Prediction and Optimization for a Non-preemptive Priority Retrial Queueing Inventory System using Artificial Neural Network and Genetic Algorithm

使用類神經網路及基因演算法預測及優化非先佔優先權式重試佇列存貨系統

王風帆(Fong-Fan Wang)

Retrial queueing inventory ； Neural network ； Genetic algorithm ； 重試隊列存貨系統 ； 類神經網路 ； 基因演算法

修平學報

36期（2018 / 03 / 01）

1 - 29

英文

Some queueing systems such as vacation model, retrial queue and polling system are complex and hard to derive performance measures using mathematical approaches. Simulation may be a better choice due to its simplicity in model build-up. However, simulation is notorious for very time-consuming, not to speak that it may not be easy to optimize continuous variables. A non-preemptive priority retrial inventory queueing system, which is complex in nature in terms of operating logic and calculation procedure, is used as a test bed for a new approach. Assuming Markovian, we first derive the performance measures and observe their behavior when system parameter values are changed. Then we use artificial neural network and integrated genetic algorithm and artificial neural network to predict and optimize the system respectively. Numerical results show the proposed method is satisfactory.

對於複雜等候系統例如假期模式、重試佇列或輪詢系統數學建模有時很困難，尤其是非馬可夫模式更是困難，一般都是依靠模擬求得系統績效，但是模擬耗時且不容易進行連續參數優化，若有其他可快速得知系統績效及優化連續參數的方法，相信有其實用價值。非先佔優先權式重試佇列存貨系統因具備複雜運作邏輯及複雜數學運算特性，很適合使用類似類神經網路之超模式方式預測及優化。本研究首先在馬可夫模式假設下，使用複雜數學求得系統績效，並觀察系統參數改變對績效的影響。接著測試所提方法適切性，使用類神經網路計算預測與實際誤差，以基因演算法搭配類神經網路優化連續型系統參數，並與商業套裝軟體執行輸出比較，結果顯示所提預測及尋優方法有令人滿意結果。

1. Artalejo, J. R.,Gómez-Corral, A.(2008).Retrial queueing systems.Berlin:Springer-Verlag.
2. Artalejo, J. R.,Orlovsky, D. S.,Dudin, A.N.(2005).Multi-server retrial model with variable number of active servers.Computers & Industrial Engineering,48(2),273-288.
3. Azadeh, A.,Faiz, Z. S.,Asadzadeh, S.M.,Tavakkoli-Moghaddam, R.(2011).An integrated artificial neural network-computer simulation for optimization of complex tandem queue systems.Mathematics and Computers in Simulation,82(4),666-678.
4. Berman, O.,Kim, E.(1999).Stochastic models for inventory management at service facilities.Stochastic Models,15(4),695-718.
5. Chakravarthy, S. R.,Krishnamoorthy, A.,Joshua, V. C.(2006).Analysis of a multi-server retrial queue with search of customers from the orbit.Performance Evaluation,63(8),776-798.
6. Chambers, M.,Mount-Campbell, C. A.(2002).Process optimization via neural network metamodeling.International Journal of Production Economics,79(2),93-100.
7. Falin, G. I.,Templeton, J. G. C.(1997).Retrial Queues.London:Chapman and Hall.
8. Guh, R. S.,Hsieh, Y. C.(1999).A neural network based model for abnormal pattern recognition of control charts.Computers & Industrial Engineering,36(1),97-108.
9. Hah, J. M.,Tien, P. L.,Yuang, M. C.(1997).Neural-network-based call admission control in ATM networks with heterogeneous arrivals.Computer Communications,20(9),732-740.
10. Hernández-Díaz, A. G.,Moreno, P.(2009).A discrete-time single-server queueing system with an N-policy, an early setup and a generalization of the Bernoulli feedback.Mathematical and Computer Modelling,49(5-6),977-990.
11. Holland, J. H.(1975).Adaptation in natural and artificial systems.The University of Michigan Press.
12. Huang, H. I.,Hsu, P. C.,Ke, J. C.(2011).Controlling arrival and service of a two-removable-server system using genetic algorithm.Expert Systems with Applications,38(8),10054-10059.
13. Ke, J. C.,Wu, C. H.,Pearn, W. L.(2013).Analysis of an infinite multi-server queue with an optional service.Computers & Industrial Engineering,65(2),216-225.
14. Krishnamoorthy, A.,Jose, K. P.(2007).Comparison of inventory systems with service, positive lead-time, loss, and retrial of customers.Journal of Applied Mathematics and Stochastic Analysis,37848.
15. Krishnamoorthy, A.,Narayanan, V. C.,Deepak, T. G.,Vineetha, P.(2006).Control policies for inventory with service time.Stochastic Analysis and Applications,24(4),889-899.
16. Lin, C. H.,Ke, J. C.(2010).Genetic algorithm for optimal thresholds of an infinite capacity multi-server system with triadic policy.Expert Systems with Applications,37(6),4276-4282.
17. Lindfield, G. R.,Penny, J. E. T.(2012).Numerical Methods using MATLAB, electronic resource.Academic Press.
18. Neuts, M. F.(1994).Matrix-Geometric Solutions in Stochastic Models.N.Y.:Dover Publications, Inc..
19. Su, C. T.(2013).Quality Engineering: Off-line methods and applications.:CRC Press.
20. Wang, F. F.(2015).Approximation and optimization of a multi-server impatient retrial inventory-queueing system with two demand classes.Quality Technology & Quantitative Management,12(3),267-290.
21. Yang D. Y.,Wang, K. H.,Kuo, Y. T.(2011).Economic application in a finite capacity multi-channel queue with second optional channel.Applied Mathematics and Computation,217(18),7412-7419.
22. Yang, D. Y.,Ke, J. C.(2014).Cost optimization of a repairable M/G/1 queue with a randomized policy and single vacation.Applied Mathematical Modelling,38(21-22),5113-5125.
23. Yang, F.(2010).Neural network metamodeling for cycle time-throughput profiles in manufacturing.European Journal of Operational Research,205(1),172-185.
24. Zhao, N.,Lian, Z.(2011).A queueing-inventory system with two classes of customers.International Journal of Production Economics,129(1),225-231.