Hierarchical modeling of stochastic manufacturing and service systems
Zhe George ZHANG, Xiaoling YIN
Hierarchical modeling of stochastic manufacturing and service systems
This paper presents a review of methodologies for analyzing stochastic manufacturing and service systems. On the basis of the scale and level of details of operations, we can study stochastic systems using micro-, meso-, and macro-scopic models. Such a classification unifies stochastic modeling theory. For each model type, we highlight the advantages and disadvantages and the applicable situations. Micro-scopic models are based on quasi-birth-and-death process because of the phase-type distributed service times and/or Markov arrival processes. Such models are appropriate for modeling the detailed operations of a manufacturing system with relatively small number of servers (production facilities). By contrast, meso-scopic and macro-scopic models are based on the functional central limit theorem (FCLT) and functional strong law of large numbers (FSLLN), respectively, under heavy-traffic regimes. These high-level models are appropriate for modeling large-scale service systems with many servers, such as call centers or large service networks. This review will help practitioners select the appropriate level of modeling to enhance their understanding of the dynamic behavior of manufacturing or service systems. Enhanced understanding will ensure that optimal policies can be designed to improve system performance. Researchers in operation analytics and optimization of manufacturing and logistics also benefit from such a review.
stochastic modeling / QBD process / PH distribution / heavy traffic limits / diffusion process
[1] |
Buzacott J A, Shanthikumar J G (1993). Stochastic Models of Manufacturing Systems. New York: Prentice Hall
|
[2] |
Chen H, Mandelbaum A (1994). Stochastic modeling and analysis of manufacturing systems. In: Yao D D, ed. Operations Research. Berlin: Springer
|
[3] |
Chen H, Yao D (2001). Fundamentals of Queueing Networks, Performance, Asymptotics, and Optimization. New York: Springer
|
[4] |
Gautam N (2012). Analysis of Queues. New York: CRC Press
|
[5] |
Halfin S, Whitt W (1981). Heavy-traffic limits for queues with many exponential servers. Operations Research, 29(3): 567–588
CrossRef
Google scholar
|
[6] |
He Q (2014). Fundamentals of Matrix-Analytic Methods. New York: Springer
|
[7] |
Jia Y, Zhang Z G, Tang L (2017). Modeling hot rolling process in steel industry by M/PH/c queues. Working paper. Simon Fraser University, WP0170056
|
[8] |
Koole G, Mandelbaum A (2002). Queueing models of call centers: An introduction. Annals of Operations Research, 113(1–4): 41–59
CrossRef
Google scholar
|
[9] |
Latouche G, Ramaswami V (1999). Introduction to Matrix Geometric Methods in Stochastic Modeling. Philadelphia: SIAM
|
[10] |
Neuts M F (1981). Matrix-Geometric Solutions in Stochastic. New York: Dover Publications
|
[11] |
Whitt W (2002). Stochastic Process Limits. New York: Springer
|
[12] |
Whitt W (2004). Efficiency-driven heavy-traffic approximations for many-server queues with abandonments. Management Science, 50(10): 1449–1461
CrossRef
Google scholar
|
[13] |
Whitt W (2005). Two fluid approximations for multi-server queues with abandonments. Operations Research Letters, 33(4): 363– 372
CrossRef
Google scholar
|
[14] |
Whitt W (2006). Fluid models for multiserver queues with abandonments. Operations Research, 54(1): 37–54
CrossRef
Google scholar
|
/
〈 | 〉 |