基于互补性服务的Geom/Geom/1排队顾客均衡策略研究
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摘要
主要研究具有两种服务的Geom/Geom/1排队系统,这两种服务提供具有互补性,即顾客只有同时都接受服务才能得到收益.通过建立均衡方程来分析顾客的行为,研究了顾客的收益与花费,得到了利润最大化的服务提供者的到达概率小于社会最优到达概率,并给出了垄断情形下的顾客均衡策略,并说明垄断者的最优价格同时使社会福利达到最优.
The paper considers the Geom/Geom/1 queue with complementary service and customers will receive the benefit after being served by two-staged services.Based on the balance equations to analyze customers' choice for service, customers' cost and benefit are analyzed and it also concludes that the joining probability of profit-maximization for the service-provider is smaller than that of social maximization. Further, we also give customer's equilibrium under the monopoly case, and obtain the conclusion that a price strategy chosen by a monopolist is also optimal under social welfare.
The paper considers the Geom/Geom/1 queue with complementary service and customers will receive the benefit after being served by two-staged services.Based on the balance equations to analyze customers' choice for service, customers' cost and benefit are analyzed and it also concludes that the joining probability of profit-maximization for the service-provider is smaller than that of social maximization. Further, we also give customer's equilibrium under the monopoly case, and obtain the conclusion that a price strategy chosen by a monopolist is also optimal under social welfare.
引文
[1]Haviv M,Kerner Y.On balking from an empty queue.Queueing Systems,2007,55(4):239-249.
[2]Economou A,Kanta S.Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs.Operations Research Letters,2008,36(6):696-699.
[3]Mandelbaum A,Yechiali U.Optimal entering rules for a customer with wait option at an M/G/1queue.Management Science,1983,29(2):174-187.
[4]Hassin R,Haviv M.To Queue or Not to Queue:Equilibrium Behavior in Queueing Systems.Heidelberg:Springer Science&Business Media,2003.
[5]Veltman A,Hassin R.Equilibrium in queueing systems with complementary products.Queueing Systems,2005,50(2-3):325-342.
[6]Sun W,Li S,Tian N,et al.Equilibrium analysis in batch-arrival queues with complementary services.Applied Mathematical Modelling,2009,33(1):224-241.
[7]Zhang Y,Wang J,Wang F.Equilibrium pricing strategies in retrial queueing systems with complementary service.Applied Mathematical Modelling,2016,40(11-12):5775-5792.
[8]田乃硕,徐秀丽,马占友.离散时间排队论.北京:科学出版社,2008.(Tian N S,Xu X L,Ma Z Y.Discrete Time Queuing Theory.Beijing:Science Press,2008.)
[9]林培群,徐建闽.BRT车站组停靠线路组合优化问题的建模求解与仿真.系统工程理论与实践,2012,32(11):2570-2576.(Lin P Q,Xu J M.BRT station set up line combination optimization problem modeling solution and simulation.Systems Engineering—Theory&Practice,2012,32(11):2570-2576.)
[10]潘全如,朱翼隽.排队论在收费站设计与管理中的应用.运筹学学报,2009,13(3):95-102.(Pan Q R,Zhu Y J.The application of queuing theory in the design and management of toll stations.Journal of Operations Research,2009,13(3):95-102.)
[11]刘春平,贾礼君,刘秀丽.具有二次可选服务的Geo/Geo/1工作休假排队.系统科学与数学,2013,33(2):141-149.(Liu C P,Jia L J,Liu X L.Geo/Geo/1 working vacation queues with two optional services.Journal of System Science and Mathematical Sciences,2013,33(2):141-149.)
[12]朱莎,朱翼隽,王逢佳.带负顾客启动期N策略的Geom/Geom/1工作休假排队.系统科学与数学,2012,32(1):36-44.(Zhu S,Zhu Y J,Wang F J.Geom/Geom/1 working vacation queue with negative customer startup N strategy.Journal of System Science and Mathematical Sciences,2012,32(1):36-44.)
[13]李泉林,杨碧蕊,鄂成国,等.大型并行服务系统的利润分配机制设计.系统科学与数学,2016,36(2):169-182.(Li Q L,Yang B R,E C G,et al.The design of profit distribution mechanism of large parallel service system.Journal of System Science and Mathematical Sciences,2016,36(2):169-182.)
[14]Gao S,Wang J.Equilibrium balking strategies in the observable Geo/Geo/1 queue with delayed multiple vacations.RAIRO-Operations Research,2016,50:119-129.
[15]Liu Z,Ma Y,Zhang Z G.Equilibrium mixed strategies in a discrete-time Markovian queue under multiple and single vacation policies.Quality Technology and Quantitative Management,2015,12:369-382.
[16]Ma Y,Liu W Q,Li J H.Equilibrium balking behavior in the Geo/Geo/1 queueing system with multiple vacations.Applied Mathematical Modelling,2013,37:3861-3878.
[17]Ma Y,Liu Z.Pricing analysis in Geo/Geo/1 queueing system.Mathematical Problems in Engineering,vol.2015,Article ID 181653,5 pages,2015.doi:10.1155/2015/181653.
[18]Wang F,Wang J,Zhang F.Equilibrium customer strategies in the Geo/Geo/1 queue with singleworking vacation.Discrete Dynamics in Nature and Society,Volume 2014,Article ID 309489,9 pages,2014,http://dx.doi.org/10.1155/2014/309489.
[19]Yang T,Wang J,Zhang F.Equilibrium balking strategies in the Geo/Geo/1 queues with server breakdowns and repairs.Quality Technology and Quantitative Management,2014,11:231-243.
[2]Economou A,Kanta S.Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs.Operations Research Letters,2008,36(6):696-699.
[3]Mandelbaum A,Yechiali U.Optimal entering rules for a customer with wait option at an M/G/1queue.Management Science,1983,29(2):174-187.
[4]Hassin R,Haviv M.To Queue or Not to Queue:Equilibrium Behavior in Queueing Systems.Heidelberg:Springer Science&Business Media,2003.
[5]Veltman A,Hassin R.Equilibrium in queueing systems with complementary products.Queueing Systems,2005,50(2-3):325-342.
[6]Sun W,Li S,Tian N,et al.Equilibrium analysis in batch-arrival queues with complementary services.Applied Mathematical Modelling,2009,33(1):224-241.
[7]Zhang Y,Wang J,Wang F.Equilibrium pricing strategies in retrial queueing systems with complementary service.Applied Mathematical Modelling,2016,40(11-12):5775-5792.
[8]田乃硕,徐秀丽,马占友.离散时间排队论.北京:科学出版社,2008.(Tian N S,Xu X L,Ma Z Y.Discrete Time Queuing Theory.Beijing:Science Press,2008.)
[9]林培群,徐建闽.BRT车站组停靠线路组合优化问题的建模求解与仿真.系统工程理论与实践,2012,32(11):2570-2576.(Lin P Q,Xu J M.BRT station set up line combination optimization problem modeling solution and simulation.Systems Engineering—Theory&Practice,2012,32(11):2570-2576.)
[10]潘全如,朱翼隽.排队论在收费站设计与管理中的应用.运筹学学报,2009,13(3):95-102.(Pan Q R,Zhu Y J.The application of queuing theory in the design and management of toll stations.Journal of Operations Research,2009,13(3):95-102.)
[11]刘春平,贾礼君,刘秀丽.具有二次可选服务的Geo/Geo/1工作休假排队.系统科学与数学,2013,33(2):141-149.(Liu C P,Jia L J,Liu X L.Geo/Geo/1 working vacation queues with two optional services.Journal of System Science and Mathematical Sciences,2013,33(2):141-149.)
[12]朱莎,朱翼隽,王逢佳.带负顾客启动期N策略的Geom/Geom/1工作休假排队.系统科学与数学,2012,32(1):36-44.(Zhu S,Zhu Y J,Wang F J.Geom/Geom/1 working vacation queue with negative customer startup N strategy.Journal of System Science and Mathematical Sciences,2012,32(1):36-44.)
[13]李泉林,杨碧蕊,鄂成国,等.大型并行服务系统的利润分配机制设计.系统科学与数学,2016,36(2):169-182.(Li Q L,Yang B R,E C G,et al.The design of profit distribution mechanism of large parallel service system.Journal of System Science and Mathematical Sciences,2016,36(2):169-182.)
[14]Gao S,Wang J.Equilibrium balking strategies in the observable Geo/Geo/1 queue with delayed multiple vacations.RAIRO-Operations Research,2016,50:119-129.
[15]Liu Z,Ma Y,Zhang Z G.Equilibrium mixed strategies in a discrete-time Markovian queue under multiple and single vacation policies.Quality Technology and Quantitative Management,2015,12:369-382.
[16]Ma Y,Liu W Q,Li J H.Equilibrium balking behavior in the Geo/Geo/1 queueing system with multiple vacations.Applied Mathematical Modelling,2013,37:3861-3878.
[17]Ma Y,Liu Z.Pricing analysis in Geo/Geo/1 queueing system.Mathematical Problems in Engineering,vol.2015,Article ID 181653,5 pages,2015.doi:10.1155/2015/181653.
[18]Wang F,Wang J,Zhang F.Equilibrium customer strategies in the Geo/Geo/1 queue with singleworking vacation.Discrete Dynamics in Nature and Society,Volume 2014,Article ID 309489,9 pages,2014,http://dx.doi.org/10.1155/2014/309489.
[19]Yang T,Wang J,Zhang F.Equilibrium balking strategies in the Geo/Geo/1 queues with server breakdowns and repairs.Quality Technology and Quantitative Management,2014,11:231-243.