{"id":"https://openalex.org/W2033688774","doi":"https://doi.org/10.1137/0204046","title":"An Elementary Solution of the Queuing System G/G/1","display_name":"An Elementary Solution of the Queuing System G/G/1","publication_year":1975,"publication_date":"1975-12-01","ids":{"openalex":"https://openalex.org/W2033688774","doi":"https://doi.org/10.1137/0204046","mag":"2033688774"},"language":"en","primary_location":{"id":"doi:10.1137/0204046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0204046","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5007183694","display_name":"Alan G. Konheim","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alan G. Konheim","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007183694"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.23666343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"4","issue":"4","first_page":"540","last_page":"545"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10974","display_name":"Advanced Queuing Theory Analysis","score":0.9857000112533569,"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":0.9857000112533569,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/queueing-theory","display_name":"Queueing theory","score":0.5598009824752808},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5332255959510803},{"id":"https://openalex.org/keywords/queue","display_name":"Queue","score":0.4430139362812042},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.366383820772171},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33726513385772705},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2820872664451599},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07983586192131042}],"concepts":[{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.5598009824752808},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5332255959510803},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.4430139362812042},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.366383820772171},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33726513385772705},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2820872664451599},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07983586192131042},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0204046","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0204046","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W2009054375","https://openalex.org/W2068961333","https://openalex.org/W2103672905"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Previous":[0,168],"article":[1,169],"An":[2,44,530,612],"Elementary":[3],"Solution":[4,698],"of":[5,32,49,52,97,179,195,206,255,259,274,294,307,317,326,342,371,421,432,439,452,463,470,482,509,583,593,615,672,699,718,730,743],"the":[6,29,47,180,318,323,340,359,492,510,562,616,621,642,647,696,716,744],"Queuing":[7,376],"System":[8,377],"G/G/1Alan":[9],"G.":[10,12],"KonheimAlan":[11],"Konheimhttps://doi.org/10.1137/0204046PDFBibTexSections":[13],"ToolsAdd":[14],"to":[15,46,491,561],"favoritesExport":[16],"CitationTrack":[17],"CitationsEmail":[18],"SectionsAboutAbstractIn":[19],"this":[20],"note":[21],"we":[22],"give":[23],"an":[24,239],"elementary":[25],"method":[26],"for":[27,217,250,358,385,533,579,620,690,714,752,776,792],"calculating":[28],"stationary":[30,643],"distribution":[31,178,619,645],"waiting":[33,418,449,617],"time":[34,186,406,419,450,564,577,618,675,750],"in":[35,76,183,272,300,310,322,345,375,521,543,636,646,661],"a":[36,100,154,184,196,232,386,422,428,453,459],"G/G/1":[37,676],"queue.[1]":[38],"Lars":[39],"V.":[40,93],"Ahlfors,":[41],"Complex":[42],"analysis.":[43],"introduction":[45],"theory":[48,96,638],"analytic":[50,613],"functions":[51],"one":[53],"complex":[54,719],"variable,":[55],"McGraw-Hill":[56],"Book":[57],"Company,":[58],"Inc.,":[59],"New":[60,248],"York-Toronto-London,":[61],"1953xii+247":[62],"MR0054016":[63],"0052.07002":[64],"Google":[65,90,144],"Scholar[2]":[66],"J.":[67],"W.":[68],"Cohen,":[69],"The":[70,95,148,177,235,315,417,448,728],"single":[71,101],"server":[72],"queue,":[73,650],"North-Holland":[74,83],"Series":[75],"Applied":[77,440,471,522,544,662,779,795],"Mathematics":[78,796],"and":[79,261,279,296,329,382,393,408,600,654,695,741,778,794],"Mechanics,":[80],"Vol.":[81,190,209,223,244,263,287,333,350,364,399,411,442,473,498,524,546,570,586,606,626,664,679,706,722],"8,":[82],"Publishing":[84],"Co.,":[85],"Amsterdam,":[86],"1969xiv+657":[87],"MR0250389":[88],"0183.49204":[89],"Scholar[3]":[91],"D.":[92],"Lindley,":[94],"queues":[98,407],"with":[99,238,390,425,456,596],"server,":[102],"Proc.":[103],"Cambridge":[104],"Philos":[105],"Soc.,":[106],"48":[107],"(1952),":[108,140],"277\u2013289":[109],"MR0046597":[110],"0046.35501":[111],"CrossrefISIGoogle":[112,166],"Scholar[4]":[113],"F\u00e9lix":[114],"Pollaczek,":[115],"Fonctions":[116],"caract\u00e9ristiques":[117],"de":[118,124],"certaines":[119],"r\u00e9partitions":[120],"d\u00e9finies":[121],"au":[122],"moyen":[123],"la":[125,130],"notion":[126],"d'ordre.":[127],"Application":[128,370],"\u00e0":[129],"th\u00e9orie":[131],"des":[132],"attentes,":[133],"C.":[134],"R.":[135],"Acad.":[136],"Sci.":[137],"Paris,":[138],"234":[139],"2334\u20132336":[141],"MR0047945":[142],"0047.37303":[143],"Scholar[5]":[145],"Frank":[146],"Spitzer,":[147],"Wiener-Hopf":[149],"equation":[150],"whose":[151],"kernel":[152],"is":[153],"probability":[155,534,637],"density,":[156],"Duke":[157],"Math.":[158],"J.,":[159],"24":[160],"(1957),":[161],"327\u2013343":[162],"10.1215/S0012-7094-57-02439-0":[163],"MR0090917":[164],"0082.32003":[165],"Scholar":[167],"FiguresRelatedReferencesCited":[170],"byDetails":[171],"Learning":[172],"Lindley\u2019s":[173],"Recursion":[174],"Cross":[175,192,213,227,246,265,291,304,313,337,354,368,378,403,415,446,477,486,502,528,550,555,574,590,610,630,639,668,683,686,710,726,738,747,755],"Ref":[176,193,214,228,247,266,292,305,314,338,355,369,379,404,416,447,478,487,503,529,551,556,575,591,611,631,640,669,684,687,711,727,739,748,756],"line":[181],"length":[182],"discrete":[185,218,429,460,563,674],"GI\u2215G\u22151":[187],"queuePerformance":[188,624],"Evaluation,":[189,243,332,569,625,678],"131":[191],"Stability":[194],"GI/G/1":[197,328,623],"Queue:":[198],"A":[199,380,488,557],"Survey31":[200],"May":[201],"2018":[202],"|":[203,283,437,468,519,541,659],"Asia-Pacific":[204],"Journal":[205,438,469,582,762],"Operational":[207],"Research,":[208,286],"35,":[210],"No.":[211,225,289,335,352,366,401,413,444,475,500,526,548,572,588,608,628,666,681,708,724],"03":[212,445],"Spitzer\u2019s":[215],"identity":[216],"random":[219,295],"walksOperations":[220],"Research":[221,348,397],"Letters,":[222,349,398,497],"46,":[224],"2":[226,402,414,589,609,629,682,725],"Overland":[229],"flow":[230],"as":[231,427,458],"queueing":[233,346],"process:":[234],"B/D/1":[236],"queue":[237,389,424,455,506,566],"arbitrary":[240],"service":[241,395],"timePerformance":[242],"106":[245],"Approach":[249],"Finding":[251],"Basic":[252],"Performance":[253],"Measures":[254],"Single":[256],"Server":[257],"QueueJournal":[258],"Probability":[260,496],"Statistics,":[262],"2014":[264],"1-D":[267],"steady":[268],"state":[269],"runoff":[270],"production":[271],"light":[273],"queuing":[275,731],"theory:":[276],"Heterogeneity,":[277],"connectivity,":[278],"scale5":[280],"December":[281],"2013":[282],"Water":[284],"Resources":[285],"49,":[288],"12":[290],"Analysis":[293,306,592,742],"burst":[297],"error":[298],"codes":[299],"2-state":[301],"Markov":[302],"channels":[303,312],"packet":[308],"errors":[309],"Gilbert-Elliott":[311],"use":[316],"distributional":[319],"Little\u2019s":[320],"law":[321],"computational":[324],"analysis":[325,420,451,729],"discrete-time":[327,387,423,454,511,622],"GI/D/c":[330],"queuesPerformance":[331],"65,":[334],"1":[336,367,549,649,667],"On":[339,479,504,641],"application":[341],"Rouch\u00e9's":[343],"theorem":[344],"theoryOperations":[347],"34,":[351],"3":[353,476,501,573],"Relaxation":[356],"Time":[357],"Discrete":[360,405],"D/G/1":[361],"QueueQueueing":[362],"Systems,":[363],"50,":[365],"Support":[372],"Vector":[373],"Machine":[374],"complete":[381],"simple":[383],"solution":[384,614],"multi-server":[388],"bulk":[391],"arrivals":[392,426,457],"deterministic":[394],"timesOperations":[396],"31,":[400,499],"matrix-analytic":[409],"methodsTop,":[410],"10,":[412,587],"autoregressive":[430,461],"process":[431,462,599],"order":[433,464],"114":[434,465],"July":[435,466,517,539,657,770],"2016":[436,467,518,540,658],"Probability,":[441,472,523,545,663],"39,":[443,474],"Numerical":[480,697],"Computations":[481],"Some":[483],"Discrete-Time":[484],"Queues":[485],"new":[489],"approach":[490,560],"Lindley":[493],"recursionStatistics":[494],"&":[495,783],"steady-state":[505],"size":[507,567],"distributions":[508,535],"GI":[512],"/":[513],"G":[514],"/1":[515],"queue1":[516],"Advances":[520,542,660],"28,":[525,547],"4":[527],"operational":[531],"calculus":[532],"via":[536],"Laplace":[537],"transforms1":[538],"Analyse":[552],"zeitdiskreter":[553],"Systeme":[554],"polynomial":[558],"factorization":[559],"GI/G/1/(N)":[565],"distributionPerformance":[568],"23,":[571],"Response":[576,749],"calculation":[578,751],"VSAT":[580,753],"networksInternational":[581],"Satellite":[584],"Communications,":[585,605,705],"polling":[594],"systems":[595],"general":[597],"input":[598],"finite":[601],"capacityIEEE":[602],"Transactions":[603,703],"on":[604,693,704,734,763],"40,":[607],"13,":[627],"Chapter":[632],"5":[633],"Computational":[634],"methods":[635,653],"waiting-time":[644],"GI/G/":[648],"I:":[651],"Transform":[652],"almost-phase-type":[655],"distributions1":[656],"19,":[665],"Approximate":[670,712],"characterisation":[671],"nonstationary":[673],"systemsPerformance":[677],"6,":[680],"References":[685],"Skinner's":[688],"Method":[689],"Computing":[691,764],"Bounds":[692],"Distributions":[694],"Continuous-Time":[700],"Queueing":[701],"ProblemsIEEE":[702],"30,":[707],"7":[709],"techniques":[713],"modeling":[715],"performance":[717],"systemsComputer":[720],"Languages,":[721],"4,":[723,758],"system":[732],"based":[733],"support":[735],"vector":[736],"machine":[737],"Simulation":[740],"Crma":[745],"Protocol":[746],"networks":[754],"Volume":[757],"Issue":[759],"4|":[760],"1975SIAM":[761],"History":[765],"Submitted:27":[766],"August":[767],"1974Published":[768],"online:13":[769],"2006":[771],"InformationCopyright":[772],"\u00a9":[773],"1975":[774],"Society":[775],"Industrial":[777,793],"MathematicsPDF":[780],"Download":[781],"Article":[782],"Publication":[784],"DataArticle":[785],"DOI:10.1137/0204046Article":[786],"page":[787],"range:pp.":[788],"540-545ISSN":[789],"(print):0097-5397ISSN":[790],"(online):1095-7111Publisher:Society":[791]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
