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Predicting Temporal Aspects of Movement for Predictive Replication in Fog Environments

Published 1 Jun 2023 in cs.DC and cs.LG | (2306.00575v4)

Abstract: To fully exploit the benefits of the fog environment, efficient management of data locality is crucial. Blind or reactive data replication falls short in harnessing the potential of fog computing, necessitating more advanced techniques for predicting where and when clients will connect. While spatial prediction has received considerable attention, temporal prediction remains understudied. Our paper addresses this gap by examining the advantages of incorporating temporal prediction into existing spatial prediction models. We also provide a comprehensive analysis of spatio-temporal prediction models, such as Deep Neural Networks and Markov models, in the context of predictive replication. We propose a novel model using Holt-Winter's Exponential Smoothing for temporal prediction, leveraging sequential and periodical user movement patterns. In a fog network simulation with real user trajectories our model achieves a 15% reduction in excess data with a marginal 1% decrease in data availability.

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References (92)
  1. Haitham M. Abu Ghazaleh. 2010. Mobility and Spatial-Temporal Traffic Prediction in Wireless Networks Using Markov Renewal Theory. Ph. D. Dissertation. University of Manitoba, Winnipeg, Canada. Advisor(s) Attahiru Sule Alfa.
  2. Marco Ajelli and Maria Litvinova. 2017. Estimating contact patterns relevant to the spread of infectious diseases in Russia. Journal of Theoretical Biology 419 (April 2017), 1–7. https://doi.org/10.1016/j.jtbi.2017.01.041
  3. Sherif Akoush and Ahmed Sameh. 2007. Mobile User Movement Prediction Using Bayesian Learning for Neural Networks. In Proceedings of the 2007 International Conference on Wireless Communications and Mobile Computing (Honolulu, Hawaii, USA) (IWCMC ’07). Association for Computing Machinery, New York, NY, USA, 191–196. https://doi.org/10.1145/1280940.1280982
  4. STF-RNN: Space Time Features-based Recurrent Neural Network for predicting people next location. In Proceedings of the 2016 IEEE Symposium Series on Computational Intelligence (Athens, Greece) (SSCI ’16). IEEE, New York, NY, USA, 1–7. https://doi.org/10.1109/SSCI.2016.7849919
  5. A data aggregation based approach to exploit dynamic spatio-temporal correlations for citywide crowd flows prediction in fog computing. Multimedia Tools and Applications 80, 20 (Jan. 2021), 31401–31433. https://doi.org/10.1007/s11042-020-10486-4
  6. Exploiting dynamic spatio-temporal graph convolutional neural networks for citywide traffic flows prediction. Neural Networks 145 (Jan. 2022), 233–247. https://doi.org/10.1016/j.neunet.2021.10.021
  7. Trajectory Pattern Mining for Urban Computing in the Cloud. IEEE Transactions on Parallel and Distributed Systems 28, 2 (May 2016), 586–599. https://doi.org/10.1109/TPDS.2016.2565480
  8. Trip destination prediction based on past GPS log using a Hidden Markov Model. Expert Systems with Applications 37, 12 (Dec. 2010), 8166–8171. https://doi.org/10.1016/j.eswa.2010.05.070
  9. CMFog: Proactive Content Migration Using Markov Chain and MADM in Fog Computing. In Proceedings of the 2020 IEEE/ACM 13th International Conference on Utility and Cloud Computing (Leicester, United Kingdom) (UCC ’20). IEEE, New York, NY, USA, 112–121. https://doi.org/10.1109/UCC48980.2020.00030
  10. A Tale of One City: Using Cellular Network Data for Urban Planning. IEEE Pervasive Computing 10, 4 (April 2011), 18–26. https://doi.org/10.1109/MPRV.2011.44
  11. Predictive Replica Placement for Mobile Users in Distributed Fog Data Stores with Client-Side Markov Models. In Proceedings of the 14th IEEE/ACM International Conference on Utility and Cloud Computing Companion (Leicester, United Kingdom) (UCC ’21). ACM, New York, NY, USA, 1–8. https://doi.org/10.1145/3492323.3495595
  12. AuctionWhisk: Using an Auction-Inspired Approach for Function Placement in Serverless Fog Platforms. Software: Practice and Experience 52, 2 (Dec. 2021), 1143–1169. https://doi.org/10.1002/spe.3058
  13. Towards Auction-Based Function Placement in Serverless Fog Platforms. In Proceedings of the Second IEEE International Conference on Fog Computing (Sydney, NSW, Australia) (ICFC 2020). IEEE, New York, NY, USA, 25–31. https://doi.org/10.1109/ICFC49376.2020.00012
  14. A Research Perspective on Fog Computing. In Proceedings of the 2nd Workshop on IoT Systems Provisioning & Management for Context-Aware Smart Cities (Malaga, Spain) (ISYCC 2017). Springer, Cham, Switzerland, 198–210. https://doi.org/10.1007/978-3-319-91764-1_16
  15. Fog computing and its role in the internet of things. In Proceedings of the First Edition of the MCC Workshop on Mobile Cloud Computing (MCC ’12). Association for Computing Machinery, New York, NY, USA, 13–16. https://doi.org/10.1145/2342509.2342513
  16. A Survey of Anticipatory Mobile Networking: Context-Based Classification, Prediction Methodologies, and Optimization Techniques. IEEE Communications Surveys & Tutorials 19, 3 (April 2017), 1790–1821. https://doi.org/10.1109/COMST.2017.2694140
  17. Joe Capka and Raouf Boutaba. 2004. Mobility Prediction in Wireless Networks Using Neural Networks. In Proceedings of the IFIP/IEEE International Conference on Management of Multimedia Networks and Services (San Diego, CA, USA) (MMNS ’04). Springer, Cham, Switzerland, 320–333.
  18. A k𝑘kitalic_k-anonymous approach to privacy preserving collaborative filtering. J. Comput. System Sci. 81, 6 (Sept. 2015), 1000–1011. https://doi.org/10.1016/j.jcss.2014.12.013
  19. End-to-end incremental learning. In Proceedings of the European conference on computer vision (Munich, Germany) (ECCV ’18). Springer, Cham, Switzerland, 241–257. https://doi.org/10.1007/978-3-030-01258-8_15
  20. Ayele Gobezie Chekol and Marta Sintayehu Fufa. 2022. A survey on next location prediction techniques, applications, and challenges. EURASIP Journal on Wireless Communications and Networking, Article 29 (March 2022), 24 pages. https://doi.org/10.1186/s13638-022-02114-6
  21. Context-aware Deep Model for Joint Mobility and Time Prediction. In Proceedings of the 13th International Conference on Web Search and Data Mining (Houston, TX, USA) (WSDM ’20). Association for Computing Machinery, New York, NY, USA, 106–114. https://doi.org/10.1145/3336191.3371837
  22. Mining large-scale smartphone data for personality studies. Personal and Ubiquitous Computing 17, 3 (Dec. 2011), 433–450. https://doi.org/10.1007/s00779-011-0490-1
  23. Evaluating mobility models for temporal prediction with high-granularity mobility data. In Proceedings of the 2012 IEEE International Conference on Pervasive Computing and Communications (Lugano, Switzerland) (PerCom ’12). IEEE, New York, NY, USA, 206–212. https://doi.org/10.1109/PerCom.2012.6199868
  24. John G. Cleary and William J. Teahan. 1997. Unbounded Length Contexts for PPM. Comput. J. 40, 23 (Jan. 1997), 67–75. https://doi.org/10.1093/comjnl/40.2_and_3.67
  25. Inferring friendship network structure by using mobile phone data. Proceedings of the National Academy of Sciences 106, 36 (Sept. 2009), 15274–15278. https://doi.org/10.1073/pnas.0900282106
  26. Proactive and reactive carpooling recommendation system based on spatiotemporal and geosocial data. In Proceedings of the IEEE 12th International Conference on Wireless and Mobile Computing, Networking and Communications (New York, NY, USA) (WiMob ’16). IEEE, New York, NY, USA, 1–8. https://doi.org/10.1109/WiMOB.2016.7763229
  27. Been There, Done That: What Your Mobility Traces Reveal about Your Behavior. In Proceedings of the Mobile Data Challenge 2012 (by Nokia) Workshop (Newcastle, United Kingdom) (MDC).
  28. Modelling disease outbreaks in realistic urban social networks. Nature 429, 6988 (May 2004), 180–184. https://doi.org/10.1038/nature02541
  29. Voilà: Tail-latency-aware fog application replicas autoscaler. In Proceedings of the 28th International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (Nice, France) (MASCOTS ’20). IEEE, New York, NY, USA, 1–8. https://doi.org/10.1109/MASCOTS50786.2020.9285953
  30. Modeling temporal effects of human mobile behavior on location-based social networks. In Proceedings of the 22nd ACM international conference on Information & Knowledge Management (San Francisco, California, USA) (CIKM ’13). Association for Computing Machinery, New York, NY, USA, 1673–1678. https://doi.org/10.1145/2505515.2505616
  31. Győző Gidófalvi and Fang Dong. 2012. When and where next: Individual mobility prediction. In Proceedings of the First ACM SIGSPATIAL International Workshop on Mobile Geographic Information Systems (Redondo Beach, California) (MobiGIS ’12). Association for Computing Machinery, New York, NY, USA, 57–64. https://doi.org/10.1145/2442810.2442821
  32. Proactive Replica Placement Using Mobility Prediction. In Proceedings of the 2008 Ninth International Conference on Mobile Data Management Workshops (Beijing, China) (MDMW ’08). IEEE, New York, NY, USA, 182–189.
  33. Continual Learning for Multivariate Time Series Tasks with Variable Input Dimensions. In Proceedings of the 2021 IEEE International Conference on Data Mining (Auckland, New Zealand) (ICDM). IEEE, New York, NY, USA, 161–170. https://doi.org/10.1109/ICDM51629.2021.00026
  34. FBase: A Replication Service for Data-Intensive Fog Applications. Technical Report. TU Berlin & ECDF, Mobile Cloud Computing Research Group, Berlin, Germany.
  35. Towards A Replication Service for Data-Intensive Fog Applications. In Proceedings of the 35th ACM Symposium on Applied Computing, Posters Track (Brno, Czech Republic) (SAC ’20). ACM, New York, NY, USA, 267–270. https://doi.org/10.1145/3341105.3374060
  36. Gradient flow in recurrent nets: the difficulty of learning long-term dependencies. In A Field Guide to Dynamical Recurrent Neural Networks. IEEE Press, 1–15.
  37. An ensemble of a boosted hybrid of deep learning models and technical analysis for forecasting stock prices. Information Sciences 594 (May 2022), 1–19. https://doi.org/10.1016/j.ins.2022.02.015
  38. A Convolutional Neural Network Approach for Modeling Semantic Trajectories and Predicting Future Locations. In Proceedings of the International Conference on Artificial Neural Networks (Rhodes, Greece) (ICANN ’18). Springer, Cham, Switzerland, 61–72. https://doi.org/10.1007/978-3-030-01418-6_7
  39. Dejiang Kong and Fei Wu. 2018. HST-LSTM: A hierarchical spatial-temporal long-short term memory network for location prediction. In Proceedings of the International Joint Conference on Artificial Intelligence (Stockholm, Sweden) (IJCAI ’18). Association for the Advancement of Artificial Intelligence, Washington, DC, USA, 2341–2347. https://doi.org/10.24963/ijcai.2018/324
  40. Vartika Koolwal and Krishna Kumar Mohbey. 2020. A comprehensive survey on trajectory-based location prediction. Iran Journal of Computer Science 3, 2 (Jan. 2020), 65–91. https://doi.org/10.1007/s42044-019-00052-z
  41. Jong-Kwon Lee and Jennifer C Hou. 2006. Modeling steady-state and transient behaviors of user mobility: formulation, analysis, and application. In Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing (Florence, Italy) (MobiHoc ’06). Association for Computing Machinery, New York, NY, USA, 85–96. https://doi.org/10.1145/1132905.1132915
  42. Trip router with individualized preferences (trip): Incorporating personalization into route planning. In Proceedings of the 18th Conference on Innovative Applications of Artificial Intelligence (IAAI ’06). Association for the Advance of Artificial Intelligence, Washington, DC, USA, 1795–1800.
  43. Zhizhong Li and Derek Hoiem. 2017. Learning without Forgetting. IEEE Transactions on Pattern Analysis and Machine Intelligence 40, 12 (Nov. 2017), 2935–2947. https://doi.org/10.1109/TPAMI.2017.2773081
  44. GeoMAN: Multi-level Attention Networks for Geo-sensory Time Series Prediction. In Proceedings of the 27th International Joint Conference on Artificial Intelligence (Stockholm, Sweden) (IJCAI ’18). Association for the Advancement of Artificial Intelligence, Washington, DC, USA, 3428–3434. https://doi.org/10.24963/ijcai.2018/476
  45. Learning and inferring transportation routines. Artificial intelligence 171, 56 (April 2007), 311–331. https://doi.org/10.1016/j.artint.2007.01.006
  46. Hong-Bin Liu. 2020. Predictive spatio-temporal modelling with neural networks. Ph. D. Dissertation. James Cook University, North Queensland, Australia. Advisor(s) Ickjai Lee. https://doi.org/10.25903/fhnp-g281
  47. Predicting the next location: A recurrent model with spatial and temporal contexts. In Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence (Phoenix, Arizona, USA). Association for the Advancement of Artificial Intelligence, Washington, DC, USA, 194–200. https://doi.org/10.1609/aaai.v30i1.9971
  48. A survey on deep learning for human mobility. Comput. Surveys 55, 1 (Nov. 2021), 1–44. https://doi.org/10.1145/3485125
  49. STAN: Spatio-Temporal Attention Network for Next Location Recommendation. In Proceedings of the Web Conference 2021 (Ljubljana, Slovenia) (WWW ’21). Association for Computing Machinery, New York, NY, USA, 2177–2185. https://doi.org/10.1145/3442381.3449998
  50. T-CONV: A Convolutional Neural Network for Multi-scale Taxi Trajectory Prediction. In Proceedings of the 2018 IEEE International Conference on Big Data and Smart Computing (BigComp) (Shanghai, China) (BigComp ’18). IEEE, New York, NY, USA, 82–89. https://doi.org/10.1109/BigComp.2018.00021
  51. Predicting Future Locations with Hidden Markov Models. In Proceedings of the 2012 ACM Conference on Ubiquitous Computing (Pittsburgh, Pennsylvania) (UbiComp ’12). Association for Computing Machinery, New York, NY, USA, 911–918. https://doi.org/10.1145/2370216.2370421
  52. A Destination Prediction Model based on historical data, contextual knowledge and spatial conceptual maps. In Proceedings of the 2012 IEEE International Conference on Communications (Ottawa, ON, Canada) (ICC ’12). IEEE, New York, NY, USA, 1416–1420.
  53. Personalized location prediction for group travellers from spatial-temporal trajectories. Future Generation Computer Systems 83 (June 2018), 278–292. https://doi.org/10.1016/j.future.2018.01.024
  54. Continual lifelong learning with neural networks: A review. Neural Networks 113 (May 2019), 54–71. https://doi.org/10.1016/j.neunet.2019.01.012
  55. Comparison of Different Methods for Next Location Prediction. In Proceedings of the European Conference on Parallel Processing (Dresden, Germany) (Euro-Par ’06). Springer, Cham, Switzerland, 909–918. https://doi.org/10.1007/11823285_96
  56. Next location prediction within a smart office building. In Proceedings of the 1st International Workshop on Exploiting Context Histories in Smart Environments (Munich, Germany) (ECHISE ’05). Fraunhofer Gesellschaft, Munich, Germany, 69–72.
  57. Prediction of Indoor Movements Using Bayesian Networks. In Proceedings of the International Symposium on Location- and Context-Awareness (Oberpfaffenhofen, Germany) (LoCA ’05). Springer, Cham, Switzerland, 211–222. https://doi.org/10.1007/11426646_20
  58. Tobias Pfandzelter and David Bermbach. 2021. Towards Predictive Replica Placement for Distributed Data Stores in Fog Environments. In Proceedings of the 9th IEEE International Conference on Cloud Engineering, Posters (San Francisco, CA, USA) (IC2E 2021). IEEE, New York, NY, USA, 280–281. https://doi.org/10.1109/IC2E52221.2021.00047
  59. Managing Data Replication and Distribution in the Fog with FReD. (March 2023). arXiv:2303.05256
  60. Bhaskar Prabhala and Thomas La Porta. 2015. Spatial and temporal considerations in next place predictions. In Proceedings of the 2015 IEEE Conference on Computer Communications Workshops (Hong Kong, China) (INFOCOM WKSHPS ’15). IEEE, New York, NY, USA, 390–395.
  61. Saishankar Katri Pulliyakode and Sheetal Kalyani. 2014. A Modified PPM Algorithm for Online Sequence Prediction Using Short Data Records. IEEE Communications Letters 19, 3 (Dec. 2014), 423–426. https://doi.org/10.1109/LCOMM.2014.2385088
  62. A hybrid Markov-based model for human mobility prediction. Neurocomputing 278 (Feb. 2018), 99–109. https://doi.org/10.1016/j.neucom.2017.05.101
  63. Probabilistic Social Sequential Model for Tour Recommendation. In Proceedings of the Tenth ACM International Conference on Web Search and Data Mining (Cambridge, United Kingdom) (WSDM ’17). Association for Computing Machinery, New York, NY, USA, 631–640. https://doi.org/10.1145/3018661.3018711
  64. Synthesizing Plausible Infrastructure Configurations for Evaluating Edge Computing Systems. In Proceedings of the 3rd USENIX Workshop on Hot Topics in Edge Computing (HotEdge ’20). USENIX Association, Berkeley, CA, USA.
  65. Cellular Census: Explorations in Urban Data Collection. IEEE Pervasive computing 6, 3 (Aug. 2007), 30–38. https://doi.org/10.1109/MPRV.2007.53
  66. Factorizing personalized Markov chains for next-basket recommendation. In Proceedings of the 19th international conference on World wide web (Raleigh, NC, USA) (WWW ’10). Association for Computing Machinery, New York, NY, USA, 811–820. https://doi.org/10.1145/1772690.1772773
  67. Performance Evaluation of LZ-Based Location Prediction Algorithms in Cellular Networks. IEEE Communications Letters 14, 8 (Aug. 2010), 707–709. https://doi.org/10.1109/LCOMM.2010.08.092033
  68. An Overview of Service Placement Problem in Fog and Edge Computing. Comput. Surveys 53, 3 (June 2020), 1–35. https://doi.org/10.1145/3391196
  69. Next Place Prediction: A Systematic Literature Review. In Proceedings of the 2nd ACM SIGSPATIAL Workshop on Prediction of Human Mobility (Seattle, WA, USA) (PredictGIS ’18). Association for Computing Machinery, New York, NY, USA, 37–45. https://doi.org/10.1145/3283590.3283596
  70. Learning to Predict Driver Route and Destination Intent. In Proceedings of the 2006 IEEE Intelligent Transportation Systems Conference (Toronto, ON, Canada) (ITSC ’06). IEEE, New York, NY, USA, 127–132. https://doi.org/10.1109/ITSC.2006.1706730
  71. Smart health: A context-aware health paradigm within smart cities. IEEE Communications Magazine 52, 8 (Aug. 2014), 74–81. https://doi.org/10.1109/MCOM.2014.6871673
  72. Predictability of WLAN Mobility and Its Effects on Bandwidth Provisioning. In Proceedings of the 25TH IEEE International Conference on Computer Communications (Barcelona, Spain) (INFOCOM ’06). IEEE, New York, NY, USA, 1–13. https://doi.org/10.1109/INFOCOM.2006.171
  73. Mobility Prediction Scheme for Optimized Load Balance in Heterogeneous Networks. In Proceedings of the IEEE Globecom Workshops (Abu Dhabi, United Arab Emirates) (GC Wkshps ’18). IEEE, New York, NY, USA, 1–6. https://doi.org/10.1109/GLOCOMW.2018.8644289
  74. Spatio-Temporal Position Prediction Model for Mobile Users Based on LSTM. In Proceedings of the 2019 IEEE 25th International Conference on Parallel and Distributed Systems (Tianjin, China) (ICPADS). IEEE, New York, NY, USA, 967–970. https://doi.org/10.1109/ICPADS47876.2019.00146
  75. Data replica placement approaches in fog computing: a review. Cluster Computing 25 (April 2022), 3561–3589. https://doi.org/10.1007/s10586-022-03575-6
  76. Gido M. van de Ven and Andreas S. Tolias. 2019. Three scenarios for continual learning. (April 2019). arXiv:1904.07734
  77. Daksh Varshneya and G. Srinivasaraghavan. 2017. Human Trajectory Prediction using Spatially aware Deep Attention Models. (May 2017). arXiv:1705.09436
  78. Deep Learning for Spatio-Temporal Data Mining: A Survey. IEEE transactions on knowledge and data engineering 34, 8 (Sept. 2020), 3681–3700. https://doi.org/10.1109/TKDE.2020.3025580
  79. Ying Zhu Yong Sun Yu Wang. 2012. Nokia mobile data challenge: Predicting semantic place and next place via mobile data. In Proceedings of the Mobile Data Challenge 2012 (by Nokia) Workshop (Newcastle, United Kingdom) (MDC). Nokia Research, Helsinki, Finland.
  80. Peter R Winters. 1960. Forecasting Sales by Exponentially Weighted Moving Averages. Management Science 6, 3 (April 1960), 324–342. https://doi.org/10.1287/mnsc.6.3.324
  81. Modeling the Intensity Function of Point Process Via Recurrent Neural Networks. In Proceedings of the 31st AAAI Conference on Artificial Intelligence (San Francisco, California, USA) (AAAI ’17). Association for the Advancement of Artificial Intelligence, Washington, DC, USA, 1597–1603. https://doi.org/10.1609/aaai.v31i1.10724
  82. Spatio-temporal check-in time prediction with recurrent neural network based survival analysis. In Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence (Stockholm, Sweden) (IJCAI-ECAI ’18). Association for the Advancement of Artificial Intelligence, Washington, DC, USA, 2976–2983. https://doi.org/10.24963/ijcai.2018/413
  83. What you are is when you are: the temporal dimension of feature types in location-based social networks. In Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (Chicago, IL, USA) (GIS ’11). Association for Computing Machinery, New York, NY, USA, 102–111. https://doi.org/10.1145/2093973.2093989
  84. Exploiting geographical influence for collaborative point-of-interest recommendation. In Proceedings of the 34th international ACM SIGIR conference on Research and development in Information Retrieval (Beijing, China) (SIGIR ’11). Association for Computing Machinery, New York, NY, USA, 325–334. https://doi.org/10.1145/2009916.2009962
  85. Mining geographic-temporal-semantic patterns in trajectories for location prediction. ACM Transactions on Intelligent Systems and Technology 5, 1 (Jan. 2014), 1–33. https://doi.org/10.1145/2542182.2542184
  86. Predicting the next location: A self-attention and recurrent neural network model with temporal context. Transactions on Emerging Telecommunications Technologies 32, 6 (March 2021). https://doi.org/10.1002/ett.3898
  87. Where to Go Next: A Spatio-Temporal Gated Network for Next POI Recommendation. IEEE Transactions on Knowledge and Data Engineering 34, 5 (July 2020), 2512–2524. https://doi.org/10.1109/TKDE.2020.3007194
  88. A time-aware trajectory embedding model for next-location recommendation. Knowledge and Information Systems 56, 3 (Oct. 2017), 559–579. https://doi.org/10.1007/s10115-017-1107-4
  89. Understanding mobility based on GPS data. In Proceedings of the 10th international conference on Ubiquitous computing (Seoul, Korea) (UbiComp ’08). Association for Computing Machinery, New York, NY, USA, 312–321. https://doi.org/10.1145/1409635.1409677
  90. GeoLife: A collaborative social networking service among user, location and trajectory. IEEE Data Engineering Bulletin 33, 2 (June 2010), 32–39.
  91. Mining interesting locations and travel sequences from GPS trajectories. In Proceedings of the 18th international conference on World wide web (Madrid, Spain) (WWW ’09). Association for Computing Machinery, New York, NY, USA, 791–800. https://doi.org/10.1145/1526709.1526816
  92. Context-based prediction for road traffic state using trajectory pattern mining and recurrent convolutional neural networks. Information Sciences 473 (Jan. 2019), 190–201. https://doi.org/10.1016/j.ins.2018.09.029

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