems: Perspectives and open problems,\u201dIEEE Trans. Automat. Control, Vol. AC-32, pp. 563\u2013572, 1987.","journal-title":"IEEE Trans. Automat. Control"},{"key":"BF01797141_CR18","unstructured":"J. Q. Hu, \u201cConvexity of sample path performances and strong consistency of infinitesimal perturbation analysis estimates,\u201dIEEE Trans. Automat. Control, July, 1991, forthcoming."},{"key":"BF01797141_CR19","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/S0022-0000(69)80011-5","volume":"3","author":"M. R. Karp","year":"1969","unstructured":"M. R. Karp and R. E. Miller, \u201cParallel program schemata,\u201dJ. Comput. Syst. Sci., Vol. 3, pp. 147\u2013195; 1969.","journal-title":"J. Comput. Syst. Sci."},{"key":"BF01797141_CR20","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1145\/322217.322232","volume":"27","author":"R. E. Ladner","year":"1980","unstructured":"R. E. Ladner and M. J. Fischer, \u201cParallel prefix computation,\u201dJ. ACM, Vol. 27, pp. 831\u2013838, 1980.","journal-title":"J. ACM"},{"key":"BF01797141_CR21","doi-asserted-by":"crossref","unstructured":"F. Lin and D. D. Yao, \u201cGeneralized semi-Markov processes: A view through supervisory control,Proc. 28th IEEE Conf. Decision and Control, 1989, pp. 1075\u20131076.","DOI":"10.1109\/CDC.1989.70297"},{"key":"BF01797141_CR22","doi-asserted-by":"crossref","first-page":"176","DOI":"10.2307\/2307574","volume":"60","author":"G. G. Lorentz","year":"1953","unstructured":"G. G. Lorentz, \u201cAn inequality for rearrangements,\u201dAmer. Math. Monthly, Vol. 60, pp. 176\u2013179, 1953.","journal-title":"Amer. Math. Monthly"},{"key":"BF01797141_CR23","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1145\/321356.321364","volume":"13","author":"R. Parikh","year":"1966","unstructured":"R. Parikh, \u201cOn context-free languages,\u201dJ. ACM, Vol. 13, pp. 570\u2013581, 1966.","journal-title":"J. ACM"},{"key":"BF01797141_CR24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0022-0000(76)80047-5","volume":"13","author":"J. L. Peterson","year":"1976","unstructured":"J. L. Peterson, \u201cComputation sequence sets,\u201dJ. Comput. Syst. Sci., Vol. 13, pp. 1\u201324, 1976.","journal-title":"J. Comput. Syst. Sci."},{"key":"BF01797141_CR25","volume-title":"Petri Net Theory and the Modeling of Systems","author":"J. L. Peterson","year":"1981","unstructured":"J. L. Peterson,Petri Net Theory and the Modeling of Systems, Prentice-Hall: Englewood Cliffs, NJ, 1981."},{"key":"BF01797141_CR26","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1137\/0325013","volume":"25","author":"P. J. Ramadge","year":"1987","unstructured":"P. J. Ramadge and W. M. Wonham, \u201cSupervisory control of a class of discrete-event processes,\u201dSIAM J. Control Optim., Vol. 25, pp. 206\u2013230, 1987.","journal-title":"SIAM J. Control Optim."},{"key":"BF01797141_CR27","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1109\/TSE.1980.230492","volume":"6","author":"C. V. Ramamoorthy","year":"1980","unstructured":"C. V. Ramamoorthy and G. S. Ho, \u201cPerformance evaluation of asynchronous concurrent systems using Petri nets,\u201dIEEE Trans. Software Eng., Vol. SE-6, pp. 440\u2013449, 1980.","journal-title":"IEEE Trans. Software Eng."},{"key":"BF01797141_CR28","volume-title":"Stochastic Processes","author":"S. M. Ross","year":"1983","unstructured":"S. M. Ross,Stochastic Processes, Wiley: New York, 1983."},{"key":"BF01797141_CR29","volume-title":"Real Analysis","author":"H. L. Royden","year":"1968","unstructured":"H. L. Royden,Real Analysis, Macmillan: New York, 1968."},{"key":"BF01797141_CR30","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/BF02056901","volume":"30","author":"L. R\u00fcschendorf","year":"1983","unstructured":"L. R\u00fcschendorf, \u201cSolution of a statistical optimization problem by rearrangement methods,\u201dMetrika, Vol. 30, pp. 55\u201361, 1983.","journal-title":"Metrika"},{"key":"BF01797141_CR31","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1287\/moor.1.4.395","volume":"1","author":"R. Schassberger","year":"1976","unstructured":"R. Schassberger, \u201cOn the equilibrium distribution of a class of finite-state generalized semi-Markov processes,\u201dMath. Oper. Res., Vol. 1, pp. 395\u2013406, 1976.","journal-title":"Math. Oper. Res."},{"key":"BF01797141_CR32","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1214\/aop\/1176995893","volume":"5","author":"R. Schassberger","year":"1978","unstructured":"R. Schassberger, \u201cInsensitivity of steady-state distributions of generalized semi-Markov processes,\u201dAnn. Probab., Vol. 5, pp. 87\u201399, 1978.","journal-title":"Ann. Probab."},{"key":"BF01797141_CR33","doi-asserted-by":"crossref","unstructured":"J. G. Shanthikumar and D. D. Yao, \u201cSecond-order stochastic properties in queueing systems,Proc. IEEE, Vol. 77, pp. 162\u2013170.","DOI":"10.1109\/5.21077"},{"key":"BF01797141_CR34","unstructured":"P. W. Shor, A. Bj\u00f6rner, and L. Lov\u00e1sz, \u201cChip-firing games on graphs,\u201dEuro. J. Combin., 1988, forthcoming."},{"key":"BF01797141_CR35","doi-asserted-by":"crossref","unstructured":"R. Suri, \u201cPerturbation analysis: The state of the art and research issues explained via the GI\/G\/1 queue,\u201dProc. IEEE, Vol. 77, pp. 114\u2013137.","DOI":"10.1109\/5.21075"},{"key":"BF01797141_CR36","doi-asserted-by":"crossref","unstructured":"P. Tsoucas and J. Walrand, \u201cMonotonicity of throughput in non-Markovian networks,\u201dJ. Appl. Probab., Vol. 26, pp. 134\u2013141.","DOI":"10.2307\/3214323"},{"key":"BF01797141_CR37","doi-asserted-by":"crossref","unstructured":"W. Whitt, \u201cContinuity of generalized semi-Markov processes,\u201dMath. Oper. Res., Vol. 5, pp. 494\u2013501.","DOI":"10.1287\/moor.5.4.494"}],"container-title":["Discrete Event Dynamic Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01797141.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF01797141\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF01797141","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T21:11:11Z","timestamp":1735765871000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF01797141"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,5]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1991,5]]}},"alternative-id":["BF01797141"],"URL":"https:\/\/doi.org\/10.1007\/bf01797141","relation":{},"ISSN":["0924-6703","1573-7594"],"issn-type":[{"value":"0924-6703","type":"print"},{"value":"1573-7594","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,5]]}}}