{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T06:59:29Z","timestamp":1779087569907,"version":"3.51.4"},"reference-count":59,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T00:00:00Z","timestamp":1595894400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T00:00:00Z","timestamp":1595894400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"DFG","award":["RTG 2236 \"UnRAVeL\""],"award-info":[{"award-number":["RTG 2236 \"UnRAVeL\""]}]},{"name":"NWO","award":["639.021.754"],"award-info":[{"award-number":["639.021.754"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Autom Reasoning"],"published-print":{"date-parts":[[2020,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We provide a memory-efficient algorithm for multi-objective model checking problems on Markov decision processes (MDPs) with multiple cost structures. The key problem at hand is to check whether there exists a scheduler for a given MDP such that all objectives over cost vectors are fulfilled. We cover multi-objective reachability and expected cost objectives, and combinations thereof. We further transfer approaches for computing quantiles over single cost bounds to the multi-cost case and highlight the ensuing challenges. An empirical evaluation shows the scalability of our new approach both in terms of memory consumption and runtime. We discuss the need for more detailed visual presentations of results beyond Pareto curves and present a first visualisation approach that exploits all the available information from the algorithm to support decision makers.<\/jats:p>","DOI":"10.1007\/s10817-020-09574-9","type":"journal-article","created":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T18:20:31Z","timestamp":1595960431000},"page":"1483-1522","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Multi-cost Bounded Tradeoff Analysis in MDP"],"prefix":"10.1007","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3268-8674","authenticated-orcid":false,"given":"Arnd","family":"Hartmanns","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0978-8466","authenticated-orcid":false,"given":"Sebastian","family":"Junges","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6143-1926","authenticated-orcid":false,"given":"Joost-Pieter","family":"Katoen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2843-5511","authenticated-orcid":false,"given":"Tim","family":"Quatmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,7,28]]},"reference":[{"key":"9574_CR1","doi-asserted-by":"crossref","unstructured":"Andova, S., Hermanns, H., Katoen, J.P.: Discrete-time rewards model-checked. In: FORMATS, LNCS, vol. 2791, pp. 88\u2013104. Springer (2003)","DOI":"10.1007\/978-3-540-40903-8_8"},{"key":"9574_CR2","doi-asserted-by":"crossref","unstructured":"Baier, C., Daum, M., Dubslaff, C., Klein, J., Kl\u00fcppelholz, S.: Energy-utility quantiles. In: NFM, LNCS, vol. 8430, pp. 285\u2013299. Springer (2014)","DOI":"10.1007\/978-3-319-06200-6_24"},{"issue":"4","key":"9574_CR3","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1145\/3292048.3292052","volume":"5","author":"C Baier","year":"2018","unstructured":"Baier, C., Dubslaff, C.: From verification to synthesis under cost-utility constraints. SIGLOG News 5(4), 26\u201346 (2018)","journal-title":"SIGLOG News"},{"key":"9574_CR4","doi-asserted-by":"crossref","unstructured":"Baier, C., Klein, J., Kl\u00fcppelholz, S., Wunderlich, S.: Maximizing the conditional expected reward for reaching the goal. In: TACAS (2), LNCS, vol. 10206, pp. 269\u2013285 (2017)","DOI":"10.1007\/978-3-662-54580-5_16"},{"key":"9574_CR5","doi-asserted-by":"crossref","unstructured":"Baier, C., Klein, J., Leuschner, L., Parker, D., Wunderlich, S.: Ensuring the reliability of your model checker: Interval iteration for Markov decision processes. In: CAV (1), LNCS, vol. 10426, pp. 160\u2013180. Springer (2017)","DOI":"10.1007\/978-3-319-63387-9_8"},{"key":"9574_CR6","doi-asserted-by":"crossref","unstructured":"Barrett, L., Narayanan, S.: Learning all optimal policies with multiple criteria. In: ICML, AICPS, vol. 307, pp. 41\u201347. ACM (2008)","DOI":"10.1145\/1390156.1390162"},{"key":"9574_CR7","unstructured":"Berthon, R., Randour, M., Raskin, J.F.: Threshold constraints with guarantees for parity objectives in Markov decision processes. In: ICALP, LIPIcs, vol.\u00a080, pp. 121:1\u2013121:15. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2017)"},{"key":"9574_CR8","doi-asserted-by":"crossref","unstructured":"Br\u00e1zdil, T., Brozek, V., Chatterjee, K., Forejt, V., Kucera, A.: Two views on multiple mean-payoff objectives in Markov decision processes. LMCS 10(1) (2014)","DOI":"10.2168\/LMCS-10(1:13)2014"},{"key":"9574_CR9","doi-asserted-by":"crossref","unstructured":"Br\u00e1zdil, T., Chatterjee, K., Chmelik, M., Forejt, V., Kret\u00ednsk\u00fd, J., Kwiatkowska, M.Z., Parker, D., Ujma, M.: Verification of Markov decision processes using learning algorithms. In: ATVA, LNCS, vol. 8837, pp. 98\u2013114. Springer (2014)","DOI":"10.1007\/978-3-319-11936-6_8"},{"key":"9574_CR10","doi-asserted-by":"publisher","first-page":"144","DOI":"10.1016\/j.jcss.2016.09.009","volume":"84","author":"T Br\u00e1zdil","year":"2017","unstructured":"Br\u00e1zdil, T., Chatterjee, K., Forejt, V., Kucera, A.: Trading performance for stability in Markov decision processes. J. Comput. Syst. Sci. 84, 144\u2013170 (2017)","journal-title":"J. Comput. Syst. Sci."},{"key":"9574_CR11","unstructured":"Bresina, J.L., J\u00f3nsson, A.K., Morris, P.H., Rajan, K.: Activity planning for the Mars exploration rovers. In: ICAPS, pp. 40\u201349. AAAI (2005)"},{"key":"9574_CR12","unstructured":"Bryce, D., Cushing, W., Kambhampati, S.: Probabilistic planning is multi-objective. Technical Report, Arizona State Univ, CSE (2007)"},{"key":"9574_CR13","doi-asserted-by":"crossref","unstructured":"Cao, Z., Guo, H., Zhang, J., Oliehoek, F.A., Fastenrath, U.: Maximizing the probability of arriving on time: a practical q-learning method. In: AAAI, pp. 4481\u20134487. AAAI Press (2017)","DOI":"10.1609\/aaai.v31i1.11170"},{"key":"9574_CR14","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.artint.2016.01.007","volume":"234","author":"K Chatterjee","year":"2016","unstructured":"Chatterjee, K., Chmelik, M., Gupta, R., Kanodia, A.: Optimal cost almost-sure reachability in POMDPs. Artif. Intell. 234, 26\u201348 (2016)","journal-title":"Artif. Intell."},{"key":"9574_CR15","doi-asserted-by":"crossref","unstructured":"Chatterjee, K., Majumdar, R., Henzinger, T.A.: Markov decision processes with multiple objectives. In: STACS, LNCS, vol. 3884, pp. 325\u2013336. Springer (2006)","DOI":"10.1007\/11672142_26"},{"key":"9574_CR16","doi-asserted-by":"crossref","unstructured":"Chen, T., Forejt, V., Kwiatkowska, M., Simaitis, A., Wiltsche, C.: On stochastic games with multiple objectives. In: MFCS, LNCS, vol. 8087, pp. 266\u2013277. Springer (2013)","DOI":"10.1007\/978-3-642-40313-2_25"},{"issue":"8","key":"9574_CR17","doi-asserted-by":"publisher","first-page":"2405","DOI":"10.1021\/ie049622+","volume":"44","author":"L Cheng","year":"2005","unstructured":"Cheng, L., Subrahmanian, E., Westerberg, A.W.: Multiobjective decision processes under uncertainty: applications, problem formulations, and solution strategies. Ind. Eng. Chem. Res. 44(8), 2405\u20132415 (2005)","journal-title":"Ind. Eng. Chem. Res."},{"key":"9574_CR18","doi-asserted-by":"crossref","unstructured":"Christman, A., Cassamano, J.: Maximizing the probability of arriving on time. In: ASMTA, LNCS, vol. 7984, pp. 142\u2013157. Springer (2013)","DOI":"10.1007\/978-3-642-39408-9_11"},{"key":"9574_CR19","unstructured":"Dai, P., Mausam, Weld, D.S., Goldsmith, J.: Topological value iteration algorithms. J. JAIR 42, 181\u2013209 (2011)"},{"key":"9574_CR20","unstructured":"Dehnert, C., Junges, S., Katoen, J.P., Quatmann, T., Volk, M.: Storm website (2018). http:\/\/stormchecker.org"},{"key":"9574_CR21","doi-asserted-by":"crossref","unstructured":"Dehnert, C., Junges, S., Katoen, J.P., Volk, M.: A Storm is coming: a modern probabilistic model checker. In: CAV (2), LNCS, vol. 10427, pp. 592\u2013600. Springer (2017)","DOI":"10.1007\/978-3-319-63390-9_31"},{"key":"9574_CR22","doi-asserted-by":"crossref","unstructured":"Eastwood, R., Alexander, R., Kelly, T.: Safe multi-objective planning with a posteriori preferences. In: HASE, pp. 78\u201385. IEEE Computer Society (2016)","DOI":"10.1109\/HASE.2016.22"},{"key":"9574_CR23","doi-asserted-by":"crossref","unstructured":"Etessami, K., Kwiatkowska, M., Vardi, M.Y., Yannakakis, M.: Multi-objective model checking of Markov decision processes. LMCS 4(4) (2008)","DOI":"10.2168\/LMCS-4(4:8)2008"},{"key":"9574_CR24","doi-asserted-by":"crossref","unstructured":"Feng, L., Wiltsche, C., Humphrey, L., Topcu, U.: Controller synthesis for autonomous systems interacting with human operators. In: ICCPS, pp. 70\u201379. ACM (2015)","DOI":"10.1145\/2735960.2735973"},{"key":"9574_CR25","doi-asserted-by":"crossref","unstructured":"Forejt, V., Kwiatkowska, M., Parker, D.: Pareto curves for probabilistic model checking. In: ATVA, LNCS, vol. 7561, pp. 317\u2013332. Springer (2012)","DOI":"10.1007\/978-3-642-33386-6_25"},{"key":"9574_CR26","doi-asserted-by":"crossref","unstructured":"Forejt, V., Kwiatkowska, M.Z., Norman, G., Parker, D.: Automated verification techniques for probabilistic systems. In: SFM, LNCS, vol. 6659, pp. 53\u2013113. Springer (2011)","DOI":"10.1007\/978-3-642-21455-4_3"},{"key":"9574_CR27","doi-asserted-by":"crossref","unstructured":"Haddad, S., Monmege, B.: Reachability in MDPs: refining convergence of value iteration. In: RP, LNCS, vol. 8762, pp. 125\u2013137. Springer (2014)","DOI":"10.1007\/978-3-319-11439-2_10"},{"key":"9574_CR28","first-page":"85","volume":"9984","author":"EM Hahn","year":"2016","unstructured":"Hahn, E.M., Hartmanns, A.: A comparison of time- and reward-bounded probabilistic model checking techniques. SETTA, LNCS 9984, 85\u2013100 (2016)","journal-title":"SETTA, LNCS"},{"issue":"2","key":"9574_CR29","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/s10703-012-0167-z","volume":"43","author":"EM Hahn","year":"2013","unstructured":"Hahn, E.M., Hartmanns, A., Hermanns, H., Katoen, J.P.: A compositional modelling and analysis framework for stochastic hybrid systems. Formal Methods in Syst. Des. 43(2), 191\u2013232 (2013)","journal-title":"Formal Methods in Syst. Des."},{"key":"9574_CR30","doi-asserted-by":"crossref","unstructured":"Hahn, E.M., Hashemi, V., Hermanns, H., Lahijanian, M., Turrini, A.: Multi-objective robust strategy synthesis for interval Markov decision processes. In: QEST, LNCS, vol. 10503, pp. 207\u2013223. Springer (2017)","DOI":"10.1007\/978-3-319-66335-7_13"},{"key":"9574_CR31","doi-asserted-by":"crossref","unstructured":"Hartmanns, A., Hermanns, H.: The Modest Toolset: An integrated environment for quantitative modelling and verification. In: TACAS, LNCS, vol. 8413, pp. 593\u2013598. Springer (2014)","DOI":"10.1007\/978-3-642-54862-8_51"},{"key":"9574_CR32","doi-asserted-by":"publisher","unstructured":"Hartmanns, A., Junges, S., Katoen, J.P., Quatmann, T.: Multi-cost bounded reachability in MDP. In: TACAS, LNCS, vol. 10806, pp. 320\u2013339. Springer (2018). https:\/\/doi.org\/10.1007\/978-3-319-89963-3_19","DOI":"10.1007\/978-3-319-89963-3_19"},{"key":"9574_CR33","doi-asserted-by":"publisher","unstructured":"Hartmanns, A., Junges, S., Katoen, J.P., Quatmann, T.: Multi-cost bounded tradeoff analysis in MDP\u2014Artifact. Zenodo (2020). https:\/\/doi.org\/10.5281\/zenodo.3894716","DOI":"10.5281\/zenodo.3894716"},{"key":"9574_CR34","doi-asserted-by":"crossref","unstructured":"Hartmanns, A., Kaminski, B.L.: Optimistic value iteration. In: CAV, Lecture Notes in Computer Science, vol\u00a012225, pp.\u00a0488\u2013511. Springer (2020). https:\/\/doi.org\/10.1007\/978-3-030-53291-8_26","DOI":"10.1007\/978-3-030-53291-8_26"},{"key":"9574_CR35","doi-asserted-by":"crossref","unstructured":"Hou, P., Yeoh, W., Varakantham, P.: Revisiting risk-sensitive MDPs: New algorithms and results. In: ICAPS. AAAI (2014)","DOI":"10.1609\/icaps.v24i1.13615"},{"key":"9574_CR36","doi-asserted-by":"crossref","unstructured":"Junges, S., Jansen, N., Dehnert, C., Topcu, U., Katoen, J.: Safety-constrained reinforcement learning for MDPs. In: TACAS, LNCS, vol. 9636, pp. 130\u2013146. Springer (2016)","DOI":"10.1007\/978-3-662-49674-9_8"},{"key":"9574_CR37","doi-asserted-by":"crossref","unstructured":"Klein, J., Baier, C., Chrszon, P., Daum, M., Dubslaff, C., Kl\u00fcppelholz, S., M\u00e4rcker, S., M\u00fcller, D.: Advances in probabilistic model checking with PRISM: variable reordering, quantiles and weak deterministic B\u00fcchi automata. STTT pp. 1\u201316 (2017)","DOI":"10.1007\/s10009-017-0456-3"},{"key":"9574_CR38","unstructured":"Kolobov, A., Mausam, Weld, D.S.: A theory of goal-oriented MDPs with dead ends. In: UAI, pp. 438\u2013447. AUAI Press (2012)"},{"key":"9574_CR39","doi-asserted-by":"crossref","unstructured":"Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: Verification of probabilistic real-time systems. In: CAV, LNCS, vol. 6806, pp. 585\u2013591. Springer (2011)","DOI":"10.1007\/978-3-642-22110-1_47"},{"key":"9574_CR40","doi-asserted-by":"crossref","unstructured":"Kwiatkowska, M., Norman, G., Parker, D.: The PRISM benchmark suite. In: QEST, pp. 203\u2013204. IEEE CS Press (2012)","DOI":"10.1109\/QEST.2012.14"},{"key":"9574_CR41","doi-asserted-by":"crossref","unstructured":"Kwiatkowska, M.Z., Norman, G., Sproston, J.: Probabilistic model checking of the IEEE 802.11 wireless local area network protocol. In: PAPM-PROBMIV, LNCS, vol. 2399, pp. 169\u2013187. Springer (2002)","DOI":"10.1007\/3-540-45605-8_11"},{"key":"9574_CR42","doi-asserted-by":"crossref","unstructured":"Lacerda, B., Parker, D., Hawes, N.: Multi-objective policy generation for mobile robots under probabilistic time-bounded guarantees. In: ICAPS, pp. 504\u2013512. AAAI Press (2017)","DOI":"10.1609\/icaps.v27i1.13865"},{"issue":"1\u20132","key":"9574_CR43","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1002\/mcda.1604","volume":"24","author":"R Lankaites Pinheiro","year":"2017","unstructured":"Lankaites Pinheiro, R., Landa-Silva, D., Atkin, J.: A technique based on trade-off maps to visualise and analyse relationships between objectives in optimisation problems. J. Multi-Criteria Decis. Anal. 24(1\u20132), 37\u201356 (2017)","journal-title":"J. Multi-Criteria Decis. Anal."},{"key":"9574_CR44","doi-asserted-by":"crossref","unstructured":"Laroussinie, F., Sproston, J.: Model checking durational probabilistic systems. In: FoSSaCS, LNCS, vol. 3441, pp. 140\u2013154. Springer (2005)","DOI":"10.1007\/978-3-540-31982-5_9"},{"issue":"10","key":"9574_CR45","doi-asserted-by":"publisher","first-page":"1629","DOI":"10.1109\/TCAD.2005.852033","volume":"24","author":"G Norman","year":"2005","unstructured":"Norman, G., Parker, D., Kwiatkowska, M.Z., Shukla, S.K.: Evaluating the reliability of NAND multiplexing with PRISM. IEEE Trans. CAD of Integ. Circuits Syst. 24(10), 1629\u20131637 (2005)","journal-title":"IEEE Trans. CAD of Integ. Circuits Syst."},{"key":"9574_CR46","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316887","volume-title":"Markov Decision Processes","author":"ML Puterman","year":"1994","unstructured":"Puterman, M.L.: Markov Decision Processes. Wiley, HobokenD (1994)"},{"key":"9574_CR47","doi-asserted-by":"crossref","unstructured":"Quatmann, T., Junges, S., Katoen, J.P.: Markov automata with multiple objectives. In: CAV (1), LNCS, vol. 10426, pp. 140\u2013159. Springer (2017)","DOI":"10.1007\/978-3-319-63387-9_7"},{"key":"9574_CR48","doi-asserted-by":"crossref","unstructured":"Quatmann, T., Katoen, J.P.: Sound value iteration. In: CAV, LNCS, vol. 10981, pp. 643\u2013661. Springer (2018)","DOI":"10.1007\/978-3-319-96145-3_37"},{"issue":"2\u20133","key":"9574_CR49","first-page":"207","volume":"50","author":"M Randour","year":"2017","unstructured":"Randour, M., Raskin, J.F., Sankur, O.: Percentile queries in multi-dimensional Markov decision processes. FMSD 50(2\u20133), 207\u2013248 (2017)","journal-title":"FMSD"},{"issue":"1","key":"9574_CR50","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1145\/290163.290168","volume":"1","author":"MK Reiter","year":"1998","unstructured":"Reiter, M.K., Rubin, A.D.: Crowds: anonymity for web transactions. ACM Trans. Inf. Syst. Secur. 1(1), 66\u201392 (1998)","journal-title":"ACM Trans. Inf. Syst. Secur."},{"key":"9574_CR51","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1613\/jair.3987","volume":"48","author":"DM Roijers","year":"2013","unstructured":"Roijers, D.M., Vamplew, P., Whiteson, S., Dazeley, R.: A survey of multi-objective sequential decision-making. J. Artif. Intell. Res. 48, 67\u2013113 (2013)","journal-title":"J. Artif. Intell. Res."},{"key":"9574_CR52","doi-asserted-by":"publisher","unstructured":"Sardar, M.U., Dubslaff, C., Kl\u00fcppelholz, S., Baier, C., Kumar, A.: Performance evaluation of thermal-constrained scheduling strategies in multi-core systems. In: EPEW, LNCS, vol. 12039, pp. 133\u2013147. Springer (2019). https:\/\/doi.org\/10.1007\/978-3-030-44411-2_9","DOI":"10.1007\/978-3-030-44411-2_9"},{"key":"9574_CR53","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1613\/jair.5153","volume":"57","author":"M Steinmetz","year":"2016","unstructured":"Steinmetz, M., Hoffmann, J., Buffet, O.: Goal probability analysis in probabilistic planning: exploring and enhancing the state of the art. J. Artif. Intell. Res. 57, 229\u2013271 (2016)","journal-title":"J. Artif. Intell. Res."},{"key":"9574_CR54","doi-asserted-by":"crossref","unstructured":"Stoelinga, M., Vaandrager, F.W.: Root contention in IEEE 1394. In: ARTS Formal Methods for Real-Time and Probabilistic Systems, LNCS, vol. 1601, pp. 53\u201374. Springer (1999)","DOI":"10.1007\/3-540-48778-6_4"},{"key":"9574_CR55","unstructured":"Teichteil-K\u00f6nigsbuch, F.: Stochastic safest and shortest path problems. In: AAAI. AAAI Press (2012)"},{"key":"9574_CR56","unstructured":"The International Probabilistic Planning Competition. http:\/\/www.icaps-conference.org\/index.php\/Main\/Competitions"},{"key":"9574_CR57","doi-asserted-by":"crossref","unstructured":"Ummels, M., Baier, C.: Computing quantiles in Markov reward models. In: FOSSACS, LNCS, vol. 7794, pp. 353\u2013368. Springer (2013)","DOI":"10.1007\/978-3-642-37075-5_23"},{"issue":"1\u20132","key":"9574_CR58","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/s10994-010-5232-5","volume":"84","author":"P Vamplew","year":"2011","unstructured":"Vamplew, P., Dazeley, R., Berry, A., Issabekov, R., Dekker, E.: Empirical evaluation methods for multiobjective reinforcement learning algorithms. Mach. Learn. 84(1\u20132), 51\u201380 (2011)","journal-title":"Mach. Learn."},{"issue":"1","key":"9574_CR59","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1006\/jmaa.1998.6015","volume":"225","author":"SX Yu","year":"1998","unstructured":"Yu, S.X., Lin, Y., Yan, P.: Optimization models for the first arrival target distribution function in discrete time. J. Math. Anal. Appl. 225(1), 193\u2013223 (1998)","journal-title":"J. Math. Anal. Appl."}],"container-title":["Journal of Automated Reasoning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10817-020-09574-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10817-020-09574-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10817-020-09574-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,4]],"date-time":"2022-11-04T22:13:05Z","timestamp":1667599985000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10817-020-09574-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,28]]},"references-count":59,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2020,10]]}},"alternative-id":["9574"],"URL":"https:\/\/doi.org\/10.1007\/s10817-020-09574-9","relation":{},"ISSN":["0168-7433","1573-0670"],"issn-type":[{"value":"0168-7433","type":"print"},{"value":"1573-0670","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,28]]},"assertion":[{"value":"23 June 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 July 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 July 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}