网络服务商的拥塞控制策略研究
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摘要
随着网络技术的发展与应用的普及，Internet正面临着许多新的挑战，主要体现在：资源相对稀缺、网络拥塞、服务多样化及竞争的加剧。传统的“尽力而为”服务模式已经不能够满足消费者应用多样化的需求，网络服务商(Internet Service Provider，ISP)必须改变当前的服务模式，必要时还需提供有质量保证的服务以满足应用的需求。但在目前的网络服务中，ISP与消费者都是基于自身的性能目标做出相应的决策。ISP根据消费者的需求信息制定规则，与此同时，消费者则在ISP制定的规则下选择自己的消费模式。因此为了更有效地利用稀缺的网络资源，给消费者提供更满意的网络服务，有必要对ISP在网络服务控制中的行为进行研究。针对上述问题与挑战，本文运用经济学的方法探讨了ISP的价格控制、资源分配、呼叫接入控制(Call Admission Control，CAC)及供需市场上的均衡问题，目的是使系统在兼顾网络服务质量保证的前提下，最大化用户的满意度与ISP的收益，使网络资源得以更有效地利用。
本文用定量与定性分析相结合的方法，研究了ISP的网络拥塞控制策略与系统均衡问题。在基于消费者需求信息的基础上，分别对基于价格控制策略的拥塞控制、基于资源分配策略的拥塞控制、基于呼叫接入控制策略的拥塞控制及在控制策略一般化基础上网络供需市场的供需均衡问题进行了深入探讨，为ISP在制定具体的控制策略时提供了一种理论分析与定量分析的参考依据。
根据研究点的不同，文章可以分为以下两个部分：
第一大部分是考虑单ISP的网络拥塞控制问题，主要章节是第2、3、4章。在基于价格控制策略的拥塞控制研究中，给出两种基于价格控制策略的拥塞控制方案。面对实际中ISP价格控制策略选择的问题，给出了一种基于消费者需求统计信息的价格控制策略比较选择方法，为ISP在制定新的定价策略、决定最优定价、比较不同定价策略优劣时提供了一种定量的参考依据。
在基于资源分配策略的拥塞控制研究中，给出了两种基于不同目标的带宽分配策略，并从非合作博弈的角度分析了这两种带宽分配策略对ISP收益、消费者利益及系统均衡的影响。
在基于CAC的拥塞控制研究中，分析了在不同服务价格条件下使期望报酬最大化的接入控制策略，以确定ISP的供应特性；此外还给出相应的仿真算法，比较了不同控制策略对ISP收益的影响，为ISP按照网络的实际状况选择合适的资源分配策略与接入控制策略提供了一个定量的分析方法。
第二大部分是考虑多ISP市场中的拥塞控制问题，主要章节是第5章。在研究多ISP市场中的价格控制策略中，给出了一种基于消费者需求统计信息的价格控制策略的选择方法，给进入ISP在采用价格控制策略控制网络拥塞问题、决定最优定价、比较不同定价策略优劣时提供了一种定量的参考依据。最后本文将所研究的拥塞控制策略一般化，研究了多ISP非合作网络供需市场上的供需均衡问题，给出了传统经济理论中供求均衡稳定性条件的对策论意义，证明了经济理论中的供求均衡稳定性条件。
本文的主要创新性工作如下：
1．将消费者的效用函数、需求信息及ISP的收益考虑到价格策略的制定中，并给出了一种基于消费者需求统计信息的价格控制策略的比较选择算法；与现有价控策略相比，本文所制定的价格策略在实现ISP利润最大化与拥塞控制的同时，还兼有简便、公平的优点。
2．将马尔科夫决策过程(Markov Decision Process，MDP)与排队网络性能势理论应用于对ISP供应特性的分析中。通过将系统的长期平均报酬转化为MDP中的稳态性能，给出了CAC基于长期平均报酬准则下的策略优化算法。该算法将对一个M*K维的整体寻优转化为K次M维的向量寻优，从而能够显著地降低由于高维状态所带来的计算复杂度。
3．应用博弈论中的有关理论与压缩映象定理寻求一类多ISP非合作对策纳什均衡存在、唯一的充分条件，给出了传统经济理论中供求均衡稳定性条件的对策论意义，证明了经济理论中的供求均衡稳定性条件；说明了经济学中蛛网模型的稳定供求均衡实际上就是对策理论中的纳什均衡，从而给出了传统经济理论中关于这一结论的新解释。
Along with the development application and wide spread of network techniques, it is facing several new challenges, mainly including: relative lack of resources, network congestion, service diversity and competition rivalry. Traditional "best effort" service can no longer satisfy the requirements of varying customer applications. Therefore, Internet service provider (ISP) should change current service mode and provide guaranteed services if necessary in this case. But in current Internet service, ISP and customers make decisions that optimize their individual performance. ISP makes the rules and accordingly the customers select their consumption modes. To make more efficient use of sparse network resources, and provide satisfying services as well, it is necessary to investigate ISP's behaviors in network control and competition. To solve the aforementioned problems and challenges, this research focuses on ISP's price control, resource allocation, admission control and equilibrium in supply-demand market with the help of economic methods, in order to maximize customer satisfaction and ISP's profit as well. In this way, network resources would be utilized more efficiently with the precondition of guaranteed services.
This paper employs quantitative as well as qualitative method for analyzing congestion control and system equilibrium. Based on customer demand information, congestion policies based on internet pricing, resource allocation and call admission control (CAC) respectively have been discussed. Furthermore, these policies are generalized, then the corresponding equilibrium problem is analyzed as well. This work attempts to suggest a reference benchmark for making specific control.
Therefore, this paper can be partitioned into two parts:
The first part focused on sinle-ISP network congestion control problem. The discussions lie in chapter 2, 3 and 4. In studying congestion control based on pricing policy, two policies based on customer demand information are presented. To deal with practical choice problem of price control policies, a comparative method for policies choosing based on statistical information of customer demand is suggested. In studying of congestion control based on resource allocation, two different bandwidth allocation policies guaranteeing the Quality of Service based on the demand information of the customers have been proposed.Then the effects of different bandwidth allocation policies on ISP's revenues, customer's benefits and system equilibrium have been analyzed as well. In studying of congestion control based on CAC, the control policy which maximizes the expected rewards under several different service prices is investigated, so as to analyze the ISP's supply characteristics. In the mean time, corresponding simulation algorithm is developed to compare influences caused by different control policies on ISP. This provides a quantitative analyzing method for ISP to choose appreciate resource allocation and admission control policies according to network status.
The second part focused on multi-ISP network congestion control problem. The discussion lies in chapter 5. In studying of multi-ISP pricing policy, an analyzing method based on statistical information of customer demand is proposed. In the end, another implication in the sense of game theory is presented for the stability condition of supply-demand equilibrium in traditional economic theory after generalizing the above congestion control policies. It can demonstrate the stability condition for supply-demand equilibrium in economic theory.
The innovations of this dissertation are summarized as followed:
1. In making pricing policies, customer's utility function, demand information and ISP's revenues are considered; Furthermore, a comparative method for policies choosing based on statistical information of customer demand is suggested. Comparing to the existing pricing policies, these policies achieve ISP's profit maximization and congestion control, at the same time, have the merits of simplicity and fairness.
2. Markov decision process (MDP) and Performance Potential theory are applied to the analysis of supply characteristics. Through converting system's long-run expected average reward into steady-state performance in MDP, a policy optimization algorithm under the rule of long-run expected average reward. This algorithm transform M * K-dimension global optimization into K times of M-dimension vector optimization. So the computing complexity brought by high-dimension state decreases evidently.
3. By applying game theory and contraction mapping theorem, a sufficient condition for the existence and uniqueness of Nash equilibrium in a multi-person non-cooperative game is proposed. Another implication in the sense of game theory is presented for the stability condition of supply-demand equilibrium in traditional economic theory. It can demonstrate the stability condition for supply-demand equilibrium in economic theory. So the stable supply-demand equilibrium of cobweb model in economics is in fact equivalent to the Nash equilibrium in game theory. That is a brand-new explanation for the conclusion in traditional economic theory.
本文用定量与定性分析相结合的方法，研究了ISP的网络拥塞控制策略与系统均衡问题。在基于消费者需求信息的基础上，分别对基于价格控制策略的拥塞控制、基于资源分配策略的拥塞控制、基于呼叫接入控制策略的拥塞控制及在控制策略一般化基础上网络供需市场的供需均衡问题进行了深入探讨，为ISP在制定具体的控制策略时提供了一种理论分析与定量分析的参考依据。
根据研究点的不同，文章可以分为以下两个部分：
第一大部分是考虑单ISP的网络拥塞控制问题，主要章节是第2、3、4章。在基于价格控制策略的拥塞控制研究中，给出两种基于价格控制策略的拥塞控制方案。面对实际中ISP价格控制策略选择的问题，给出了一种基于消费者需求统计信息的价格控制策略比较选择方法，为ISP在制定新的定价策略、决定最优定价、比较不同定价策略优劣时提供了一种定量的参考依据。
在基于资源分配策略的拥塞控制研究中，给出了两种基于不同目标的带宽分配策略，并从非合作博弈的角度分析了这两种带宽分配策略对ISP收益、消费者利益及系统均衡的影响。
在基于CAC的拥塞控制研究中，分析了在不同服务价格条件下使期望报酬最大化的接入控制策略，以确定ISP的供应特性；此外还给出相应的仿真算法，比较了不同控制策略对ISP收益的影响，为ISP按照网络的实际状况选择合适的资源分配策略与接入控制策略提供了一个定量的分析方法。
第二大部分是考虑多ISP市场中的拥塞控制问题，主要章节是第5章。在研究多ISP市场中的价格控制策略中，给出了一种基于消费者需求统计信息的价格控制策略的选择方法，给进入ISP在采用价格控制策略控制网络拥塞问题、决定最优定价、比较不同定价策略优劣时提供了一种定量的参考依据。最后本文将所研究的拥塞控制策略一般化，研究了多ISP非合作网络供需市场上的供需均衡问题，给出了传统经济理论中供求均衡稳定性条件的对策论意义，证明了经济理论中的供求均衡稳定性条件。
本文的主要创新性工作如下：
1．将消费者的效用函数、需求信息及ISP的收益考虑到价格策略的制定中，并给出了一种基于消费者需求统计信息的价格控制策略的比较选择算法；与现有价控策略相比，本文所制定的价格策略在实现ISP利润最大化与拥塞控制的同时，还兼有简便、公平的优点。
2．将马尔科夫决策过程(Markov Decision Process，MDP)与排队网络性能势理论应用于对ISP供应特性的分析中。通过将系统的长期平均报酬转化为MDP中的稳态性能，给出了CAC基于长期平均报酬准则下的策略优化算法。该算法将对一个M*K维的整体寻优转化为K次M维的向量寻优，从而能够显著地降低由于高维状态所带来的计算复杂度。
3．应用博弈论中的有关理论与压缩映象定理寻求一类多ISP非合作对策纳什均衡存在、唯一的充分条件，给出了传统经济理论中供求均衡稳定性条件的对策论意义，证明了经济理论中的供求均衡稳定性条件；说明了经济学中蛛网模型的稳定供求均衡实际上就是对策理论中的纳什均衡，从而给出了传统经济理论中关于这一结论的新解释。
Along with the development application and wide spread of network techniques, it is facing several new challenges, mainly including: relative lack of resources, network congestion, service diversity and competition rivalry. Traditional "best effort" service can no longer satisfy the requirements of varying customer applications. Therefore, Internet service provider (ISP) should change current service mode and provide guaranteed services if necessary in this case. But in current Internet service, ISP and customers make decisions that optimize their individual performance. ISP makes the rules and accordingly the customers select their consumption modes. To make more efficient use of sparse network resources, and provide satisfying services as well, it is necessary to investigate ISP's behaviors in network control and competition. To solve the aforementioned problems and challenges, this research focuses on ISP's price control, resource allocation, admission control and equilibrium in supply-demand market with the help of economic methods, in order to maximize customer satisfaction and ISP's profit as well. In this way, network resources would be utilized more efficiently with the precondition of guaranteed services.
This paper employs quantitative as well as qualitative method for analyzing congestion control and system equilibrium. Based on customer demand information, congestion policies based on internet pricing, resource allocation and call admission control (CAC) respectively have been discussed. Furthermore, these policies are generalized, then the corresponding equilibrium problem is analyzed as well. This work attempts to suggest a reference benchmark for making specific control.
Therefore, this paper can be partitioned into two parts:
The first part focused on sinle-ISP network congestion control problem. The discussions lie in chapter 2, 3 and 4. In studying congestion control based on pricing policy, two policies based on customer demand information are presented. To deal with practical choice problem of price control policies, a comparative method for policies choosing based on statistical information of customer demand is suggested. In studying of congestion control based on resource allocation, two different bandwidth allocation policies guaranteeing the Quality of Service based on the demand information of the customers have been proposed.Then the effects of different bandwidth allocation policies on ISP's revenues, customer's benefits and system equilibrium have been analyzed as well. In studying of congestion control based on CAC, the control policy which maximizes the expected rewards under several different service prices is investigated, so as to analyze the ISP's supply characteristics. In the mean time, corresponding simulation algorithm is developed to compare influences caused by different control policies on ISP. This provides a quantitative analyzing method for ISP to choose appreciate resource allocation and admission control policies according to network status.
The second part focused on multi-ISP network congestion control problem. The discussion lies in chapter 5. In studying of multi-ISP pricing policy, an analyzing method based on statistical information of customer demand is proposed. In the end, another implication in the sense of game theory is presented for the stability condition of supply-demand equilibrium in traditional economic theory after generalizing the above congestion control policies. It can demonstrate the stability condition for supply-demand equilibrium in economic theory.
The innovations of this dissertation are summarized as followed:
1. In making pricing policies, customer's utility function, demand information and ISP's revenues are considered; Furthermore, a comparative method for policies choosing based on statistical information of customer demand is suggested. Comparing to the existing pricing policies, these policies achieve ISP's profit maximization and congestion control, at the same time, have the merits of simplicity and fairness.
2. Markov decision process (MDP) and Performance Potential theory are applied to the analysis of supply characteristics. Through converting system's long-run expected average reward into steady-state performance in MDP, a policy optimization algorithm under the rule of long-run expected average reward. This algorithm transform M * K-dimension global optimization into K times of M-dimension vector optimization. So the computing complexity brought by high-dimension state decreases evidently.
3. By applying game theory and contraction mapping theorem, a sufficient condition for the existence and uniqueness of Nash equilibrium in a multi-person non-cooperative game is proposed. Another implication in the sense of game theory is presented for the stability condition of supply-demand equilibrium in traditional economic theory. It can demonstrate the stability condition for supply-demand equilibrium in economic theory. So the stable supply-demand equilibrium of cobweb model in economics is in fact equivalent to the Nash equilibrium in game theory. That is a brand-new explanation for the conclusion in traditional economic theory.
引文
[1] D. F. Ferguson, C. Nikolaou, and Y. Yemini. An economy for flow control in computer networks. In IEEE Conference on Computer Communications, pages 110-118, 1989.
[2] Lee W. McKnight and Jahangir Boroumand. Pricing internet services: After flat rate. Telecommunications Policy, 24: 569-590, 2000.
[3] T. Henderson, J. Crowcroft, and S. Bhatti. Admission policies in loss queuing models with heterogeneous arrivals. Management Science, 44(3): 311-320, 1998.
[4] R. Braden, D. Clark, and S. Shenker. Integrated services in the internet architecture: A overview. Technical report, IETF RFC, 1994.
[5] S. Blake. An architecture for differentiated services. Technical report, IETF RFC, 1998.
[6] S. Floyd and V. Jacobson. Random early detection gateways for congestion avoidance. IEEE/ACM Transactions on Networking, 1(4): 397-413, 1993.
[7] 井元伟，岳晓宁，王玉琢，沈晓军．基于交叉干扰的多优先级网络线性激励价控．控制与决策，20(1)：23-26，2005．
[8] 岳晓宁，井元伟，张秀华．多用户非线性网络系统各优先级价差分析．东北大学学报(自然科学版)，26(3)：205-208，2005．
[9] Andrew Odlyzko. Internet pricing and the history of communications. Computer Networks, 36: 493-517, 2001.
[10] Jun Wang and F. Li. Kin. Understanding internet pricing: an objectiveoriented classification. In IEEE Canadian Conference on Electrical and Computer Engineering, volume 2, pages 703-708, 2003.
[11] Andrew Odlyzko. Paris metro pricing: the minimalist differentiated services solution. In Proceedings of the 7th International Workshop on Quality of Service, pages 159-161, 1999.
[12] 陈波，周亚平，陈继光．带缓冲器的巴黎地铁定价策略．运筹与管理，14(1)：86-89，2005．
[13] X. R. Cao and Hong-Xia Shen. Internet pricing: Comparison and example. In Proceedings of the 39th IEEE Conference on Decision and Control, pages 2284-2289, 2000.
[14] X. R. Cao, Hong-Xia Shen, and Rodolfo Militoetc. Internet pricing with a game theoretical approach: Concepts and examples. IEEE Conference on Networking, 10: 208-216, 2002.
[15] J. L. POchard and V. Anantharam. Network pricing using game theoretic approach. In Proceedings of the 38th IEEE Conference on Decision and Control, volume 4, pages 4008-4013, 1999.
[16] Jorn Altmann, Hans Danen, and Oliver. How to market-manage a qos network. In 21st Annual Joint Conference of the IEEE Computer and Communications Societies, volume 1, pages 284-293, 2002.
[17] 岳晓宁，井元伟，尹风杰．一类垄断的网络系统最佳供给与动态定价分析．东北大学学报(自然科学版)，27(3)：237-239，2006．
[18] 陈波，周亚平，华中生．基于需求的实时网络定价策略．运筹与管理，3：72-75．2005．
[19] 陈波，周亚平，华中生．基于顾客消费信息的网络定价分析与仿真．中国管理科学，13(4)：111-114，2005．
[20] 陈继光，周亚平，陈波．网络服务中基于流量的定价策．运筹与管理，14(4)：101-106，2005．
[21] S. Low and P. Varaiya. An algorithm for optimal service provisioning using resource pricing. In Proc. IEEE INFOCOM, pages 368-373, 1994.
[22] J. Sairamesh, D. Ferguson, and Y. Yemini. An approach to pricing, optimal allocation and quality of service provisioning in high-speed networks. In Proe. IEEE INFOCOM, pages 1111-1119, 1995.
[23] K. Lee. Adaptive network support for mobile multimedia. In Proc. 1st Annual International Conference on Mobile Computing and Networking, pages 62-74, Nov 1995.
[24] Y. Korilis, A. Lazar, and A. Orda. Architecting noncooperative networks. IEEE J. Select. Areas Commun, 13(7): 1241-1251, 1995.
[25] T. Bonald and L. Massoulie. Impact of fairness of internet performance. In Proc. ACM Sigmetrics, pages 82-91, 2001.
[26] F. P. Kelly, A. Maulloo, and D. Tan. Rate control for communication networks: Shadow prices, proportional fairness and stability. J. Oper. Res. Soc, 49: 237-252, 1998.
[27] S. Kunniyur and R. Srikant. End-to-end congestion control: Utility functions, random losses and ecn marks. In Proc. IEEE INFOCOM, pages 26-30, 2000.
[28] J. Mo and J. Walrand. Fair end-to-end window based congestion control. IEEE/ACM Trans. Networking' 8: 556-567, 2000.
[29] Cheng-Shang Chang and Zhen Liu. A bandwidth sharing theory for a large number of http-like connections. IEEE/ACM Transactions on Networking, 12(5): 952-962, 2004.
[30] Mahmoud, Naghshineh, and M. Schwartz. Distributed call admission control in mobile/wireless networks. IEEE Journal On Selected Areas In Communications, 14(4): 711-717, 1996.
[31] W. Su and Gerla. The bridge to global integration. IEEE Global Telecommunications Conference, 4: 2245-2250, 1998.
[32] F. P. Kelly. On tariffs, policing and admission control for multi-service networks. Operations Research Letters, 15: 1-9, 1994.
[33] E. Takahashi and Y. Tanaka. Auction method and its performance in a dynamic bandwidth allocation service. In 1st European Conference on Universal Multi-service Network, pages 292-299, 2000.
[34] E. Takahashi and Y. Tanaka. Auction-based effective bandwidth allocation mechanism. In 10th International Conference on Telecommunications, pages 1046-1050, 2003.
[35] 陈晓梅，卢锡城，王怀民．基于微观经济学方法的网络资源分配研究．计算机研究与发展，38(11)：1354-1353，2001．
[36] Zbigniew Dziong and L. G. Mason. Fair-efficient call admission control policies for broadband networks-a game theoretic framework. IEEE/ACM Transactions on Networking, 4(1): 123-136, 1996.
[37] L. S. Gopal and T. E. Stern. Optimal call blocking policies in an integrated services environment. In Proc. Corf Inform. Sci. Syst, pages 383-388, 1983.
[38] K. W. Ross and D. H. K. Tsarrg. Optimal circuit access policies in an isdn environment: A markov decision approach. IEEE Transactions on Communications, 37: 934-939, 1989.
[39] T. Gda and Y. Watanabe. Optimal trunk reservation for a group with multislot traffic stream. IEEE Transactions on Communications, 38(7): 1078-1084, 1990.
[40] K. Q. Liao, Z. Dziong, and L. G. Mason. Dynamic link bandwidth allocation in an integrated services network. In Proc. ICC, Boston, 1989.
[41] Marbach and J. N. Tsitsiklis. Simulation-based optimization of markov reward processes. IEEE Transactions on Automatic Control, 46(2): 191-209, 2001.
[42] E. Carrizosa, E. Conde, and M. Munoz-Marquez. Admission policies in loss queuing models with heterogeneous arrivals. Management Science, 44(3): 311-320, 1998.
[43] L. A. Dasilva, P. David, and A. Nail. Equilibrium pricing in multi-service priority-based networks. In IEEE Globe COM 97', 1997.
[44] T. Heikkinen. Distributed scheduling and dynamic pricing in a communication network. Wireless Networks, 10(3), 1999.
[45] Mackie-Mason, L. Murphy, and J. Murphy. Internet Economics, chapter Responsive Pricing in the Internet. MIT Press, Cambridge MA, 1997.
[46] C. J. Oh and S. Chang. Incentives for strategic vertical alliances in online information product markets. Information Economics and Policy, 12: 155-180. 2005.
[47] 梁樑，郭强，陈华平．不同带宽ISP的定价博弈与结盟动因分析．管理科学学报，6(6)：47-53，2003．
[48] 毛晶莹．网络经济时代的多网络竞争模型研究．科研管理，1：128-130，2005．
[49] 吕志勇，陈宏民，李瑞海．中国电信产业市场化改革绩效的动态博弈分析．系统工程理论方法应用，14(1)：62-67，2005．
[50] A. Gupta, D. O. Stahl, and A. B. Whinston. A stochastic equilibrium model of internet pricing. Journal of Economic Dynamics and Control, 21: 697-720, 1997.
[51] Market managed multi-service internet. Technical report.
[52] R. Cocchi, D. Estrin, S. Shenker, and L. Zhang. Pricing in computer networks: Motivation, formulation and example. IEEE/ACM Transactions on Networking, 1(6): 614-627, 1993.
[53] S. Shenker, D. Clark, D. Estrin, and S. Herzog. Pricing in computer networks: Reshaping the research agenda. A CM Computer Communications Review, 26(2): 19-43, 1996.
[54] L. McKnight and J. Bailey. Internet Economics. Cambridge: MIT Press, 1997.
[55] R. Edell and P. P. Varaiya. Providing internet access: What we learn from the index trial. Technical report, Keynote Talk at Infocom 99, New York, 1999.
[56] T. Basar and R. Srikant. Revenue-maximizing pricing and capacity expansion in a many-users regime. In Proceedings of Conference on Computer Communications.
[57] M. Mason and R. Varian. Pricing congestible network resources. IEEE Transactions on Automatic Control, 13: 1141-1149, 1995.
[58] P. Marbach. Pricing differentiated services network: Bursty traffic. In Proceedings of Conference on Computer Communications, pages 184-193, 2001.
[59] P. Marbach. Priority service and max-min fairness. In Proceedings of Conference on Computer Communications, 2002.
[60] A. Gupta, D. O. Stahl, and A. B. Whinston. The economics of network management. Communications of ACM, 42: 57-63, 1999.
[61] M. Falkner, M. Devetsikiotis, and I. Lambadaris. An overview of pricing concepts for broadband ip networks. IEEE Communications Review, 3: 2-13, 2000.
[62] Xinjie Chang and D. W. Petr. A survey of pricing for integrated service networks. Computer Communications, 24(18): 1808-1818, 1996.
[63] D. Clark. A model for cost allocation and pricing in the internet. Technical report, Technical Report, 1995.
[64] D. Clark. Internet Economics, chapter Internet Cost Allocation and Pricing. MIT Press, Cambridge MA, 1997.
[65] P. Reichl, D. Hausheer, and B. Stiller. The cumulus pricing model as an adaptive framework for feasible, efficient, and user-friendly tariffing of internet services. The International Journal of Computer and Telecommunications Networking, 43(1): 3-24, 2003.
[66] A. Gupta, D. O. Stahl, and A. B. Whinston. Pricing of services on the internet. Technical report, Technical Report, University of Texas, 1997.
[67] A. Gupta, D. O. Stahl, and A. B. Whinston. Internet Economics, chapter Priority Pricing of Integrated Services Networks. MIT Press, Cambridge MA, 1997.
[68] Lazar and Semmret. Auctions for network resource sharing. Technical report, CTR Technical Report CU/CTR/TR 468-97-02, Columbia University, 1997.
[69] 中国互联网信息中心．中国互联网络发展状况统计报告．
[70] H. R. Varian. Internet Services : The Economics of Quality of Service in Networked Markets, chapter Estimating the Demand for Bandwidth. MIT Press, Cambridge, 2001.
[71] 张铭洪．网络经济学教程．科学出版社出版，北京，2002．
[72] R．S．Pindyck and D．L．Rubinfeld．Microeconomics (5th Edition)．清华大学出版社出版，北京，2004．
[73] 中国社会调查事务所．中国网民网络消费调查报告．
[74] 侯定丕．博弈论导论．中国科学技术大学出版社，合肥，2004．
[75] Y. Korilis, A. Lazar, and A. Orda. Achieving network optima using stackelberg routing strategies. IEEE/ACM Transactions on Networking, 5(1): 161-173, 1997.
[76] K. Park, M. Sitharam, and S. Chen. Quality of service provision in noncooperative networks with diverse user requirements. Decision Support Systems, 28: 101-122, 2000.
[77] P. Fuzesi and A. Vidacs. Game theoretic analysis of network dimensioning strategies in differentiated services networks. IEEE International Conference on Communications, 2: 1069-1073, 2002.
[78] R. A. Howard. Dynamic Programming and Markov Processes. Wiley, New York, 1960.
[79] D. Blackwell. Discrete dynamic programming. Ann. Math. Statist, 33: 719-726, 1962.
[80] C. Derman. On sequential decision and markov chains. Mgt. Sci., 9: 16-24, 1962.
[81] O. V. Viskov and A. N. Shiryaev. On controls leadings to optimal stationary models. Trudy Mat. Inst. Steklov, 71: 35-45, 1964.
[82] D. P. Heyman and M. J. Sobel. Stochastic Models Operations Research Stochastic Optimization. New York: McGraw-Hill, 1984.
[83] J. Bother. Optimal decision procedures for finite markov chains. In Proc. Adv. Appl, pages 328-339, 1973.
[84] C. Derman. Denumerable state markovian decision processes-average cost criterion. Ann. Math. Statist., 37: 1545-1554, 1966.
[85] S. M. Ross. Non-discounted denUmerable markovian decision model. Ann. Math. Statist., 39(2): 412-423, 1968.
[86] L. I. Sennott. Average cost optimal stationary policies in infinite state markov decision processes with unbounded cost. Operational. Research, 37: 636-633, 1989.
[87] D. P. Bertsekas. Dynamic Programming and Optimal Control. Athena Scientific, 1995.
[88] X. R. Cao and H. F. Chen. Perturbation realization, potentials, and sensitivity analysis of markov processes. IEEE Transactions on Automatic Control, 42(10): 1382-1393, 1997.
[89] J. G. Kemeny, J. L. Snell, and A. W. Knapp. Denumerable Markov Chains. Springer-Verlag, New York, 1976.
[90] X. R. Cao. The relations among potentials, perturbation analysis and markov decision processes. Discrete Event Dynamic Systems: Theory and Applications, 8(1): 71-78, 1998.
[91] 殷保群，周亚平，杨孝先．状态相关闭排队网络中的性能灵敏度公式．控制理论与应用，16(2)：255-257，1999．
[92] 褚荣伟．寡头市场产量与价格推测变差之间的关系．中国管理科学，12(4)：20-23，2004．
[93] T. C. E. CHENG and Y. N. WU. A multiproduct, multicriterion supplydemand network equilibrium model. Operations Research, 54(3): 544-554, 2006.
[94] 顾政华，李旭宏．基于供需均衡分析的高速公路效益产生机理研究．交通运输系统工程与信息，4(4)：99-103，2004．
[95] 毛锋，肖劲松，毛凤霞．循环经济与“双剩余”理论．北京大学学报(哲学社会科学版)，41(6)：78-84，2004．
[96] 罗勇，涂奉生．不完全信息下产品升级组合定价研究．南开大学学报(自然科学版)，38(3)：42-48，2005．
[97] 吴德胜，石琴，汪明．Max-min DEA模型及效率讨价还价均衡解．管理科学学报，8(5)：90-94，2005．
[98] 杨波，唐小我，艾兴政．纵向垄断市场的信息分享机制与产品定价．中国管理科学，31(1)：76-81，2005．
[99] 周晶，黄园高．具有弹性需求收费道路的定价策略分析．系统工程学报，20(1)：19-23，2005．
[100] 钟麦英，汤兵勇，黄小．H∞控制理论在纳什均衡动态对策问题中的应用研究．控制与决策，16(2)：186-190，2001．
[101] Manfred Nermuth. Information Structures in Economics. Springer Verlag Berlin Heidelberg, New York, 1982.
[102] Zhou Ya-ping, Yin Bao-qun, Xi Hong-sheng, Zou Chang-chun, and Sun Deming. Sufficient condition of existence for a class of n-person uncooperative game's stable equilibrium. Journal of University of Science and Technology Beijing, 20: 36-39, 1998.
[103] C. C. Zou, H. S. Xi, and B. Q. Yin. Derivative estimates parallel simulation algorithms based on performance potentials theory. In Proc. of IFAC 14th World Congress, pages 49-54, 1999.
[104] 周亚平，殷保群，奚宏生．多商品市场供需均衡的稳定性分析．工业工程，2(2)：37-39，1999．
[105] N. L. Brown. Traffic flow measurement: Experiences with NeTraMet. Technical report, 1996.
[106] S. Handelman, N. L. Brown, and G. Ruth. Ietf real time flow measurement working group. Technical report, IETF Internet Draft, 1996.
[2] Lee W. McKnight and Jahangir Boroumand. Pricing internet services: After flat rate. Telecommunications Policy, 24: 569-590, 2000.
[3] T. Henderson, J. Crowcroft, and S. Bhatti. Admission policies in loss queuing models with heterogeneous arrivals. Management Science, 44(3): 311-320, 1998.
[4] R. Braden, D. Clark, and S. Shenker. Integrated services in the internet architecture: A overview. Technical report, IETF RFC, 1994.
[5] S. Blake. An architecture for differentiated services. Technical report, IETF RFC, 1998.
[6] S. Floyd and V. Jacobson. Random early detection gateways for congestion avoidance. IEEE/ACM Transactions on Networking, 1(4): 397-413, 1993.
[7] 井元伟，岳晓宁，王玉琢，沈晓军．基于交叉干扰的多优先级网络线性激励价控．控制与决策，20(1)：23-26，2005．
[8] 岳晓宁，井元伟，张秀华．多用户非线性网络系统各优先级价差分析．东北大学学报(自然科学版)，26(3)：205-208，2005．
[9] Andrew Odlyzko. Internet pricing and the history of communications. Computer Networks, 36: 493-517, 2001.
[10] Jun Wang and F. Li. Kin. Understanding internet pricing: an objectiveoriented classification. In IEEE Canadian Conference on Electrical and Computer Engineering, volume 2, pages 703-708, 2003.
[11] Andrew Odlyzko. Paris metro pricing: the minimalist differentiated services solution. In Proceedings of the 7th International Workshop on Quality of Service, pages 159-161, 1999.
[12] 陈波，周亚平，陈继光．带缓冲器的巴黎地铁定价策略．运筹与管理，14(1)：86-89，2005．
[13] X. R. Cao and Hong-Xia Shen. Internet pricing: Comparison and example. In Proceedings of the 39th IEEE Conference on Decision and Control, pages 2284-2289, 2000.
[14] X. R. Cao, Hong-Xia Shen, and Rodolfo Militoetc. Internet pricing with a game theoretical approach: Concepts and examples. IEEE Conference on Networking, 10: 208-216, 2002.
[15] J. L. POchard and V. Anantharam. Network pricing using game theoretic approach. In Proceedings of the 38th IEEE Conference on Decision and Control, volume 4, pages 4008-4013, 1999.
[16] Jorn Altmann, Hans Danen, and Oliver. How to market-manage a qos network. In 21st Annual Joint Conference of the IEEE Computer and Communications Societies, volume 1, pages 284-293, 2002.
[17] 岳晓宁，井元伟，尹风杰．一类垄断的网络系统最佳供给与动态定价分析．东北大学学报(自然科学版)，27(3)：237-239，2006．
[18] 陈波，周亚平，华中生．基于需求的实时网络定价策略．运筹与管理，3：72-75．2005．
[19] 陈波，周亚平，华中生．基于顾客消费信息的网络定价分析与仿真．中国管理科学，13(4)：111-114，2005．
[20] 陈继光，周亚平，陈波．网络服务中基于流量的定价策．运筹与管理，14(4)：101-106，2005．
[21] S. Low and P. Varaiya. An algorithm for optimal service provisioning using resource pricing. In Proc. IEEE INFOCOM, pages 368-373, 1994.
[22] J. Sairamesh, D. Ferguson, and Y. Yemini. An approach to pricing, optimal allocation and quality of service provisioning in high-speed networks. In Proe. IEEE INFOCOM, pages 1111-1119, 1995.
[23] K. Lee. Adaptive network support for mobile multimedia. In Proc. 1st Annual International Conference on Mobile Computing and Networking, pages 62-74, Nov 1995.
[24] Y. Korilis, A. Lazar, and A. Orda. Architecting noncooperative networks. IEEE J. Select. Areas Commun, 13(7): 1241-1251, 1995.
[25] T. Bonald and L. Massoulie. Impact of fairness of internet performance. In Proc. ACM Sigmetrics, pages 82-91, 2001.
[26] F. P. Kelly, A. Maulloo, and D. Tan. Rate control for communication networks: Shadow prices, proportional fairness and stability. J. Oper. Res. Soc, 49: 237-252, 1998.
[27] S. Kunniyur and R. Srikant. End-to-end congestion control: Utility functions, random losses and ecn marks. In Proc. IEEE INFOCOM, pages 26-30, 2000.
[28] J. Mo and J. Walrand. Fair end-to-end window based congestion control. IEEE/ACM Trans. Networking' 8: 556-567, 2000.
[29] Cheng-Shang Chang and Zhen Liu. A bandwidth sharing theory for a large number of http-like connections. IEEE/ACM Transactions on Networking, 12(5): 952-962, 2004.
[30] Mahmoud, Naghshineh, and M. Schwartz. Distributed call admission control in mobile/wireless networks. IEEE Journal On Selected Areas In Communications, 14(4): 711-717, 1996.
[31] W. Su and Gerla. The bridge to global integration. IEEE Global Telecommunications Conference, 4: 2245-2250, 1998.
[32] F. P. Kelly. On tariffs, policing and admission control for multi-service networks. Operations Research Letters, 15: 1-9, 1994.
[33] E. Takahashi and Y. Tanaka. Auction method and its performance in a dynamic bandwidth allocation service. In 1st European Conference on Universal Multi-service Network, pages 292-299, 2000.
[34] E. Takahashi and Y. Tanaka. Auction-based effective bandwidth allocation mechanism. In 10th International Conference on Telecommunications, pages 1046-1050, 2003.
[35] 陈晓梅，卢锡城，王怀民．基于微观经济学方法的网络资源分配研究．计算机研究与发展，38(11)：1354-1353，2001．
[36] Zbigniew Dziong and L. G. Mason. Fair-efficient call admission control policies for broadband networks-a game theoretic framework. IEEE/ACM Transactions on Networking, 4(1): 123-136, 1996.
[37] L. S. Gopal and T. E. Stern. Optimal call blocking policies in an integrated services environment. In Proc. Corf Inform. Sci. Syst, pages 383-388, 1983.
[38] K. W. Ross and D. H. K. Tsarrg. Optimal circuit access policies in an isdn environment: A markov decision approach. IEEE Transactions on Communications, 37: 934-939, 1989.
[39] T. Gda and Y. Watanabe. Optimal trunk reservation for a group with multislot traffic stream. IEEE Transactions on Communications, 38(7): 1078-1084, 1990.
[40] K. Q. Liao, Z. Dziong, and L. G. Mason. Dynamic link bandwidth allocation in an integrated services network. In Proc. ICC, Boston, 1989.
[41] Marbach and J. N. Tsitsiklis. Simulation-based optimization of markov reward processes. IEEE Transactions on Automatic Control, 46(2): 191-209, 2001.
[42] E. Carrizosa, E. Conde, and M. Munoz-Marquez. Admission policies in loss queuing models with heterogeneous arrivals. Management Science, 44(3): 311-320, 1998.
[43] L. A. Dasilva, P. David, and A. Nail. Equilibrium pricing in multi-service priority-based networks. In IEEE Globe COM 97', 1997.
[44] T. Heikkinen. Distributed scheduling and dynamic pricing in a communication network. Wireless Networks, 10(3), 1999.
[45] Mackie-Mason, L. Murphy, and J. Murphy. Internet Economics, chapter Responsive Pricing in the Internet. MIT Press, Cambridge MA, 1997.
[46] C. J. Oh and S. Chang. Incentives for strategic vertical alliances in online information product markets. Information Economics and Policy, 12: 155-180. 2005.
[47] 梁樑，郭强，陈华平．不同带宽ISP的定价博弈与结盟动因分析．管理科学学报，6(6)：47-53，2003．
[48] 毛晶莹．网络经济时代的多网络竞争模型研究．科研管理，1：128-130，2005．
[49] 吕志勇，陈宏民，李瑞海．中国电信产业市场化改革绩效的动态博弈分析．系统工程理论方法应用，14(1)：62-67，2005．
[50] A. Gupta, D. O. Stahl, and A. B. Whinston. A stochastic equilibrium model of internet pricing. Journal of Economic Dynamics and Control, 21: 697-720, 1997.
[51] Market managed multi-service internet. Technical report.
[52] R. Cocchi, D. Estrin, S. Shenker, and L. Zhang. Pricing in computer networks: Motivation, formulation and example. IEEE/ACM Transactions on Networking, 1(6): 614-627, 1993.
[53] S. Shenker, D. Clark, D. Estrin, and S. Herzog. Pricing in computer networks: Reshaping the research agenda. A CM Computer Communications Review, 26(2): 19-43, 1996.
[54] L. McKnight and J. Bailey. Internet Economics. Cambridge: MIT Press, 1997.
[55] R. Edell and P. P. Varaiya. Providing internet access: What we learn from the index trial. Technical report, Keynote Talk at Infocom 99, New York, 1999.
[56] T. Basar and R. Srikant. Revenue-maximizing pricing and capacity expansion in a many-users regime. In Proceedings of Conference on Computer Communications.
[57] M. Mason and R. Varian. Pricing congestible network resources. IEEE Transactions on Automatic Control, 13: 1141-1149, 1995.
[58] P. Marbach. Pricing differentiated services network: Bursty traffic. In Proceedings of Conference on Computer Communications, pages 184-193, 2001.
[59] P. Marbach. Priority service and max-min fairness. In Proceedings of Conference on Computer Communications, 2002.
[60] A. Gupta, D. O. Stahl, and A. B. Whinston. The economics of network management. Communications of ACM, 42: 57-63, 1999.
[61] M. Falkner, M. Devetsikiotis, and I. Lambadaris. An overview of pricing concepts for broadband ip networks. IEEE Communications Review, 3: 2-13, 2000.
[62] Xinjie Chang and D. W. Petr. A survey of pricing for integrated service networks. Computer Communications, 24(18): 1808-1818, 1996.
[63] D. Clark. A model for cost allocation and pricing in the internet. Technical report, Technical Report, 1995.
[64] D. Clark. Internet Economics, chapter Internet Cost Allocation and Pricing. MIT Press, Cambridge MA, 1997.
[65] P. Reichl, D. Hausheer, and B. Stiller. The cumulus pricing model as an adaptive framework for feasible, efficient, and user-friendly tariffing of internet services. The International Journal of Computer and Telecommunications Networking, 43(1): 3-24, 2003.
[66] A. Gupta, D. O. Stahl, and A. B. Whinston. Pricing of services on the internet. Technical report, Technical Report, University of Texas, 1997.
[67] A. Gupta, D. O. Stahl, and A. B. Whinston. Internet Economics, chapter Priority Pricing of Integrated Services Networks. MIT Press, Cambridge MA, 1997.
[68] Lazar and Semmret. Auctions for network resource sharing. Technical report, CTR Technical Report CU/CTR/TR 468-97-02, Columbia University, 1997.
[69] 中国互联网信息中心．中国互联网络发展状况统计报告．
[70] H. R. Varian. Internet Services : The Economics of Quality of Service in Networked Markets, chapter Estimating the Demand for Bandwidth. MIT Press, Cambridge, 2001.
[71] 张铭洪．网络经济学教程．科学出版社出版，北京，2002．
[72] R．S．Pindyck and D．L．Rubinfeld．Microeconomics (5th Edition)．清华大学出版社出版，北京，2004．
[73] 中国社会调查事务所．中国网民网络消费调查报告．
[74] 侯定丕．博弈论导论．中国科学技术大学出版社，合肥，2004．
[75] Y. Korilis, A. Lazar, and A. Orda. Achieving network optima using stackelberg routing strategies. IEEE/ACM Transactions on Networking, 5(1): 161-173, 1997.
[76] K. Park, M. Sitharam, and S. Chen. Quality of service provision in noncooperative networks with diverse user requirements. Decision Support Systems, 28: 101-122, 2000.
[77] P. Fuzesi and A. Vidacs. Game theoretic analysis of network dimensioning strategies in differentiated services networks. IEEE International Conference on Communications, 2: 1069-1073, 2002.
[78] R. A. Howard. Dynamic Programming and Markov Processes. Wiley, New York, 1960.
[79] D. Blackwell. Discrete dynamic programming. Ann. Math. Statist, 33: 719-726, 1962.
[80] C. Derman. On sequential decision and markov chains. Mgt. Sci., 9: 16-24, 1962.
[81] O. V. Viskov and A. N. Shiryaev. On controls leadings to optimal stationary models. Trudy Mat. Inst. Steklov, 71: 35-45, 1964.
[82] D. P. Heyman and M. J. Sobel. Stochastic Models Operations Research Stochastic Optimization. New York: McGraw-Hill, 1984.
[83] J. Bother. Optimal decision procedures for finite markov chains. In Proc. Adv. Appl, pages 328-339, 1973.
[84] C. Derman. Denumerable state markovian decision processes-average cost criterion. Ann. Math. Statist., 37: 1545-1554, 1966.
[85] S. M. Ross. Non-discounted denUmerable markovian decision model. Ann. Math. Statist., 39(2): 412-423, 1968.
[86] L. I. Sennott. Average cost optimal stationary policies in infinite state markov decision processes with unbounded cost. Operational. Research, 37: 636-633, 1989.
[87] D. P. Bertsekas. Dynamic Programming and Optimal Control. Athena Scientific, 1995.
[88] X. R. Cao and H. F. Chen. Perturbation realization, potentials, and sensitivity analysis of markov processes. IEEE Transactions on Automatic Control, 42(10): 1382-1393, 1997.
[89] J. G. Kemeny, J. L. Snell, and A. W. Knapp. Denumerable Markov Chains. Springer-Verlag, New York, 1976.
[90] X. R. Cao. The relations among potentials, perturbation analysis and markov decision processes. Discrete Event Dynamic Systems: Theory and Applications, 8(1): 71-78, 1998.
[91] 殷保群，周亚平，杨孝先．状态相关闭排队网络中的性能灵敏度公式．控制理论与应用，16(2)：255-257，1999．
[92] 褚荣伟．寡头市场产量与价格推测变差之间的关系．中国管理科学，12(4)：20-23，2004．
[93] T. C. E. CHENG and Y. N. WU. A multiproduct, multicriterion supplydemand network equilibrium model. Operations Research, 54(3): 544-554, 2006.
[94] 顾政华，李旭宏．基于供需均衡分析的高速公路效益产生机理研究．交通运输系统工程与信息，4(4)：99-103，2004．
[95] 毛锋，肖劲松，毛凤霞．循环经济与“双剩余”理论．北京大学学报(哲学社会科学版)，41(6)：78-84，2004．
[96] 罗勇，涂奉生．不完全信息下产品升级组合定价研究．南开大学学报(自然科学版)，38(3)：42-48，2005．
[97] 吴德胜，石琴，汪明．Max-min DEA模型及效率讨价还价均衡解．管理科学学报，8(5)：90-94，2005．
[98] 杨波，唐小我，艾兴政．纵向垄断市场的信息分享机制与产品定价．中国管理科学，31(1)：76-81，2005．
[99] 周晶，黄园高．具有弹性需求收费道路的定价策略分析．系统工程学报，20(1)：19-23，2005．
[100] 钟麦英，汤兵勇，黄小．H∞控制理论在纳什均衡动态对策问题中的应用研究．控制与决策，16(2)：186-190，2001．
[101] Manfred Nermuth. Information Structures in Economics. Springer Verlag Berlin Heidelberg, New York, 1982.
[102] Zhou Ya-ping, Yin Bao-qun, Xi Hong-sheng, Zou Chang-chun, and Sun Deming. Sufficient condition of existence for a class of n-person uncooperative game's stable equilibrium. Journal of University of Science and Technology Beijing, 20: 36-39, 1998.
[103] C. C. Zou, H. S. Xi, and B. Q. Yin. Derivative estimates parallel simulation algorithms based on performance potentials theory. In Proc. of IFAC 14th World Congress, pages 49-54, 1999.
[104] 周亚平，殷保群，奚宏生．多商品市场供需均衡的稳定性分析．工业工程，2(2)：37-39，1999．
[105] N. L. Brown. Traffic flow measurement: Experiences with NeTraMet. Technical report, 1996.
[106] S. Handelman, N. L. Brown, and G. Ruth. Ietf real time flow measurement working group. Technical report, IETF Internet Draft, 1996.
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