Optimal Admission and Price Control in a Retrial Queueing System
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- 英文论文题名：Optimal Admission and Price Control in a Retrial Queueing System
- 论文作者：Zaiming Liu ; Wei Deng ; Gang Chen
- 英文论文作者：Zaiming Liu ; Wei Deng ; Gang Chen ; School of Mathematics and Statistics ; Central South University
- 年：2017
- 作者机构：School of Mathematics and Statistics,Central South University;
- 英文论文关键词：Retrial queueing system ; Markov decision process ; Matrix analytic method ; Performance evaluation
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O226
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：237k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, we analyze the optimal control policy to minimize the average costs in a retrial queueing system. At any decision epoch, the manager uses admission probabilities a's to control the arriving customers and determines a cancellation price c for the unsuccessful retrial customer, which will lead to him out of system with the probability of G(c) otherwise back to the orbit. We cast the problem as a Markov decision process and derive that the optimal policy has a pure threshold form. We also show that the two thresholds are monotonic in system parameters. Furthermore, based on the structure of the optimal policy,we construct a performance evaluation model for computing efficiently the optimal thresholds. The expression of the average cost is given by solving the quasi-birth-death(QBD) process. Finally, some numerical experiments are presented to illustrate the effect of the system parameters on the optimal policy.
In this paper, we analyze the optimal control policy to minimize the average costs in a retrial queueing system. At any decision epoch, the manager uses admission probabilities a's to control the arriving customers and determines a cancellation price c for the unsuccessful retrial customer, which will lead to him out of system with the probability of G(c) otherwise back to the orbit. We cast the problem as a Markov decision process and derive that the optimal policy has a pure threshold form. We also show that the two thresholds are monotonic in system parameters. Furthermore, based on the structure of the optimal policy,we construct a performance evaluation model for computing efficiently the optimal thresholds. The expression of the average cost is given by solving the quasi-birth-death(QBD) process. Finally, some numerical experiments are presented to illustrate the effect of the system parameters on the optimal policy.
In this paper, we analyze the optimal control policy to minimize the average costs in a retrial queueing system. At any decision epoch, the manager uses admission probabilities a's to control the arriving customers and determines a cancellation price c for the unsuccessful retrial customer, which will lead to him out of system with the probability of G(c) otherwise back to the orbit. We cast the problem as a Markov decision process and derive that the optimal policy has a pure threshold form. We also show that the two thresholds are monotonic in system parameters. Furthermore, based on the structure of the optimal policy,we construct a performance evaluation model for computing efficiently the optimal thresholds. The expression of the average cost is given by solving the quasi-birth-death(QBD) process. Finally, some numerical experiments are presented to illustrate the effect of the system parameters on the optimal policy.
引文
[1]G.Falin,A survey of retrial queues,Queueing systems 7(2):127-167,1990.
[2]J.R.Artalejo,Accessible bibliography on retrial queues:progress in 2000-2009,Mathematical and computer modelling 51(9):1071-1081,2010.
[3]B.K.Kumar,R.Rukmani,V.Thangaraj,On multiserver feedback retrial queue with finite buffer,Applied Mathematical Modelling 33(4):2062-2083,2009.
[4]J.Wang,F.Zhang,Strategic joining in M/M/1 retrial queues,European Journal of Operational Research 230(1):76-87,2013.
[5]P.Manuel,B.Sivakumar,G.Arivarignan,A perishable inventory system with service facilities and retrial customers,Computers&Industrial Engineering 54(3):484-501,2008.
[6]D.P.Heyman,Optimal operating policies for M/G/1 queuing systems,Operations Research 16(2):362-382,1968.
[7]S.Stidham Jr,R.Weber,A survey of markov decision models for control of networks of queues,Queueing systems 13(1-3):291-314,1993.
[8]S.Yoon,M.E.Lewis,Optimal pricing and admission control in a queueing system with periodically varying parameters,Queueing Systems 47(3):177-199,2004.
[9]D.W.Low,Optimal dynamic pricing policies for an M/M/s queue,Operations Research 22(3):545-561,1974.
[10]J.-D.Son,Optimal admission and pricing control problem with deterministic service times and sideline profit,Queueing Systems 60(1-2):71-85,2008.
[11]L.Li,A stochastic theory of the firm,Mathematics of operations research 13(3):447-466,1988.
[12]J.Gayon,I.Degirmenci,F.Karaesmen,E.¨Ormeci,Dynamic pricing and replenishment in a production/inventory system with markov-modulated demand,Probability in Engineering and Informational Sciences 2004.
[13]L.Xia,Event-based optimization of admission control in open queueing networks,Discrete Event Dynamic Systems24(2):133-151,2014.
[14]S.-L.Hew,L.B.White,Optimal integrated call admission control and dynamic pricing with handoffs and price-affected arrivals,in:Communications,2005 Asia-Pacific Conference on IEEE,396-400,2005.
[15]S.Benjaafar,J.-P.Gayon,S.Tepe,Optimal control of a production-inventory system with customer impatience,Operations Research Letters 38(4):267-272,2010.
[16]L.Breuer,et al.,Threshold policies for controlled retrial queues with heterogeneous servers,Annals of Operations Research 141(1):139-162,2006.
[17]M.L.Puterman,Markov decision processes:discrete stochastic dynamic programming,John Wiley&Sons,2014.
[18]E.B.C?il,E.L.¨Ormeci,F.Karaesmen,Effects of system parameters on the optimal policy structure in a class of queueing control problems,Queueing Systems 61(4):273-304,2009.
[19]Y.Aviv,A.Federgruen,The value iteration method for countable state markov decision processes,Operations research letters 24(5):223-234,1999.
[20]L.I.Sennott,Stochastic dynamic programming and the control of queueing systems,Vol.504,John Wiley&Sons,2009.
[21]R.Cavazos-Cadena,L.I.Sennott,Comparing recent assumptions for the existence of average optimal stationary policies,Operations research letters 11(1):33-37,1992.
[22]H.C.Tijms,Stochastic models:an algorithmic approach,Vol.303,John Wiley&Sons Inc,1994.
[23]G.Koole,Monotonicity in Markov reward and decision chains:Theory and applications,Vol.1,Now Publishers Inc,2007.
[2]J.R.Artalejo,Accessible bibliography on retrial queues:progress in 2000-2009,Mathematical and computer modelling 51(9):1071-1081,2010.
[3]B.K.Kumar,R.Rukmani,V.Thangaraj,On multiserver feedback retrial queue with finite buffer,Applied Mathematical Modelling 33(4):2062-2083,2009.
[4]J.Wang,F.Zhang,Strategic joining in M/M/1 retrial queues,European Journal of Operational Research 230(1):76-87,2013.
[5]P.Manuel,B.Sivakumar,G.Arivarignan,A perishable inventory system with service facilities and retrial customers,Computers&Industrial Engineering 54(3):484-501,2008.
[6]D.P.Heyman,Optimal operating policies for M/G/1 queuing systems,Operations Research 16(2):362-382,1968.
[7]S.Stidham Jr,R.Weber,A survey of markov decision models for control of networks of queues,Queueing systems 13(1-3):291-314,1993.
[8]S.Yoon,M.E.Lewis,Optimal pricing and admission control in a queueing system with periodically varying parameters,Queueing Systems 47(3):177-199,2004.
[9]D.W.Low,Optimal dynamic pricing policies for an M/M/s queue,Operations Research 22(3):545-561,1974.
[10]J.-D.Son,Optimal admission and pricing control problem with deterministic service times and sideline profit,Queueing Systems 60(1-2):71-85,2008.
[11]L.Li,A stochastic theory of the firm,Mathematics of operations research 13(3):447-466,1988.
[12]J.Gayon,I.Degirmenci,F.Karaesmen,E.¨Ormeci,Dynamic pricing and replenishment in a production/inventory system with markov-modulated demand,Probability in Engineering and Informational Sciences 2004.
[13]L.Xia,Event-based optimization of admission control in open queueing networks,Discrete Event Dynamic Systems24(2):133-151,2014.
[14]S.-L.Hew,L.B.White,Optimal integrated call admission control and dynamic pricing with handoffs and price-affected arrivals,in:Communications,2005 Asia-Pacific Conference on IEEE,396-400,2005.
[15]S.Benjaafar,J.-P.Gayon,S.Tepe,Optimal control of a production-inventory system with customer impatience,Operations Research Letters 38(4):267-272,2010.
[16]L.Breuer,et al.,Threshold policies for controlled retrial queues with heterogeneous servers,Annals of Operations Research 141(1):139-162,2006.
[17]M.L.Puterman,Markov decision processes:discrete stochastic dynamic programming,John Wiley&Sons,2014.
[18]E.B.C?il,E.L.¨Ormeci,F.Karaesmen,Effects of system parameters on the optimal policy structure in a class of queueing control problems,Queueing Systems 61(4):273-304,2009.
[19]Y.Aviv,A.Federgruen,The value iteration method for countable state markov decision processes,Operations research letters 24(5):223-234,1999.
[20]L.I.Sennott,Stochastic dynamic programming and the control of queueing systems,Vol.504,John Wiley&Sons,2009.
[21]R.Cavazos-Cadena,L.I.Sennott,Comparing recent assumptions for the existence of average optimal stationary policies,Operations research letters 11(1):33-37,1992.
[22]H.C.Tijms,Stochastic models:an algorithmic approach,Vol.303,John Wiley&Sons Inc,1994.
[23]G.Koole,Monotonicity in Markov reward and decision chains:Theory and applications,Vol.1,Now Publishers Inc,2007.