Decentralized Resource Allocation Mechanisms in Networks: Realization and Implementation

We discuss how decentralized network resource allocation problems fit within the context of mechanism design (realization theory and implementation theory), and how mechanism design can provide useful insight into the nature of decentralized network resource allocation problems. The discussion is guided by the unicast problem with routing and Quality of Service (QoS) requirements, and the multi-rate multicast service provisioning problem in networks. For these problems we present decentralized resource allocation mechanisms that achieve the solution of the corresponding centralized resource allocation problem and are informationally efficient. We show how the aforementioned mechanisms can be embedded into the general framework of realization theory, and indicate how realization theory can be used to establish the mechanisms’ informational efficiency in certain instances. We also present a conjecture related to implementation in Nash equilibria of the optimal centralized solution of the unicast service provisioning problem.

[1]  Henry L. Owen,et al.  SONET/SDH multicast routing algorithms in symmetrical three stage networks , 1995, Proceedings IEEE International Conference on Communications ICC '95.

[2]  Frank P. Kelly,et al.  Measurement-Based Usage Charges in Comminucations Networks , 2000, Oper. Res..

[3]  R. Srikant,et al.  Congestion control for fair resource allocation in networks with multicast flows , 2004, IEEE/ACM Transactions on Networking.

[4]  Joel Mokyr.  Twenty-Five Centuries of Technological Change: Harwood Fundamentals of Pure and Applied Economics , 1990 .

[5]  Leandros Tassiulas,et al.  Optimization based rate control for multirate multicast sessions , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[6]  G. Debreu,et al.  Theory of Value , 1959 .

[7]  Jeffrey K. MacKie-Mason,et al.  Some FAQs about Usage-Based Pricing , 1995, Comput. Networks ISDN Syst..

[8]  O. H. Brownlee,et al.  ACTIVITY ANALYSIS OF PRODUCTION AND ALLOCATION , 1952 .

[9]  FACTS AND THEORIES OF THE WELFARE STATE Dorothy Wedderburn THE early months of the third post-war Labour Government in Britain provide a fitting opportunity to review the present state of the debate , 2005 .

[10]  Donald F. Towsley,et al.  Decentralized Computation of Weighted Max-Min Fair Bandwidth Allocation in Networks with Multicast Flows , 2001, IWDC.

[11]  Kai-Yeung Siu,et al.  On Max-Min Fair Congestion Control for Multicast ABR Service in ATM , 1997, IEEE J. Sel. Areas Commun..

[12]  Scott Jordan,et al.  The Role of Price in the Connection Establishment Process , 1995 .

[13]  Leandros Tassiulas,et al.  Fair allocation of resources in multirate multicast trees , 1999, Seamless Interconnection for Universal Services. Global Telecommunications Conference. GLOBECOM'99. (Cat. No.99CH37042).

[14]  Stanley Reiter,et al.  Informational efficiency of iterative processes and the size of message spaces , 1974 .

[15]  J. S. Jordan.  The Informational Requirements of Local Stability in Decentralized Allocation Mechanisms , 1982 .

[16]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[17]  Thomas Marschak,et al.  Network Mechanisms, Informational Efficiency, and Hierarchies , 1998 .

[18]  John. Moore,et al.  Nash Implementation: A Full Characterization , 1990 .

[19]  L. Shen,et al.  Linear Algebra , 1968 .

[20]  Leandros Tassiulas,et al.  A scalable low-overhead rate control algorithm for multirate multicast sessions , 2002, IEEE J. Sel. Areas Commun..

[21]  Liam Murphy,et al.  Distributed Pricing For Embedded ATM Networks , 1994 .

[22]  Danny Raz,et al.  Global optimization using local information with applications to flow control , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[23]  E. Maskin,et al.  Implementation Theory∗ , 2002 .

[24]  Andrew Postlewaite,et al.  Implementation in differential information economies , 1986 .

[25]  T. Palfrey.  Implementation in Bayesian Equilibrium: The Multiple Equilibrium Problem in Mechanism Design , 1990 .

[26]  Herbert E. Scarf,et al.  The Computation of Economic Equilibria , 1974 .

[27]  Deborah Estrin,et al.  Pricing in computer networks: motivation, formulation, and example , 1993, TNET.

[28]  Jeffrey K. MacKie-Mason,et al.  A Market-Based Approach to Optimal Resource Allocation in Integrated-Services Connection-Oriented Networks , 2002, Oper. Res..

[29]  Steven H. Low,et al.  Optimization flow control—I: basic algorithm and convergence , 1999, TNET.

[30]  D. Teneketzis,et al.  Pricing for Rate Allocation in Unicast Service Provisioning is Informationally Efficient , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[31]  T. Palfrey,et al.  Implementation with Incomplete Information in Exchange Economies , 1989 .

[32]  Leandros Tassiulas,et al.  Fair allocation of discrete bandwidth layers in multicast networks , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[33]  Leandros Tassiulas,et al.  Back pressure based multicast scheduling for fair bandwidth allocation , 2005, IEEE Transactions on Neural Networks.

[34]  John N. Tsitsiklis,et al.  Efficiency loss in a network resource allocation game: the case of elastic supply , 2004, IEEE Transactions on Automatic Control.

[35]  L. McKnight,et al.  Internet economics , 1997 .

[36]  T. Koopmans.  Three Essays on the State of Economic Science , 1958 .

[37]  E. Maskin.  The Theory of Implementation in Nash Equilibrium: A Survey , 1983 .

[38]  Frank Kelly,et al.  On tariffs, policing and admission control for multiservice networks , 1993, Oper. Res. Lett..

[39]  Andrew Whinston,et al.  A Stochastic Equilibrium Model of Internet Pricing , 1997 .

[40]  Francesco Mallegni,et al.  The Computation of Economic Equilibria , 1973 .

[41]  Vernon L. Smith,et al.  Papers in Experimental Economics: Incentive Compatible Experimental Processes for the Provision of Public Goods , 1979 .

[42]  John N. Tsitsiklis,et al.  Efficiency Loss in a Cournot Mechanism for Network Resource Allocation , .

[43]  Stanley Reiter,et al.  Economic Environments for Which There Are Pareto Satisfactory Mechanisms , 1977 .

[44]  Donald F. Towsley,et al.  Multicast-based loss inference with missing data , 2002, IEEE J. Sel. Areas Commun..

[45]  C. Parris,et al.  A RESOURCE BASED PRICING POLICY FOR REAL-TIME CHANNELS IN A PACKET-SWITCHING NETWORK , 1992 .

[46]  Demosthenis Teneketzis,et al.  A pricing methodology for resource allocation and routing in integrated-services networks with quality of service requirements , 2002, Math. Methods Oper. Res..

[47]  P. Samuelson,et al.  Foundations of Economic Analysis. , 1948 .

[48]  L. Hurwicz.  Studies in Resource Allocation Processes: Optimality and informational efficiency in resource allocation processes , 1977 .

[49]  Gustavo de Veciana,et al.  Resource Allocation in Multi-Service Networks via Pricing: Statistical Multiplexing , 1998, Comput. Networks.

[50]  L. Hurwicz.  The Design of Mechanisms for Resource Allocation , 1973 .

[51]  Donald F. Towsley,et al.  Optimization-Based Congestion Control for Multicast Communications , 2002, NETWORKING.

[52]  R. Srikant,et al.  End-to-end congestion control schemes: utility functions, random losses and ECN marks , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[53]  R. Srikant,et al.  End-to-end congestion control schemes: utility functions, random losses and ECN marks , 2003, TNET.

[54]  Stanley Reiter,et al.  On the Existence of a Locally Stable Dynamic Process With a Statically Minimal Message Space , 1983 .

[55]  Tomas Sjöström,et al.  Implementation in perfect equilibria , 1993 .

[56]  K. Arrow,et al.  General Competitive Analysis , 1971 .

[57]  C. Parris,et al.  A Framework for the Study of Pricing in Integrated Networks , 1992 .

[58]  Alicia Alvaro García-Herrero,et al.  The Role of Global Risk Aversion in Explaining Sovereign Spreads , 2007 .

[59]  Maurice Allais.  A la recherche d'une discipline économique , 1950 .

[60]  Matthew O. Jackson,et al.  A crash course in implementation theory , 2001, Soc. Choice Welf..

[61]  Tudor Mihai Stoenescu.  Decentralized resource allocation mechanisms in networks. , 2004 .

[62]  B. Hajek,et al.  Strategic Buyers in a Sum Bid Game for Flat Networks , 2004 .

[63]  A. Lerner,et al.  Economic Theory and Socialist Economy , 1934 .

[64]  T. Scitovszky.  A Note on Welfare Propositions in Economics , 1941 .

[65]  C. L. Sheng.  A Theory of Value , 1991 .

[66]  Harold Hotelling.  Edgeworth's Taxation Paradox and the Nature of Demand and Supply Functions , 1932, Journal of Political Economy.

[67]  S. Reiter,et al.  The informational size of message spaces , 1974 .

[68]  Jean Walrand,et al.  Average bandwidth and delay for reliable multicast , 2000 .

[69]  N. I. Bukharin,et al.  ABC of communism , 1920 .

[70]  Michael J. Donahoo,et al.  Core Migration for Dynamic Multicast Routing , 1995 .

[71]  Thomas R. Palfrey,et al.  Nash Implementation Using Undominated Strategies , 1991 .

[72]  Tatsuyoshi Saijo,et al.  STRATEGY SPACE REDUCTION IN MASKIN'S THEOREM: SUFFICIENT CONDITIONS FOR NASH IMPLEMENTATION , 1988 .

[73]  Stanley Reiter,et al.  Information and Performance in the (New)2 Welfare Economics , 1977 .

[74]  Dilip Abreu,et al.  Subgame perfect implementation: A necessary and almost sufficient condition , 1990 .

[75]  S. Mannor,et al.  Efficiency loss in a resource allocation game: A single link in elastic supply , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[76]  E. Maskin,et al.  The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility , 1979 .

[77]  William Thomson,et al.  Concepts Of Implementation , 1996 .

[78]  Demosthenis Teneketzis,et al.  An approach to service provisioning with quality of service requirements in ATM networks , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[79]  V. Lenin,et al.  The State and Revolution , 2020 .

[80]  Jon M. Peha,et al.  Optimal pricing for integrated services networks , 1997 .

[81]  L. A. Goodman,et al.  Social Choice and Individual Values , 1951 .

[82]  S. Reiter,et al.  Game forms with minimal message spaces , 1988 .

[83]  Hideo Kanemitsu,et al.  INFORMATIONAL EFFICIENCY AND DECENTRALIZATION IN OPTIMAL RESOURCE ALLOCATION , 1966 .

[84]  Luis C. Corchón.  The Theory of Implementation of Socially Optimal Decisions in Economics , 1996 .

[85]  A. Lerner.  The Concept of Monopoly and the Measurement of Monopoly Power , 1934 .

[86]  E. Maskin.  Nash Equilibrium and Welfare Optimality , 1999 .

[87]  Richard J. La,et al.  Charge-sensitive TCP and rate control in the Internet , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[88]  F. Hayek.  Economics and knowledge , 1937 .

[89]  Jim Kurose,et al.  Topology discovery service for router-assisted multicast transport , 2002, 2002 IEEE Open Architectures and Network Programming Proceedings. OPENARCH 2002 (Cat. No.02EX571).

[90]  B. Hajek,et al.  Optimal allocation of a divisible good to strategic buyers , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[91]  Hitoshi Matsushima,et al.  Virtual implementation in iteratively undominated strategies: complete information , 1992 .

[92]  G. Debreu.  The Coefficient of Resource Utilization , 1951 .

[93]  E. H. Clarke.  Incentives in public decision-making , 1980 .

[94]  H. Piaggio.  Mathematical Analysis , 1955, Nature.

[95]  Stanley Reiter,et al.  The Knowledge Revealed by an Allocation Process and the Informational Size of the Message Space , 1974 .

[96]  M. Jackson.  Implementation in Undominated Strategies: A Look at Bounded Mechanisms , 1992 .

[97]  Theodore Groves,et al.  Information, Incentives, and Economic Mechanisms: Essays in Honor of Leonid Hurwicz , 1987 .

[98]  Vilfredo Pareto.  La courbe des revenus , 1964 .

[99]  Sneha Kumar Kasera,et al.  Scalable reliable multicast using multiple multicast channels , 2000, TNET.

[100]  Liam Murphy,et al.  Bandwidth Allocation By Pricing In ATM Networks , 1994, Broadband Communications.

[101]  Frank Kelly,et al.  Rate control for communication networks: shadow prices, proportional fairness and stability , 1998, J. Oper. Res. Soc..

[102]  Donald F. Towsley,et al.  The impact of multicast layering on network fairness , 1999, SIGCOMM '99.

[103]  Leandros Tassiulas,et al.  Distributed algorithms for computation of fair rates in multirate multicast trees , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[104]  H. Fawcett.  Manual of Political Economy , 1995 .

[105]  H. Hotelling.  THE GENERAL WELFARE IN RELATION TO PROBLEMS OF TAXATION AND OF RAILWAY AND UTILITY RATES. IN: RAILWAYS , 1938 .

[106]  Thomas R. Palfrey,et al.  Chapter 61 Implementation theory , 2002 .

[107]  Friedrich A. von Hayek,et al.  Collectivist economic planning;: Critical studies on the possibilities of socialism, , 1975 .

[108]  Abram Burk.  A Reformulation of Certain Aspects of Welfare Economics , 1938 .

[109]  Eric Maskin,et al.  Chapter 5 Implementation theory , 2002 .

[110]  Frank Kelly,et al.  Charging and rate control for elastic traffic , 1997, Eur. Trans. Telecommun..

[111]  Icinqsley Laffer..  THE FOUNDATIONS OF WELFARE ECONOMICS , 1951 .

[112]  M. Dobb,et al.  Economic Theory and the Problems of a Socialist Economy , 1933 .

[113]  Leandros Tassiulas,et al.  A Simple Rate Control Algorithm for Maximizing Total User Utility. , 2001, INFOCOM 2001.

[114]  L. Hurwicz.  On informationally decentralized systems , 1977 .

[115]  H. Dickinson,et al.  Price Formation in a Socialist Community , 1933 .

[116]  Laurent Massoulié,et al.  Bandwidth sharing: objectives and algorithms , 2002, TNET.

[117]  Leonid Hurwicz.  On Informational Decentralization and Efficiency of Resource Allocation Mechanisms , 1986 .

[118]  Matthew O. Jackson,et al.  Undominated Nash Implementation in Bounded Mechanisms , 1994 .

[119]  Leandros Tassiulas,et al.  Fair allocation of utilities in multirate multicast networks: a framework for unifying diverse fairness objectives , 2002, IEEE Trans. Autom. Control..

[120]  Katta G. Murty,et al.  Nonlinear Programming Theory and Algorithms , 2007, Technometrics.

[121]  Israel Cidon,et al.  Connection establishment in high-speed networks , 1993, TNET.

[122]  Friedrich A. von Hayek,et al.  Socialist Calculation: The Competitive `Solution' , 1940 .

[123]  N. Kaldor.  The Philosophy of Economics: Welfare Propositions of Economics and Interpersonal Comparisons of Utility , 1939 .

[124]  V. Pareto,et al.  The New Theories of Economics , 1897, Journal of Political Economy.

[125]  Léon Walras.  Éléments d'économie politique pure, ou, Théorie de la richesse sociale , 1976 .

[126]  K. Arrow.  A Difficulty in the Concept of Social Welfare , 1950, Journal of Political Economy.

[127]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

[128]  David Watson,et al.  Protocol scrubbing: network security through transparent flow modification , 2004, IEEE/ACM Transactions on Networking.

[129]  Otto Neurath.  Durch die Kriegswirtschaft zur Naturalwirtschaft , 1919 .

[130]  Ellen W. Zegura,et al.  Center selection and migration for wide-area multicast routing , 1997, J. High Speed Networks.

[131]  V. Smith.  Research in Experimental Economics , 1979 .

[132]  Pravin Varaiya,et al.  Correction to "A new approach to service provisioning in ATM networks" , 1993, TNET.