{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T15:26:13Z","timestamp":1761924373395,"version":"build-2065373602"},"reference-count":41,"publisher":"Elsevier BV","issue":"3","license":[{"start":{"date-parts":[[1995,9,1]],"date-time":"1995-09-01T00:00:00Z","timestamp":809913600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Performance Evaluation"],"published-print":{"date-parts":[[1995,9]]},"DOI":"10.1016\/0166-5316(94)00024-e","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T13:16:45Z","timestamp":1027603005000},"page":"217-240","source":"Crossref","is-referenced-by-count":14,"title":["A polynomial factorization approach to the discrete time GI\/G\/1\/(N) queue size distribution"],"prefix":"10.1016","volume":"23","author":[{"given":"Gerhard","family":"Ha\u03b2linger","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/0166-5316(94)00024-E_BIB1","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1109\/TCOM.1980.1094582","article-title":"Computing the Waiting Time Distribution for the G\/G\/1 Queue by Signal Processing Methods","volume":"28","author":"Ackroyd","year":"1980","journal-title":"IEEE Trans. Com."},{"key":"10.1016\/0166-5316(94)00024-E_BIB2","doi-asserted-by":"crossref","first-page":"189","DOI":"10.2307\/3214330","article-title":"Time Series Formed from the Superposition of Discrete Renewal Processes","volume":"26","author":"Blight","year":"1989","journal-title":"J. Appl. Prob."},{"key":"10.1016\/0166-5316(94)00024-E_BIB3","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/BF01159088","article-title":"Steady-State Probabilities of the PH\/PH\/1 Queue","volume":"3","author":"Le Boudee","year":"1988","journal-title":"Queueing Systems"},{"key":"10.1016\/0166-5316(94)00024-E_BIB4","first-page":"1","article-title":"Approximation von Verteilungsfunktionen","volume":"9","author":"Bux","year":"1977"},{"key":"10.1016\/0166-5316(94)00024-E_BIB5","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BF01158522","article-title":"Exact and Approximate Numerical Solutions of Steady-State Distributions Arising in the Queue GI\/G\/1","volume":"10","author":"Chaudhry","year":"1992","journal-title":"Queueing Systems"},{"key":"10.1016\/0166-5316(94)00024-E_BIB6","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1287\/ijoc.2.3.273","article-title":"Robustness of Rootfinding in Single-Server Queueing Models","volume":"2","author":"Chaudhry","year":"1990","journal-title":"ORSA J. Comput."},{"key":"10.1016\/0166-5316(94)00024-E_BIB7","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/BF02187099","article-title":"Numerial Analysis for Bulk-Arrival Queueing Systems: Root-Finding and Steady-State Probabilities in GI'\/M\/1-Queues","volume":"8","author":"Chaudhry","year":"1987","journal-title":"Ann. Op. Res."},{"key":"10.1016\/0166-5316(94)00024-E_BIB8","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/BF02241861","article-title":"Complexity Analysis of a Process for Simultaneously Obtaining all Zeros of Polynomials","volume":"43","author":"Deren","year":"1989","journal-title":"Computing"},{"key":"10.1016\/0166-5316(94)00024-E_BIB9","series-title":"Stochastic Analysis of Computer and Communication Systems","first-page":"217","article-title":"Single Server Queues with Vacations","author":"Doshi","year":"1990"},{"key":"10.1016\/0166-5316(94)00024-E_BIB10","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1057\/palgrave.jors.0390210","article-title":"An Application of Little's Result to the G\/G\/1 (LCFS\/P) Queue","volume":"39","author":"Fakinos","year":"1988","journal-title":"J. Op. Res. Soc."},{"volume":"Vol. 2","year":"1971","author":"Feller","key":"10.1016\/0166-5316(94)00024-E_BIB11"},{"key":"10.1016\/0166-5316(94)00024-E_BIB12","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/0166-5316(92)90011-5","article-title":"Approximations for the per-class Waiting Time and Interdeparture Time in the \u03f5 GI\/GI\/1 Queue","volume":"14","author":"Fischer","year":"1992","journal-title":"Performance Evaluation"},{"key":"10.1016\/0166-5316(94)00024-E_BIB13","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1287\/opre.37.1.141","article-title":"Numerical Solution of the Waiting Time Distribution and Idle Time Distribution of the Arithmetic GI\/G\/1 Queue","volume":"37","author":"Grassmann","year":"1989","journal-title":"Op. Res."},{"key":"10.1016\/0166-5316(94)00024-E_BIB14","series-title":"Proc. of the MMB-Conference","first-page":"15","article-title":"Analysis of Open Queueing Networks with Discrete Time Renewal Processes (in German)","volume":"286","author":"Ha\u03b2linger","year":"1991"},{"volume":"Vol. 1","year":"1974","author":"Henrici","key":"10.1016\/0166-5316(94)00024-E_BIB15"},{"key":"10.1016\/0166-5316(94)00024-E_BIB16","doi-asserted-by":"crossref","first-page":"790","DOI":"10.2307\/3214016","article-title":"Oscillating Random Walk Models for GI\/G\/1 Vacation Systems with Bernoulli Schedules","volume":"23","author":"Keilson","year":"1986","journal-title":"J. Appl. Prob."},{"key":"10.1016\/0166-5316(94)00024-E_BIB17","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1080\/02331938508843018","article-title":"An Analytical Interpretation of the Discrete Approximation for the GI\/GI\/1 Queue","volume":"16","author":"Kimura","year":"1985","journal-title":"Optimazation"},{"key":"10.1016\/0166-5316(94)00024-E_BIB18","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1111\/j.2517-6161.1970.tb00819.x","article-title":"Inequalities in the Theory of Queues","author":"Kingman","year":"1970","journal-title":"J. Roy. Statist. Soc. Ser. B"},{"volume":"Vol. 1\/2","year":"1975","author":"Kleinrock","key":"10.1016\/0166-5316(94)00024-E_BIB19"},{"key":"10.1016\/0166-5316(94)00024-E_BIB20","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1137\/0204046","article-title":"An Elementary Solution of the Queueing System GI\/G\/1","volume":"4","author":"Konheim","year":"1975","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0166-5316(94)00024-E_BIB21","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1057\/jors.1988.30","article-title":"A Maximum Entropy Analysis of the G\/G\/1 Queue at Equilibrium","volume":"39","author":"Kouvatsos","year":"1988","journal-title":"J. Op. Res. Soc."},{"key":"10.1016\/0166-5316(94)00024-E_BIB22","first-page":"396","article-title":"Approximate Formulae for General Single Server Systems with Single and Batch Arrivals","volume":"20","author":"Kr\u00e4mer","year":"1978","journal-title":"Angewandte Informatik"},{"key":"10.1016\/0166-5316(94)00024-E_BIB23","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1109\/TCOM.1979.1094270","article-title":"Approximate Analysis of General Queueing Networks by Decomposition","volume":"27","author":"Kuehn","year":"1979","journal-title":"IEEE Trans. Com."},{"key":"10.1016\/0166-5316(94)00024-E_BIB24","first-page":"277","article-title":"The Theory of Queues with a Single Server","volume":"48","author":"Lindley","year":"1952"},{"key":"10.1016\/0166-5316(94)00024-E_BIB25","doi-asserted-by":"crossref","first-page":"675","DOI":"10.2307\/1427464","article-title":"A Single Server Queue with Server Vacations and a Class of Non-Renewal Arrival Processes","volume":"22","author":"Lucantoni","year":"1990","journal-title":"Adv. Appl. Prob."},{"key":"10.1016\/0166-5316(94)00024-E_BIB26","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1080\/15326348508807003","article-title":"Efficient Algorithms for Solving the Non-Linear Matrix Equations Arising in Phase Type Queues","volume":"1","author":"Lucantoni","year":"1985","journal-title":"Comm. Statist.-Stochastic Models"},{"key":"10.1016\/0166-5316(94)00024-E_BIB27","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1287\/opre.16.3.651","article-title":"Some Inequalities in Queueing","volume":"16","author":"Marshall","year":"1968","journal-title":"Op. Res."},{"key":"10.1016\/0166-5316(94)00024-E_BIB28","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0166-5316(91)90042-2","article-title":"An Analytic Solution of the Waiting Time Distribution for the Discrete-Time GI\/G\/1 Queue","volume":"13","author":"Murata","year":"1991","journal-title":"Performance Evaluation"},{"year":"1981","author":"Neuts","key":"10.1016\/0166-5316(94)00024-E_BIB29"},{"year":"1989","author":"Neuts","key":"10.1016\/0166-5316(94)00024-E_BIB30"},{"key":"10.1016\/0166-5316(94)00024-E_BIB31","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1111\/j.1467-9574.1974.tb00745.x","article-title":"Theory and Numerical Solution of a Discrete Queueing Problem","volume":"20","author":"Ponstein","year":"1974","journal-title":"Statistica Neerlandica"},{"key":"10.1016\/0166-5316(94)00024-E_BIB32","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1287\/trsc.20.2.65","article-title":"Iterative Algorithms for Bulk Arrival, Bulk Service Queues with Poisson and Non-Poisson Arrivals","volume":"20","author":"Powell","year":"1986","journal-title":"Transport. Sci."},{"key":"10.1016\/0166-5316(94)00024-E_BIB33","article-title":"An Analytical Solution to the Discrete Time Single Server Queue with Semi-Markovian Arrivals","author":"Rieger","year":"1992","journal-title":"Queueing Systems"},{"key":"10.1016\/0166-5316(94)00024-E_BIB34","doi-asserted-by":"crossref","first-page":"749","DOI":"10.2307\/3214104","article-title":"Bounds on the Expected Waiting Time in a GI\/G\/1 Queue: Upgrading for low Traffic Intensity","volume":"24","author":"Rosberg","year":"1987","journal-title":"J. Appl. Prob."},{"key":"10.1016\/0166-5316(94)00024-E_BIB35","doi-asserted-by":"crossref","first-page":"417","DOI":"10.2307\/3212767","article-title":"Bounds on the Delay Distribution in GI\/G\/1 Queues","volume":"11","author":"Ross","year":"1974","journal-title":"J. Appl. Prob."},{"key":"10.1016\/0166-5316(94)00024-E_BIB36","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1080\/15326349208807217","article-title":"MEDA: Mixed Erlang Distributions as Phase-Type Representations of Empirical Distribution Functions","volume":"8","author":"Schmickler","year":"1992","journal-title":"Comm. Statist.-Stochastic Models"},{"key":"10.1016\/0166-5316(94)00024-E_BIB37","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/0377-2217(86)90222-5","article-title":"An Algorithm for Ph\/Ph\/c-Queues","volume":"23","author":"Seelen","year":"1986","journal-title":"Eur. J. Op. Res."},{"year":"1986","author":"Tijms","key":"10.1016\/0166-5316(94)00024-E_BIB38"},{"key":"10.1016\/0166-5316(94)00024-E_BIB39","series-title":"Teletraffic Analysis and Computer Performance Evaluation","first-page":"341","article-title":"Discrete-Time Analysis for the Interdeparture Distribution of GI\/G\/1 Queues","author":"Tran-Gia","year":"1986"},{"key":"10.1016\/0166-5316(94)00024-E_BIB40","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1002\/j.1538-7305.1984.tb00005.x","article-title":"On Approximations for Queues","volume":"63","author":"Whitt","year":"1984","journal-title":"AT&T Bell Lab. Techn. J."},{"key":"10.1016\/0166-5316(94)00024-E_BIB41","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/BF01720216","article-title":"Approximating the Stationary Waiting Time Distribution Function of GI\/GI\/1 Queues with Arithmetic Interarrivai Time and Service Time Distribution Function","author":"Wolf","year":"1982","journal-title":"Op. Res. Spectrum"}],"container-title":["Performance Evaluation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:016653169400024E?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:016653169400024E?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T22:46:46Z","timestamp":1733266006000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/016653169400024E"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,9]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,9]]}},"alternative-id":["016653169400024E"],"URL":"https:\/\/doi.org\/10.1016\/0166-5316(94)00024-e","relation":{},"ISSN":["0166-5316"],"issn-type":[{"type":"print","value":"0166-5316"}],"subject":[],"published":{"date-parts":[[1995,9]]}}}