{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,20]],"date-time":"2026-10-20T12:32:51Z","timestamp":1792499571782,"version":"4.5.0"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2022,1,29]],"date-time":"2022-01-29T00:00:00Z","timestamp":1643414400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2022,1,29]],"date-time":"2022-01-29T00:00:00Z","timestamp":1643414400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2023,4]]},"DOI":"10.1007\/s00500-021-06656-7","type":"journal-article","created":{"date-parts":[[2022,1,29]],"date-time":"2022-01-29T00:02:43Z","timestamp":1643414563000},"page":"4107-4123","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Performance analysis and evaluation of ternary optical computer based on asynchronous multiple vacations"],"prefix":"10.1007","volume":"27","author":[{"given":"Xianchao","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xianchuan","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Man","family":"Ling","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dayou","family":"Hou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai","family":"Song","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,1,29]]},"reference":[{"key":"6656_CR2","doi-asserted-by":"publisher","unstructured":"Ambs P (2010) Optical computing: a 60-year adventure. Adv Opt Technol. https:\/\/doi.org\/10.1155\/2010\/372652","DOI":"10.1155\/2010\/372652"},{"issue":"6","key":"6656_CR40","doi-asserted-by":"publisher","first-page":"699","DOI":"10.1287\/opre.4.6.699","volume":"26","author":"PJ Burke","year":"1956","unstructured":"Burke PJ (1956) The output of a queueing system. Oper Res 26(6):699\u2013704","journal-title":"Oper Res"},{"issue":"4","key":"6656_CR45","doi-asserted-by":"publisher","first-page":"1144","DOI":"10.1214\/aoms\/1177698238","volume":"39","author":"PJ Burke","year":"1968","unstructured":"Burke PJ (1968) The output process of a stationary M\/M\/s queueing system. Ann Math Stat 39(4):1144\u20131152","journal-title":"Ann Math Stat"},{"issue":"3","key":"6656_CR25","first-page":"280","volume":"19","author":"H Gao","year":"2013","unstructured":"Gao H, Jin Y, Song K (2013) Extension of C language in ternary optical computer. J Shanghai Univ (Nat Sci) 19(3):280\u2013285 ((in Chinese))","journal-title":"J Shanghai Univ (Nat Sci)"},{"key":"6656_CR38","doi-asserted-by":"publisher","DOI":"10.1002\/9781118625651","volume-title":"Fundamentals of queueing theory, 4th edn","author":"D Gross","year":"2008","unstructured":"Gross D, Shortie JF, Thompson JM et al (2008) Fundamentals of queueing theory, 4th edn. Wiley, New Jersey"},{"key":"6656_CR1","doi-asserted-by":"publisher","first-page":"2161","DOI":"10.1364\/AO.9.002161","volume":"9","author":"RA Heinz","year":"1970","unstructured":"Heinz RA, Artman JO, Lee SH (1970) Matrix multiplication by optical methods. Appl Opt 9:2161\u20132168","journal-title":"Appl Opt"},{"issue":"2","key":"6656_CR6","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1360\/03yf9012","volume":"46","author":"Y Jin","year":"2003","unstructured":"Jin Y, He HC, L\u00fc YT (2003) Ternary optical computer principle. Sci China F Inf Sci 46(2):145\u2013150","journal-title":"Sci China F Inf Sci"},{"key":"6656_CR7","first-page":"98","volume":"118","author":"Y Jin","year":"2005","unstructured":"Jin Y, He HC, L\u00fc YT (2005) Ternary optical computer architecture. Phys Scr 118:98\u2013101","journal-title":"Phys Scr"},{"issue":"11","key":"6656_CR13","doi-asserted-by":"publisher","first-page":"2159","DOI":"10.1007\/s11432-010-4091-9","volume":"53","author":"Y Jin","year":"2010","unstructured":"Jin Y, Shen YF, Peng JJ et al (2010) Principles and construction of MSD adder in ternary optical computer. Sci China F Inf Sci 53(11):2159\u20132168","journal-title":"Sci China F Inf Sci"},{"issue":"3","key":"6656_CR21","first-page":"361","volume":"43","author":"Y Jin","year":"2013","unstructured":"Jin Y, Ouyang S, Song K et al (2013) Management of many data bits in ternary optical computers. Sci China (Inf Sci) 43(3):361\u2013373 ((in Chinese))","journal-title":"Sci China (Inf Sci)"},{"issue":"5","key":"6656_CR23","first-page":"584","volume":"53","author":"Y Jin","year":"2019","unstructured":"Jin Y, Zhang SL, Li S et al (2019) The computing-data file: a key technology of applying ternary optical computer. J Shanghai Jiaotong Univ (Chin Ed) 53(5):584\u2013592","journal-title":"J Shanghai Jiaotong Univ (Chin Ed)"},{"key":"6656_CR39","volume-title":"Queueing systems: theory,","author":"L Kleinrock","year":"1975","unstructured":"Kleinrock L (1975) Queueing systems: theory, vol 1. Wikey-Interscience, New York"},{"issue":"2","key":"6656_CR24","first-page":"181","volume":"24","author":"S Li","year":"2018","unstructured":"Li S, Jin Y, Liu YJ (2018) Initial SZG file generation software for ternary optical computer. J Shanghai Univ (Nat Sci) 24(2):181\u2013191 ((in Chinese))","journal-title":"J Shanghai Univ (Nat Sci)"},{"issue":"4","key":"6656_CR32","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1080\/00051144.2019.1639118","volume":"60","author":"S Li","year":"2019","unstructured":"Li S, Li WJ, Zhang HH et al (2019) Research and implementation of parallel artificial bee colony algorithm based on ternary optical computer. Automatika 60(4):422\u2013431","journal-title":"Automatika"},{"key":"6656_CR33","doi-asserted-by":"crossref","unstructured":"Liu SB, Jin Y, Peng JJ et al. (2009) The response time measurement system of optical computer component. In: International conference on information engineering and computer science. IEEE, NJ, pp 1986\u20131990","DOI":"10.1109\/ICIECS.2009.5364632"},{"key":"6656_CR43","volume-title":"Matrix-geometric solutions on stochastic models-an algorithmic approach","author":"MF Neuts","year":"1981","unstructured":"Neuts MF (1981) Matrix-geometric solutions on stochastic models-an algorithmic approach. The Johns Hopkins University Press, Baltimore and London"},{"issue":"6","key":"6656_CR18","first-page":"743","volume":"46","author":"S Ouyang","year":"2016","unstructured":"Ouyang S, Peng JJ, Jin Y et al (2016) Structure and theory of dual-space storage for ternary optical computer. Sci China (Inf Sci) 46(6):743\u2013762 ((in Chinese))","journal-title":"Sci China (Inf Sci)"},{"issue":"5","key":"6656_CR11","doi-asserted-by":"publisher","first-page":"1134","DOI":"10.1109\/TC.2012.285","volume":"63","author":"JJ Peng","year":"2014","unstructured":"Peng JJ, Shen R, Jin Y et al (2014) Design and implementation of modified signed-digit adder. IEEE Trans Comput 63(5):1134\u20131143","journal-title":"IEEE Trans Comput"},{"issue":"7","key":"6656_CR28","first-page":"846","volume":"47","author":"JJ Peng","year":"2017","unstructured":"Peng JJ, Wei XY, Zhang XF et al (2017) Implementation of parallel FFT algorithm on a ternary optical computer. Sci China (Inf Sci) 47(7):846\u2013862 ((in Chinese))","journal-title":"Sci China (Inf Sci)"},{"key":"6656_CR29","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1016\/j.optcom.2017.10.033","volume":"410","author":"JJ Peng","year":"2018","unstructured":"Peng JJ, Fu YY, Zhang XF et al (2018) Implementation of DFT application on ternary optical computer. Optics Commun 410:424\u2013430","journal-title":"Optics Commun"},{"key":"6656_CR4","first-page":"102152","volume":"13","author":"ANZ Rashed","year":"2019","unstructured":"Rashed ANZ, Mohammed AE-NA, Zaky WF et al (2019) The switching of optoelectronics to full optical computing operations based on nonlinear metamaterials. Res Phys 13:102152","journal-title":"Res Phys"},{"issue":"1","key":"6656_CR10","first-page":"012107-1","volume":"57","author":"YF Shen","year":"2014","unstructured":"Shen YF, Pan L (2014) Principle of a one-step MSD adder for a ternary optical computer. Sci China (Ser F) 57(1):012107-1-012107\u201310","journal-title":"Sci China (Ser F)"},{"issue":"5","key":"6656_CR20","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1007\/s11741-011-0770-1","volume":"15","author":"K Song","year":"2011","unstructured":"Song K, Jin Y (2011) Overall plan and design of the task management system of ternary optical computer. J Shanghai Univ 15(5):467\u2013472","journal-title":"J Shanghai Univ"},{"issue":"7","key":"6656_CR14","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1364\/AO.51.000917","volume":"51","author":"K Song","year":"2012","unstructured":"Song K, Yan LP (2012) Design and implementation of the one-step MSD adder of optical computer. Appl Opt 51(7):917\u2013926","journal-title":"Appl Opt"},{"key":"6656_CR15","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.optcom.2019.05.007","volume":"448","author":"K Song","year":"2019","unstructured":"Song K, Chen G, Jin QQ et al (2019) Design of MSD multiplier for ternary optical computer processor based on minimum module. Opt Commun 448:33\u201342","journal-title":"Opt Commun"},{"key":"6656_CR30","doi-asserted-by":"publisher","first-page":"64499","DOI":"10.1109\/ACCESS.2020.2984902","volume":"8","author":"K Song","year":"2020","unstructured":"Song K, Jin QQ, Chen G et al (2020) Algorithm on higher-order derivative based on ternary optical computer. IEEE Access 8:64499\u201364513","journal-title":"IEEE Access"},{"key":"6656_CR41","volume-title":"Probability, Markov chains, queues, and simulation-the mathematical basis of performance modeling","author":"WJ Stewart","year":"2009","unstructured":"Stewart WJ (2009) Probability, Markov chains, queues, and simulation-the mathematical basis of performance modeling. Princeton University Press, New Jersey"},{"issue":"1","key":"6656_CR42","first-page":"7","volume":"13","author":"NS Tian","year":"2000","unstructured":"Tian NS, Li QL (2000) The M\/M\/c queue with PH synchronous vacations. Syst Sci Math Sci 13(1):7\u201316","journal-title":"Syst Sci Math Sci"},{"key":"6656_CR44","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-33723-4","volume-title":"Vacation queueing models theory and applications","author":"NS Tian","year":"2006","unstructured":"Tian NS, Zhang ZG (2006) Vacation queueing models theory and applications. Springer, New York"},{"issue":"12","key":"6656_CR12","doi-asserted-by":"publisher","first-page":"2352","DOI":"10.1364\/AO.49.002352","volume":"49","author":"XC Wang","year":"2010","unstructured":"Wang XC, Peng JJ, Li M et al (2010) Carry-free vector\u2013matrix multiplication on a dynamically reconfigurable optical platform. Appl Opt 49(12):2352\u20132362","journal-title":"Appl Opt"},{"issue":"5","key":"6656_CR19","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1364\/AO.50.000662","volume":"50","author":"XC Wang","year":"2011","unstructured":"Wang XC, Peng JJ, Ouyang S (2011) Control method for the optical components of a dynamically reconfigurable optical platform. Appl Opt 50(5):662\u2013670","journal-title":"Appl Opt"},{"key":"6656_CR9","doi-asserted-by":"publisher","first-page":"67214","DOI":"10.1109\/ACCESS.2020.2983773","volume":"8","author":"XC Wang","year":"2020","unstructured":"Wang XC, Zhang J, Gao S et al (2020a) Performance analysis and evaluation of ternary optical computer based on a queueing system with synchronous multi-vacations. IEEE Access 8:67214\u201367227","journal-title":"IEEE Access"},{"key":"6656_CR34","doi-asserted-by":"crossref","unstructured":"Wang XC, Zhang SL, Zhang M, et al (2017) Performance analysis of a ternary optical computer based on M\/M\/1 queueing system. In: International conference on algorithms and architectures for parallel processing. Springer, Switzerland AG, pp 331\u2013344","DOI":"10.1007\/978-3-319-65482-9_22"},{"key":"6656_CR36","unstructured":"Wang XC, Zhang SL, Gao S et al. (2019) Response time of a ternary optical computer that is based on queuing systems. J Supercomput, pp 1\u201320"},{"key":"6656_CR37","doi-asserted-by":"crossref","unstructured":"Wang XC, Zhang J, Gao S et al. (2020b) Response time of a ternary optical computer based on complex queueing system with synchronous multi-vacations. In: International conference on applications and techniques in cyber security and intelligence. Springer, Switzerland AG, pp 1180\u20131188","DOI":"10.1007\/978-3-030-25128-4_149"},{"issue":"2","key":"6656_CR35","first-page":"140","volume":"39","author":"Q Xu","year":"2017","unstructured":"Xu Q, Wang XC (2017) Service model and performance analysis of ternary optical computer based on complex queuing system. J Natl Univ Defense Technol 39(2):140\u2013145 ((in Chinese))","journal-title":"J Natl Univ Defense Technol"},{"issue":"4","key":"6656_CR27","first-page":"539","volume":"46","author":"Q Xu","year":"2016","unstructured":"Xu Q, Jin Y, Shen YF et al (2016) MSD iterative division algorithm and implementation technique for a ternary optical computer. Sci China (Inf Sci) 46(4):539\u2013550 ((in Chinese))","journal-title":"Sci China (Inf Sci)"},{"issue":"16","key":"6656_CR16","doi-asserted-by":"publisher","first-page":"4661","DOI":"10.1364\/AO.56.004661","volume":"56","author":"Q Xu","year":"2017","unstructured":"Xu Q, Wang XC, Xu C (2017) Design and implementation of the modified signed digit multiplication routine on a ternary optical computer. Appl Opt 56(16):4661\u20134669","journal-title":"Appl Opt"},{"issue":"10","key":"6656_CR8","doi-asserted-by":"publisher","first-page":"1415","DOI":"10.1007\/s11432-008-0140-z","volume":"51","author":"JY Yan","year":"2008","unstructured":"Yan JY, Jin Y, Zuo KZ (2008) Decrease-radix design principle for carrying\/borrowing free multi-valued and application in ternary optical computer. Sci China F Inf Sci 51(10):1415\u20131426","journal-title":"Sci China F Inf Sci"},{"key":"6656_CR3","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/j.optcom.2017.09.078","volume":"407","author":"F Zangeneh-nejad","year":"2018","unstructured":"Zangeneh-nejad F, Khavasi A, Rejaei B (2018) Analog optical computing by half-wavelength slabs. Opt Commun 407:338\u2013343","journal-title":"Opt Commun"},{"issue":"2","key":"6656_CR26","first-page":"180","volume":"20","author":"Q Zhang","year":"2014","unstructured":"Zhang Q, Jin Y, Song K et al (2014) MPI programming based on ternary optical computer in supercomputer. J Shanghai Univ (Nat Sci) 20(2):180\u2013189 ((in Chinese))","journal-title":"J Shanghai Univ (Nat Sci)"},{"issue":"6","key":"6656_CR17","first-page":"1391","volume":"54","author":"HL Zhang","year":"2017","unstructured":"Zhang HL, Zhou J, Zhang SL et al (2017) Design and implementation of positive and negative discriminator of MSD data for ternary optical processor. J Comput Res Dev 54(6):1391\u20131404 ((in Chinese))","journal-title":"J Comput Res Dev"},{"key":"6656_CR22","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.optcom.2018.07.038","volume":"428","author":"SL Zhang","year":"2018","unstructured":"Zhang SL, Peng JJ, Shen YF et al (2018) Programming model and implementation mechanism for ternary optical computer. Opt Commun 428:26\u201334","journal-title":"Opt Commun"},{"key":"6656_CR31","doi-asserted-by":"publisher","first-page":"125750","DOI":"10.1016\/j.optcom.2020.125750","volume":"470","author":"SL Zhang","year":"2020","unstructured":"Zhang SL, Shen YF, Zhao ZY (2020) Design and implementation of a three-lane CA traffic flow model on ternary optical computer. Opt Commun 470:125750","journal-title":"Opt Commun"},{"key":"6656_CR5","doi-asserted-by":"publisher","first-page":"124674","DOI":"10.1016\/j.optcom.2019.124674","volume":"458","author":"Y Zhou","year":"2020","unstructured":"Zhou Y, Chen R, Chen W et al (2020) Optical analog computing devices designed by deep neural network. Opt Commun 458:124674","journal-title":"Opt Commun"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-06656-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-021-06656-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-06656-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,14]],"date-time":"2023-03-14T10:13:37Z","timestamp":1678788817000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-021-06656-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,29]]},"references-count":45,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["6656"],"URL":"https:\/\/doi.org\/10.1007\/s00500-021-06656-7","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,29]]},"assertion":[{"value":"4 December 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest. And the funders had no role in the design of the study.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"All authors have read and agreed to the submitted version of the manuscript.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}