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We explain how the equivalences we propose can be used to reduce transition systems of expressions, and demonstrate how to apply the equivalences to compare the stationary behaviour. The equivalences guarantee a coincidence of performance indices for stochastic systems, and can be used for performance analysis simplification. We use a case study to outline a method of modelling, performance evaluation and behaviour preserving reduction of concurrent computing systems, and apply it to the dining philosophers system.<\/jats:p>","DOI":"10.1017\/s0960129513000029","type":"journal-article","created":{"date-parts":[[2013,5,14]],"date-time":"2013-05-14T13:40:42Z","timestamp":1368538842000},"source":"Crossref","is-referenced-by-count":2,"title":["Equivalence relations for modular performance evaluation in dtsPBC"],"prefix":"10.1017","volume":"24","author":[{"given":"IGOR V.","family":"TARASYUK","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2013,5,14]]},"reference":[{"key":"S0960129513000029_ref46","volume-title":"Petri net theory and modeling of systems","author":"Peterson","year":"1981"},{"key":"S0960129513000029_ref44","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-31862-0_32"},{"key":"S0960129513000029_ref21","first-page":"51","volume-title":"Arbeitsberichte des IMMD","author":"Hillston","year":"1994"},{"key":"S0960129513000029_ref53","volume-title":"Technical Report DIAB-10-03-1","author":"Tarasyuk","year":"2010"},{"key":"S0960129513000029_ref6","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1998.2706"},{"key":"S0960129513000029_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.peva.2011.11.002"},{"key":"S0960129513000029_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-60029-9_29"},{"key":"S0960129513000029_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04457-5"},{"key":"S0960129513000029_ref52","volume-title":"Berichte aus dem Department f\u00fcr Informatik","author":"Tarasyuk","year":"2008"},{"key":"S0960129513000029_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(03)00343-0"},{"key":"S0960129513000029_ref47","first-page":"41","volume-title":"Proceedings of 4th International Workshop on Process Algebra and Performance Modelling (PAPM)","author":"Priami","year":"1996"},{"key":"S0960129513000029_ref30","doi-asserted-by":"publisher","DOI":"10.1007\/11817963_23"},{"key":"S0960129513000029_ref41","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(92)90008-4"},{"key":"S0960129513000029_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.peva.2010.04.001"},{"key":"S0960129513000029_ref49","volume-title":"Berichte aus dem Department f\u00fcr Informatik","author":"Tarasyuk","year":"2005"},{"key":"S0960129513000029_ref40","volume-title":"Communication and concurrency","author":"Milner","year":"1989"},{"key":"S0960129513000029_ref1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9574.00139"},{"key":"S0960129513000029_ref39","doi-asserted-by":"publisher","DOI":"10.1109\/TCOM.1976.1093424"},{"key":"S0960129513000029_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.peva.2010.09.002"},{"key":"S0960129513000029_ref15","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-69108-1_13"},{"key":"S0960129513000029_ref19","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1995.1123"},{"key":"S0960129513000029_ref42","unstructured":"Molloy M. 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