{"id":"https://openalex.org/W4385985929","doi":"https://doi.org/10.1007/s10626-022-00373-5","title":"Extending the network calculus algorithmic toolbox for ultimately pseudo-periodic functions: pseudo-inverse and composition","display_name":"Extending the network calculus algorithmic toolbox for ultimately pseudo-periodic functions: pseudo-inverse and composition","publication_year":2023,"publication_date":"2023-08-18","ids":{"openalex":"https://openalex.org/W4385985929","doi":"https://doi.org/10.1007/s10626-022-00373-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10626-022-00373-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10626-022-00373-5","pdf_url":null,"source":{"id":"https://openalex.org/S134484881","display_name":"Discrete Event Dynamic Systems","issn_l":"0924-6703","issn":["0924-6703","1573-7594"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Event Dynamic Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s10626-022-00373-5","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054966862","display_name":"Raffaele Zippo","orcid":"https://orcid.org/0000-0001-9111-7471"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]},{"id":"https://openalex.org/I1300504238","display_name":"Piaggio (Italy)","ror":"https://ror.org/00r254y42","country_code":"IT","type":"company","lineage":["https://openalex.org/I1300504238"]},{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["DE","IT"],"is_corresponding":true,"raw_author_name":"Raffaele Zippo","raw_affiliation_strings":["Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 di Firenze, Via di S. Marta 3, Firenze, 50139, Italy","Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 di Pisa, Largo Lucio Lazzarino 1, Pisa, 56122, Italy","Distributed Computer Systems Lab (DISCO), TU Kaiserslautern, Paul-Ehrlich-Stra\u00dfe 34, Kaiserslautern, 67663, Germany","Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 di Pisa, Pisa, Italy","Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 di Firenze, Firenze, Italy","Distributed Computer Systems Lab (DISCO), TU Kaiserslautern, Kaiserslautern, Germany"],"raw_orcid":"https://orcid.org/0000-0001-9111-7471","affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 di Firenze, Via di S. Marta 3, Firenze, 50139, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 di Pisa, Largo Lucio Lazzarino 1, Pisa, 56122, Italy","institution_ids":["https://openalex.org/I1300504238","https://openalex.org/I108290504"]},{"raw_affiliation_string":"Distributed Computer Systems Lab (DISCO), TU Kaiserslautern, Paul-Ehrlich-Stra\u00dfe 34, Kaiserslautern, 67663, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 di Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]},{"raw_affiliation_string":"Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 di Firenze, Firenze, Italy","institution_ids":["https://openalex.org/I45084792"]},{"raw_affiliation_string":"Distributed Computer Systems Lab (DISCO), TU Kaiserslautern, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038842699","display_name":"Paul Nikolaus","orcid":"https://orcid.org/0000-0001-5277-0267"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Paul Nikolaus","raw_affiliation_strings":["Distributed Computer Systems Lab (DISCO), TU Kaiserslautern, Paul-Ehrlich-Stra\u00dfe 34, Kaiserslautern, 67663, Germany","Distributed Computer Systems Lab (DISCO), TU Kaiserslautern, Kaiserslautern, Germany"],"raw_orcid":"https://orcid.org/0000-0001-5277-0267","affiliations":[{"raw_affiliation_string":"Distributed Computer Systems Lab (DISCO), TU Kaiserslautern, Paul-Ehrlich-Stra\u00dfe 34, Kaiserslautern, 67663, Germany","institution_ids":["https://openalex.org/I153267046"]},{"raw_affiliation_string":"Distributed Computer Systems Lab (DISCO), TU Kaiserslautern, Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008205801","display_name":"Giovanni Stea","orcid":"https://orcid.org/0000-0001-5310-6763"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]},{"id":"https://openalex.org/I1300504238","display_name":"Piaggio (Italy)","ror":"https://ror.org/00r254y42","country_code":"IT","type":"company","lineage":["https://openalex.org/I1300504238"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giovanni Stea","raw_affiliation_strings":["Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 di Pisa, Largo Lucio Lazzarino 1, Pisa, 56122, Italy","Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 di Pisa, Pisa, Italy"],"raw_orcid":"https://orcid.org/0000-0001-5310-6763","affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 di Pisa, Largo Lucio Lazzarino 1, Pisa, 56122, Italy","institution_ids":["https://openalex.org/I1300504238","https://openalex.org/I108290504"]},{"raw_affiliation_string":"Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 di Pisa, Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054966862"],"corresponding_institution_ids":["https://openalex.org/I108290504","https://openalex.org/I1300504238","https://openalex.org/I153267046","https://openalex.org/I45084792"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.3935,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61403722,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"33","issue":"3","first_page":"181","last_page":"219"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10138","display_name":"Network Traffic and Congestion Control","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10138","display_name":"Network Traffic and Congestion Control","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10847","display_name":"Advanced Optical Network Technologies","score":0.9919000267982483,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/network-calculus","display_name":"Network calculus","score":0.6621748208999634},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5653852224349976},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.473186731338501},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.47082096338272095},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4682294726371765},{"id":"https://openalex.org/keywords/tree-traversal","display_name":"Tree traversal","score":0.46420058608055115},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44818827509880066},{"id":"https://openalex.org/keywords/operand","display_name":"Operand","score":0.41478657722473145},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3899902105331421},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36604493856430054}],"concepts":[{"id":"https://openalex.org/C2778693205","wikidata":"https://www.wikidata.org/wiki/Q7000967","display_name":"Network calculus","level":3,"score":0.6621748208999634},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5653852224349976},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.473186731338501},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.47082096338272095},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4682294726371765},{"id":"https://openalex.org/C140745168","wikidata":"https://www.wikidata.org/wiki/Q1210082","display_name":"Tree traversal","level":2,"score":0.46420058608055115},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44818827509880066},{"id":"https://openalex.org/C55526617","wikidata":"https://www.wikidata.org/wiki/Q719375","display_name":"Operand","level":2,"score":0.41478657722473145},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3899902105331421},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36604493856430054},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C5119721","wikidata":"https://www.wikidata.org/wiki/Q220501","display_name":"Quality of service","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10626-022-00373-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10626-022-00373-5","pdf_url":null,"source":{"id":"https://openalex.org/S134484881","display_name":"Discrete Event Dynamic Systems","issn_l":"0924-6703","issn":["0924-6703","1573-7594"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Event Dynamic Systems","raw_type":"journal-article"},{"id":"pmh:oai:arpi.unipi.it:11568/1161648","is_oa":true,"landing_page_url":"https://link.springer.com/article/10.1007/s10626-022-00373-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10626-022-00373-5.pdf","source":{"id":"https://openalex.org/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https://openalex.org/I108290504"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10626-022-00373-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10626-022-00373-5","pdf_url":null,"source":{"id":"https://openalex.org/S134484881","display_name":"Discrete Event Dynamic Systems","issn_l":"0924-6703","issn":["0924-6703","1573-7594"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Event Dynamic Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8175194624","display_name":null,"funder_award_id":"PRA 2020","funder_id":"https://openalex.org/F4320324499","funder_display_name":"Universit\u00e0 di Pisa"}],"funders":[{"id":"https://openalex.org/F4320317295","display_name":"Dipartimenti di Eccellenza","ror":null},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320322648","display_name":"Universit\u00e0 degli Studi di Firenze","ror":"https://ror.org/04jr1s763"},{"id":"https://openalex.org/F4320324499","display_name":"Universit\u00e0 di Pisa","ror":"https://ror.org/03ad39j10"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1541262242","https://openalex.org/W1986632072","https://openalex.org/W1986730974","https://openalex.org/W1997922019","https://openalex.org/W2053693415","https://openalex.org/W2096686215","https://openalex.org/W2101112998","https://openalex.org/W2144656204","https://openalex.org/W2155303087","https://openalex.org/W2157074735","https://openalex.org/W2169256552","https://openalex.org/W2171067922","https://openalex.org/W2271586634","https://openalex.org/W2761066510","https://openalex.org/W2898323738","https://openalex.org/W2944570273","https://openalex.org/W2980526088","https://openalex.org/W2995538827","https://openalex.org/W3012189484","https://openalex.org/W3037498081","https://openalex.org/W3045851897","https://openalex.org/W3086774734","https://openalex.org/W3089243972","https://openalex.org/W3143519999","https://openalex.org/W3180067238","https://openalex.org/W3184118166","https://openalex.org/W4206809386","https://openalex.org/W4237072601","https://openalex.org/W4247726752","https://openalex.org/W4251791868","https://openalex.org/W4293200732","https://openalex.org/W4321608564","https://openalex.org/W4379382675"],"related_works":["https://openalex.org/W2556282987","https://openalex.org/W1533508804","https://openalex.org/W2136735429","https://openalex.org/W170547082","https://openalex.org/W2587876411","https://openalex.org/W2358332176","https://openalex.org/W1970370079","https://openalex.org/W2050923821","https://openalex.org/W55831818","https://openalex.org/W2090270863"],"abstract_inverted_index":{"Abstract":[0],"Network":[1],"Calculus":[2],"(NC)":[3],"is":[4],"an":[5,155],"algebraic":[6,156],"theory":[7],"that":[8,109,151],"represents":[9],"traffic":[10,45],"and":[11,68,102,121,148],"service":[12],"guarantees":[13,25],"as":[14,94,114],"curves":[15,117],"in":[16,20,134],"a":[17,29],"Cartesian":[18],"plane,":[19],"order":[21],"to":[22,41,63,104],"compute":[23,64],"performance":[24],"for":[26,70,77,173,188],"flows":[27],"traversing":[28],"network.":[30],"NC":[31,100,111,135],"uses":[32],"transformation":[33],"operations,":[34,55,139,197],"e.g.,":[35],"min-plus":[36],"convolution":[37],"of":[38,51,85,128,138,195,201],"two":[39],"curves,":[40,181],"model":[42],"how":[43],"the":[44,49,75,83,98,141,174,184,192],"profile":[46],"changes":[47],"with":[48],"traversal":[50],"network":[52],"nodes.":[53],"Such":[54],"while":[56],"mathematically":[57],"well-defined,":[58],"can":[59],"quickly":[60],"become":[61],"unmanageable":[62],"using":[65],"simple":[66],"pen":[67],"paper":[69],"any":[71],"non-trivial":[72],"case,":[73],"hence":[74],"need":[76],"algorithmic":[78,160,186,193],"descriptions.":[79],"Previous":[80],"work":[81],"identified":[82],"class":[84],"piecewise":[86],"affine":[87],"functions":[88],"which":[89],"are":[90,152,179],"ultimately":[91],"pseudo-periodic":[92],"(UPP)":[93],"being":[95],"closed":[96],"under":[97],"main":[99],"operations":[101,112,176],"able":[103],"be":[105],"described":[106],"finitely.":[107],"Algorithms":[108],"embody":[110],"taking":[113],"operands":[115,178],"UPP":[116,180],"have":[118,162],"been":[119,164],"defined":[120],"proved":[122],"correct,":[123],"thus":[124,182],"enabling":[125],"software":[126],"implementations":[127],"these":[129,196],"operations.":[130],"However,":[131],"recent":[132],"advancements":[133],"make":[136],"use":[137],"namely":[140],"lower":[142],"pseudo-inverse":[143,146],",":[144,147,150],"upper":[145],"composition":[149],"well-defined":[153],"from":[154],"standpoint,":[157],"but":[158],"whose":[159],"aspects":[161],"not":[163],"addressed":[165],"yet.":[166],"In":[167],"this":[168],"paper,":[169],"we":[170],"introduce":[171],"algorithms":[172],"above":[175],"when":[177],"extending":[183],"available":[185],"toolbox":[187],"NC.":[189],"We":[190],"discuss":[191],"properties":[194],"providing":[198],"formal":[199],"proofs":[200],"correctness.":[202]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-01-04T23:08:39.989793","created_date":"2025-10-10T00:00:00"}
