{"id":"https://openalex.org/W2067687151","doi":"https://doi.org/10.1142/s0129626411000035","title":"A PRODUCT FORM SOLUTION FOR TREE NETWORKS WITH DIVISIBLE LOADS","display_name":"A PRODUCT FORM SOLUTION FOR TREE NETWORKS WITH DIVISIBLE LOADS","publication_year":2011,"publication_date":"2011-03-01","ids":{"openalex":"https://openalex.org/W2067687151","doi":"https://doi.org/10.1142/s0129626411000035","mag":"2067687151"},"language":"en","primary_location":{"id":"doi:10.1142/s0129626411000035","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129626411000035","pdf_url":null,"source":{"id":"https://openalex.org/S18360026","display_name":"Parallel Processing Letters","issn_l":"0129-6264","issn":["0129-6264","1793-642X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066801270","display_name":"Thomas G. Robertazzi","orcid":"https://orcid.org/0000-0002-2382-1843"},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"THOMAS G. ROBERTAZZI","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY 11794, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY 11794, USA","institution_ids":["https://openalex.org/I59553526"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066801270"],"corresponding_institution_ids":["https://openalex.org/I59553526"],"apc_list":null,"apc_paid":null,"fwci":1.5697,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.85105084,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"21","issue":"01","first_page":"13","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9908999800682068,"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/T10772","display_name":"Distributed systems and fault tolerance","score":0.9879000186920166,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6423989534378052},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.6306933760643005},{"id":"https://openalex.org/keywords/queueing-theory","display_name":"Queueing theory","score":0.5765135288238525},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.5565297603607178},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5108456015586853},{"id":"https://openalex.org/keywords/closed-form-expression","display_name":"Closed-form expression","score":0.49980664253234863},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.45016464591026306},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.43287187814712524},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3756711483001709},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27715209126472473},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2319360375404358},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1581571102142334},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.1065572202205658}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6423989534378052},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.6306933760643005},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.5765135288238525},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.5565297603607178},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5108456015586853},{"id":"https://openalex.org/C4530962","wikidata":"https://www.wikidata.org/wiki/Q777407","display_name":"Closed-form expression","level":2,"score":0.49980664253234863},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.45016464591026306},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.43287187814712524},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3756711483001709},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27715209126472473},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2319360375404358},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1581571102142334},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.1065572202205658},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129626411000035","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129626411000035","pdf_url":null,"source":{"id":"https://openalex.org/S18360026","display_name":"Parallel Processing Letters","issn_l":"0129-6264","issn":["0129-6264","1793-642X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W98859305","https://openalex.org/W160112449","https://openalex.org/W1491464987","https://openalex.org/W1501013319","https://openalex.org/W1566928164","https://openalex.org/W1944519314","https://openalex.org/W1972428513","https://openalex.org/W1978006658","https://openalex.org/W1983347794","https://openalex.org/W2006999214","https://openalex.org/W2029707805","https://openalex.org/W2036894611","https://openalex.org/W2060840612","https://openalex.org/W2060964575","https://openalex.org/W2077095314","https://openalex.org/W2094055697","https://openalex.org/W2104669157","https://openalex.org/W2115525458","https://openalex.org/W2120360181","https://openalex.org/W2141455535","https://openalex.org/W2141491381","https://openalex.org/W2146402319","https://openalex.org/W2610334247"],"related_works":["https://openalex.org/W1833210188","https://openalex.org/W2583394830","https://openalex.org/W2053854390","https://openalex.org/W2997221951","https://openalex.org/W2546696010","https://openalex.org/W1992741870","https://openalex.org/W3174582865","https://openalex.org/W2290643187","https://openalex.org/W1882733036","https://openalex.org/W1969740176"],"abstract_inverted_index":{"A":[0],"product":[1,42,58],"form":[2,43,59],"solution":[3,37,44,60],"for":[4,45,67],"the":[5,27,41],"optimal":[6],"fractions":[7],"of":[8,33,56],"divisible":[9,68],"load":[10,28,69],"to":[11,13,40],"distribute":[12],"processors":[14],"in":[15,29,50],"a":[16,30,62],"multi-level":[17],"tree":[18],"network":[19],"is":[20,38],"described.":[21],"Here":[22],"optimality":[23],"involves":[24],"parallel":[25],"processing":[26],"minimal":[31],"amount":[32],"time.":[34],"This":[35],"tractable":[36],"similar":[39],"equilibrium":[46],"state":[47],"probabilities":[48],"arising":[49],"Markovian":[51],"queueing":[52],"networks.":[53],"The":[54],"existence":[55],"this":[57],"answers":[61],"long":[63],"standing":[64],"open":[65],"question":[66],"scheduling.":[70]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}