, Beta, vol.1, issue.22521

, Inv-Gamma, vol.3, issue.2

, ) Gamma(0.5, 2) Weibull

, Inv-Gamma

]. S. Abrishami, M. Naghibzadeh, and D. H. Epema, Deadline-constrained workflow scheduling algorithms for Infrastructure as a Service Clouds, Future Generation Computer Systems, vol.29, issue.1, pp.158-169, 2013.
DOI : 10.1016/j.future.2012.05.004

M. Amirijoo, J. Hansson, and S. H. Son, Specification and management of QoS in real-time databases supporting imprecise computations, IEEE Transactions on Computers, vol.55, issue.3, pp.304-319, 2006.
DOI : 10.1109/TC.2006.45

V. Arabnejad, K. Bubendorfer, and B. Ng, Budget distribution strategies for scientific workflow scheduling in commercial clouds, 2016 IEEE 12th International Conference on e-Science (e-Science), pp.137-146, 2016.
DOI : 10.1109/eScience.2016.7870894

M. U. Bokhari, Q. Makki, and Y. K. Tamandani, A Survey on Cloud Computing, Big Data Analytics of Advances in Intelligent Systems and Computing, 2018.
DOI : 10.1109/EMEIT.2011.6023923

G. Buttazzo, Handling overload conditions in real-time systems, Real-Time Systems, Architecture, Scheduling, and Application

E. Byun, Y. Kee, J. Kim, and S. Maeng, Cost optimized provisioning of elastic resources for application workflows, Future Generation Computer Systems, vol.27, issue.8, pp.1011-1026, 2011.
DOI : 10.1016/j.future.2011.05.001

R. N. Calheiros and R. Buyya, Meeting Deadlines of Scientific Workflows in Public Clouds with Tasks Replication, IEEE Transactions on Parallel and Distributed Systems, vol.25, issue.7, pp.1787-1796, 2014.
DOI : 10.1109/TPDS.2013.238

Y. Caniou, E. Caron, A. K. Chang, and Y. Robert, Budgetaware scheduling algorithms for scientific workflows with stochastic task weights on heterogeneous iaas cloud platforms, 27th International Heterogeneity in Computing Workshop HCW 2013, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01808831

L. Canon, A. Kong-win-chang, F. Vivien, and Y. Robert, Code for scheduling independent stochastic tasks under deadline and budget constraints, 2018.

H. Casanova, M. Gallet, and F. Vivien, Non-clairvoyant Scheduling of Multiple Bag-of-Tasks Applications, Euro-Par 2010 -Parallel Processing , 16th International Euro-Par Conference, pp.168-179, 2010.
DOI : 10.1142/S0129054105002930

URL : https://hal.archives-ouvertes.fr/inria-00527111

J. Y. Chung, J. W. Liu, and K. J. Lin, Scheduling periodic jobs that allow imprecise results, IEEE Transactions on Computers, vol.39, issue.9, pp.1156-1174, 1990.
DOI : 10.1109/12.57057

H. M. Fard, R. Prodan, and T. Fahringer, A Truthful Dynamic Workflow Scheduling Mechanism for Commercial Multicloud Environments, IEEE Transactions on Parallel and Distributed Systems, vol.24, issue.6, pp.1203-1212, 2013.
DOI : 10.1109/TPDS.2012.257

D. Feitelson, Workload modeling for computer systems performance evaluation, pp.1-607, 2014.
DOI : 10.1017/CBO9781139939690

W. Feng and J. W. Liu, An extended imprecise computation model for time-constrained speech processing and generation, [1993] Proceedings of the IEEE Workshop on Real-Time Applications, pp.76-80, 1993.
DOI : 10.1109/RTA.1993.263112

T. S. Ferguson, Optimal stopping and applications, 2008.

Y. Gao, Y. Wang, S. K. Gupta, and M. Pedram, An energy and deadline aware resource provisioning, scheduling and optimization framework for cloud systems, 2013 International Conference on Hardware/Software Codesign and System Synthesis (CODES+ISSS), 2013.
DOI : 10.1109/CODES-ISSS.2013.6659018

A. Grekioti and N. V. Shakhlevich, Scheduling Bag-of-Tasks Applications to Optimize Computation Time and Cost, Parallel Processing and Applied Mathematics. PPAM 2013, 2014.
DOI : 10.1007/978-3-642-55195-6_1

H. Hassan, J. Simó, and A. Crespo, Flexible real-time mobile robotic architecture based on behavioural models, Engineering Applications of Artificial Intelligence, vol.14, issue.5, pp.685-702, 2001.
DOI : 10.1016/S0952-1976(01)00029-X

E. Hwang and K. H. Kim, Minimizing Cost of Virtual Machines for Deadline-Constrained MapReduce Applications in the Cloud, 2012 ACM/IEEE 13th International Conference on Grid Computing, pp.130-138, 2012.
DOI : 10.1109/Grid.2012.19

F. Jumel and F. Simonot-lion, Management of anytime tasks in real time applications, XIV Workshop on Supervising and Diagnostics of Machining Systems, Karpacz/Pologne, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00099612

H. Kobayashi and N. Yamasaki, RT-frontier: a real-time operating system for practical imprecise computation, Proceedings. RTAS 2004. 10th IEEE Real-Time and Embedded Technology and Applications Symposium, 2004., pp.255-264, 2004.
DOI : 10.1109/RTTAS.2004.1317271

J. W. Liu, K. J. Lin, W. K. Shih, A. C. Yu, J. Y. Chung et al., Algorithms for scheduling imprecise computations, Foundations of Real-Time Computing: Scheduling and Resource Management, pp.203-249, 1991.
DOI : 10.1007/978-1-4615-3956-8_8

URL : http://counter.cs.umd.edu/~rich/courses/cmsc818G-s98/papers/liu_imprecise.ps

K. Liu, H. Jin, J. Chen, X. Liu, D. Yuan et al., A Compromised-Time-Cost Scheduling Algorithm in SwinDeW-C for Instance-Intensive Cost-Constrained Workflows on a Cloud Computing Platform, The International Journal of High Performance Computing Applications, vol.24, issue.4, pp.445-456, 2010.
DOI : 10.1155/2006/271608

M. Malawski, G. Juve, E. Deelman, and J. Nabrzyski, Cost-and deadline-constrained provisioning for scientific workflow ensembles in iaas clouds, High Performance Computing, Networking, Storage and Analysis (SC), 2012 International Conference for, pp.1-11, 2012.
DOI : 10.1109/sc.2012.38

URL : http://pegasus.isi.edu/publications/2012/Malawski-Ensemble.pdf

M. Malawski, G. Juve, E. Deelman, and J. Nabrzyski, Algorithms for cost- and deadline-constrained provisioning for scientific workflow ensembles in IaaS clouds, Future Generation Computer Systems, vol.48, pp.1-18, 2015.
DOI : 10.1016/j.future.2015.01.004

URL : https://manuscript.elsevier.com/S0167739X15000059/pdf/S0167739X15000059.pdf

M. Mao, J. Li, and M. Humphrey, Cloud auto-scaling with deadline and budget constraints, 11th IEEE/ACM International Conference on Grid Computing, pp.41-48, 2010.
DOI : 10.18130/v31b83

URL : https://libraetd.lib.virginia.edu/downloads/jh343s65j?filename=dissertation.pdf

J. Meng, S. Chakradhar, and A. Raghunathan, Best-effort parallel execution framework for recognition and mining applications, 2009 IEEE International Symposium on Parallel Distributed Processing, pp.1-12, 2009.

R. Nelson, Probability, stochastic processes, and queueing theory: the mathematics of computer performance modeling, 1995.
DOI : 10.1007/978-1-4757-2426-4

A. M. Oprescu and T. Kielmann, Bag-of-Tasks Scheduling under Budget Constraints, 2010 IEEE Second International Conference on Cloud Computing Technology and Science, pp.351-359, 2010.
DOI : 10.1109/CloudCom.2010.32

URL : http://www.cs.vu.nl/%7Ekielmann/papers/bats.pdf

A. Oprescu, T. Kielmann, and H. Leahu, BUDGET ESTIMATION AND CONTROL FOR BAG-OF-TASKS SCHEDULING IN CLOUDS, Parallel Processing Letters, vol.21, issue.02, pp.219-243, 2011.
DOI : 10.1177/1094342010369114

A. M. Oprescu, T. Kielmann, and H. Leahu, Stochastic Tail-Phase Optimization for Bag-of-Tasks Execution in Clouds, 2012 IEEE Fifth International Conference on Utility and Cloud Computing, pp.204-208, 2012.
DOI : 10.1109/UCC.2012.23

URL : http://www.cs.vu.nl/~kielmann/papers/ucc2012.pdf

D. Poola, S. K. Garg, R. Buyya, Y. Yang, and K. Ramamohanarao, Robust Scheduling of Scientific Workflows with Deadline and Budget Constraints in Clouds, 2014 IEEE 28th International Conference on Advanced Information Networking and Applications, pp.858-865, 2014.
DOI : 10.1109/AINA.2014.105

URL : http://www.cloudbus.org/~raj/papers/Cloud-WorkflowSched-AINA2014.pdf

S. Singh and I. Chana, Cloud resource provisioning: survey, status and future research directions, Knowledge and Information Systems, vol.46, issue.4, pp.1005-1069, 2016.
DOI : 10.1109/ICICICT.2014.6781244

S. Singh and I. Chana, A Survey on Resource Scheduling in Cloud Computing: Issues and Challenges, Journal of Grid Computing, vol.9, issue.4, pp.217-264, 2016.
DOI : 10.1007/s10723-011-9196-x

F. Tian and K. Chen, Towards Optimal Resource Provisioning for Running MapReduce Programs in Public Clouds, 2011 IEEE 4th International Conference on Cloud Computing, pp.155-162, 2011.
DOI : 10.1109/CLOUD.2011.14

URL : http://www.cs.wright.edu/%7Ekeke.chen/papers/predict-mr.pdf

C. Vecchiola, R. N. Calheiros, D. Karunamoorthy, and R. Buyya, Deadline-driven provisioning of resources for scientific applications in hybrid clouds with Aneka, Future Generation Computer Systems, vol.28, issue.1, pp.58-65, 2012.
DOI : 10.1016/j.future.2011.05.008

C. Q. Wu, X. Lin, D. Yu, W. Xu, and L. Li, End-to-End Delay Minimization for Scientific Workflows in Clouds under Budget Constraint, IEEE Transactions on Cloud Computing, vol.3, issue.2, pp.169-181, 2015.
DOI : 10.1109/TCC.2014.2358220

R. N°-9178 and R. Inovallée,