Discrete-event stochastic systems with correlated inputs: Modeling and performance evaluation

Weimin DAI, Jian-Qiang HU, Lei LEI

PDF(437 KB)
PDF(437 KB)
Front. Eng ›› 2022, Vol. 9 ›› Issue (2) : 214-220. DOI: 10.1007/s42524-022-0192-6
REVIEW ARTICLE
REVIEW ARTICLE

Discrete-event stochastic systems with correlated inputs: Modeling and performance evaluation

Author information +
History +

Abstract

In the majority of the previous works on discrete-event stochastic systems, they have been assumed to have independent input processes. However, in many applications, these input processes can be highly correlated. Furthermore, the performance measures of the systems with correlated inputs can be significantly different from those with independent inputs. In this paper, we provide an overview on some commonly used methods for modeling correlated input processes, and we discuss the difficulties and possible future research topics in the study of discrete-event stochastic systems with correlated inputs.

Keywords

discrete-event stochastic system / correlated input / performance evaluation

Cite this article

Download citation ▾
Weimin DAI, Jian-Qiang HU, Lei LEI. Discrete-event stochastic systems with correlated inputs: Modeling and performance evaluation. Front. Eng, 2022, 9(2): 214‒220 https://doi.org/10.1007/s42524-022-0192-6

References

[1]
Altiok,T Melamed,B 2001. The case for modeling correlation in manufacturing systems. IIE Transactions, 33( 9): 779– 791
CrossRef Google scholar
[2]
Bardsley,E 2017. A finite mixture approach to univariate data simulation with moment matching. Environmental Modelling & Software, 90: 27– 33
CrossRef Google scholar
[3]
Biller,B 2009. Copula-based multivariate input models for stochastic simulation. Operations Research, 57( 4): 878– 892
CrossRef Google scholar
[4]
Biller,B Gunes Corlu,C 2012. Copula-based multivariate input modeling. Surveys in Operations Research and Management Science, 17( 2): 69– 84
CrossRef Google scholar
[5]
Biller,B Nelson,B L 2003. Modeling and generating multivariate time-series input processes using a vector autoregressive technique. ACM Transactions on Modeling and Computer Simulation, 13( 3): 211– 237
CrossRef Google scholar
[6]
Biller,B Nelson,B L 2008. Evaluation of the ARTAFIT method for fitting time-series input processes for simulation. INFORMS Journal on Computing, 20( 3): 485– 498
CrossRef Google scholar
[7]
BoxG E JenkinsG M ReinselG C LjungG M (1970). Time Series Analysis: Forecasting and Control. Hoboken, NJ: John Wiley & Sons
[8]
Cario,M C Nelson,B L 1998. Numerical methods for fitting and simulating autoregressive-to-anything processes. INFORMS Journal on Computing, 10( 1): 72– 81
CrossRef Google scholar
[9]
Carrizosa,E Olivares-Nadal,A V Ramírez-Cobo,P 2016. Robust newsvendor problem with autoregressive demand. Computers & Operations Research, 68: 123– 133
CrossRef Google scholar
[10]
CesarJ V R (2015). Markovian Arrival Processes: The Identifiability Issue and Other Applied Aspects. Dissertation for the Doctoral Degree. Leganés: Universidad Carlos III de Madrid
[11]
Choi,D I Kim,T S Lee,S 2008. Analysis of an MMPP/G/1/K queue with queue length dependent arrival rates, and its application to preventive congestion control in telecommunication networks. European Journal of Operational Research, 187( 2): 652– 659
CrossRef Google scholar
[12]
Darsow,W F Nguyen,B Olsen,E T 1992. Copulas and Markov processes. Illinois Journal of Mathematics, 36( 4): 600– 642
CrossRef Google scholar
[13]
Diaz,R Bailey,M P Kumar,S 2016. Analyzing a lost-sale stochastic inventory model with Markov-modulated demands: A simulation-based optimization study. Journal of Manufacturing Systems, 38: 1– 12
CrossRef Google scholar
[14]
Embrechts,P 2009. Copulas: A personal view. Journal of Risk and Insurance, 76( 3): 639– 650
CrossRef Google scholar
[15]
Fischer,W Meier-Hellstern,K 1993. The Markov-modulated Poisson process (MMPP) cookbook. Performance Evaluation, 18( 2): 149– 171
CrossRef Google scholar
[16]
Frey,R McNeil,A 2003. Dependent defaults in models of portfolio credit risk. Journal of Risk, 6( 1): 59– 92
CrossRef Google scholar
[17]
Gaur,V Giloni,A Seshadri,S 2005. Information sharing in a supply chain under ARMA demand. Management Science, 51( 6): 961– 969
CrossRef Google scholar
[18]
Giloni,A Hurvich,C Seshadri,S 2014. Forecasting and information sharing in supply chains under ARMA demand. IIE Transactions, 46( 1): 35– 54
CrossRef Google scholar
[19]
Girish M K, Hu J Q (1999). Modeling of correlated arrival processes in the Internet. In: Proceedings of the 38th IEEE Conference on Decision and Control. Phoenix, AZ, 4454–4459
[20]
Gong,W B Hu,J Q 1992. The MacLaurin series for the GI/G/1 queue. Journal of Applied Probability, 29( 1): 176– 184
CrossRef Google scholar
[21]
Hu,J Q 1996. The departure process of the GI/G/1 queue and its MacLaurin series. Operations Research, 44( 5): 810– 815
CrossRef Google scholar
[22]
Hu,J Q Zhang,C Zhu,C B 2016. (s, S) inventory systems with correlated demands. INFORMS Journal on Computing, 28( 4): 603– 611
CrossRef Google scholar
[23]
Ibragimov,R 2009. Copula-based characterizations for higher order Markov processes. Econometric Theory, 25( 3): 819– 846
CrossRef Google scholar
[24]
Jagerman,D L Melamed,B 1992. The transition and autocorrelation structure of TES processes. Communications in Statistics: Stochastic Models, 8( 2): 193– 219
CrossRef Google scholar
[25]
Jaoua,A L’Ecuyer,P Delorme,L 2013. Call-type dependence in multiskill call centers. Simulation, 89( 6): 722– 734
CrossRef Google scholar
[26]
Kugiumtzis,D Bora-Senta,E 2014. Simulation of multivariate non-Gaussian autoregressive time series with given autocovariance and marginals. Simulation Modelling Practice and Theory, 44: 42– 53
CrossRef Google scholar
[27]
Kuhl,M E Ivy,J S Lada,E K Steiger,N M Wagner,M A Wilson,J R 2010. Univariate input models for stochastic simulation. Journal of Simulation, 4( 2): 81– 97
CrossRef Google scholar
[28]
Lee,H L Padmanabhan,V Whang,S 1997. Information distortion in a supply chain: The bullwhip effect. Management Science, 43( 4): 546– 558
CrossRef Google scholar
[29]
Lee,H L So,K C Tang,C S 2000. The value of information sharing in a two-level supply chain. Management Science, 46( 5): 626– 643
CrossRef Google scholar
[30]
Lei,L Hu,J Q Zhu,C B 2022. Discrete-event stochastic systems with copula correlated input processes. IISE Transactions, 54: 321– 331
CrossRef Google scholar
[31]
Lim,S Y Hur,S Noh,S J 2006. Departure process of a single server queuing system with Markov renewal input and general service time distribution. Computers & Industrial Engineering, 51( 3): 519– 525
CrossRef Google scholar
[32]
Livny,M Melamed,B Tsiolis,A K 1993. The impact of autocorrelation on queuing systems. Management Science, 39( 3): 322– 339
CrossRef Google scholar
[33]
Lucantoni,D M 1991. New results on the single server queue with a batch Markovian arrival process. Communications in Statistics:Stochastic Models, 7( 1): 1– 46
CrossRef Google scholar
[34]
Marshall,A W Olkin,I 1988. Families of multivariate distributions. Journal of the American Statistical Association, 83( 403): 834– 841
CrossRef Google scholar
[35]
Melamed,B 1991. TES: A class of methods for generating autocorrelated uniform variates. ORSA Journal on Computing, 3( 4): 317– 329
CrossRef Google scholar
[36]
MelamedB (1993). An overview of TES processes and modeling methodology. In: Donatiello L, Nelson R, eds. Performance Evaluation of Computer and Communication Systems. Berlin, Heidelberg: Springer, 359– 393
[37]
Melamed,B Hill,J R 1995. A survey of TES modeling applications. Simulation, 64( 6): 353– 370
CrossRef Google scholar
[38]
NelsenR B (2006). An Introduction to Copulas. 2nd ed. New York, NY: Springer Science & Business Media
[39]
Neuts,M F 1979. A versatile Markovian point process. Journal of Applied Probability, 16( 4): 764– 779
CrossRef Google scholar
[40]
Patuwo,B E Disney,R L McNickle,D C 1993. The effect of correlated arrivals on queues. IIE Transactions, 25( 3): 105– 110
CrossRef Google scholar
[41]
Pereira D C, del Rio Vilas D, Monteil N R, Prado R R, del Valle A G (2012). Autocorrelation effects in manufacturing systems performance: A simulation analysis. In: Proceedings of the Winter Simulation Conference (WSC). Berlin: IEEE, 1–12
[42]
Runnenburg,J T 1962. Some numerical results on waiting-time distributions for dependent arrival-intervals. Statistica Neerlandica, 16( 4): 337– 347
CrossRef Google scholar
[43]
Shang,K H 2012. Single-stage approximations for optimal policies in serial inventory systems with nonstationary demand. Manufacturing & Service Operations Management, 14( 3): 414– 422
CrossRef Google scholar
[44]
Szekli,R Disney,R L Hur,S 1994. MR/GI/1 queues by positively correlated arrival stream. Journal of Applied Probability, 31( 2): 497– 514
CrossRef Google scholar
[45]
Zhang,X 2004. Technical note: Evolution of ARMA demand in supply chains. Manufacturing & Service Operations Management, 6( 2): 195– 198
CrossRef Google scholar
[46]
Zhu,Y Li,H 1993. The MacLaurin expansion for a G/G/1 queue with Markov-modulated arrivals and services. Queuing Systems, 14( 1–2): 125– 134
CrossRef Google scholar

RIGHTS & PERMISSIONS

2022 Higher Education Press
AI Summary AI Mindmap
PDF(437 KB)

Accesses

Citations

Detail

Sections
Recommended

/