Abstract
In multirate multicast different users in the same multicast group can receive services at different rates depending on their own requirements and the congestion level of the network. In this two-part paper we present a general framework for addressing the optimal rate control problem in multirate multicast where the objective is the maximization of a social welfare function expressed by the sum of the users’ utility functions. In Part II we present a market based mechanism and an adjustment process that have the following features. They satisfy the informational constraints imposed by the nature of multirate multicast; and when they are combined with the results of Part I they result in an optimal solution of the corresponding centralized multirate multicast problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bazaraa MS, Sherali HD, Shetty CM (1993) Nonlinear programming theory and algorithms. Wiley, New York
Bially T, Gold B, Seneff S (1980) A technique for adaptive voice flow control in integrated packet networks. IEEE Trans Commun 28(3):325–333
Deb S, Srikant R (2004) Congestion control for fair resource allocation in networks with multicast flows. IEEE/ACM Trans Netw 12(2):261–273
Eaves B (1972) Homotopies for computation of fixed points. Math Program 3(1):1–27
Graves E, Srikant R, Towsley D (2001) Decentralized computation of weighted max-min fair bandwidth allocation in networks with multicast flows. In: Proceedings Tyrrhenian international workshop on digital communications (IWDC), Taormina, Italy
Hurwicz L (1973) The design of mechanisms for resource allocation. Am Econ Rev 63(2):1–30
Hurwicz L (1986) On informational decentralization and efficiency in resource allocation mechanisms. Math Econ 25:238–250
Kar K, Sarkar S, Tassiulas L (2001) Optimization based rate control for multirate multicast sessions. In: Proceedings of INFOCOM, Alaska
Kar K, Sarkar S, Tassiulas L (2002) A scalable low overhead rate control algorithm for multirate multicast sessions. IEEE J Select Commun 20(8):1541–1557. Special issue in Network Support for Multicast Communications
Kishino F, Manabe K, Hayashi Y, Yasuda H (1989) Variable bit-rate coding of video signals for ATM networks. IEEE J Select Commun 7(5)
Li X, Paul S, Ammar MH (1998) Layered video multicast with retransmission (LVMR): evaluation of hierarchical rate control. In: Proceedings of IEEE INFOCOM, San Francisco
Mangasarian O (1994) Nonlinear programming. SIAM, New York
Mas-Colell A, Whinston MD, Green JR (1995) Microeconomic theory. Oxford University Press, New York
McCanne S, Jacobson V, Vetterli M (1996) Receiver driven layered multicast. In: Proceedings of ACM SIGCOMM, Stanford
Merrill O (1972) Applications and extensions of an algorithm that computes fixed points of certainUpper semi-continuous point to set mappings. PhD thesis, University of Michigan
Mount K, Reiter S (1971) The informational size of message spaces. J Econ Theory 8:161–192
Nesterov Y, Nemirovsky A (1994) Interior point polynomial algorithms in convex programming. SIAM, New York
Renengar J (2001) A mathematical view of interior-point methods in convex optimization. MPS-SIAM Series on Optimization, Cornell University
Rubenstein D, Kurose J, Towsley D (1999) The impact of multicast layering on network fairness. In: Proceedings of ACM SIGCOMM, Cambridge
Sarkar S, Tassiulas L (1999) Fair allocation of resources in multirate multicast trees. In: Proceedings of Globecom
Sarkar S Tassiulas L (2000a) Distributed algorithms for computation of fair rates in multirate multicast trees. In: Proceedings of IEEE INFOCOM, Tel Aviv
Sarkar S, Tassiulas L (2000b) Fair allocation of disrete bandwidth layers in multicast networks. In: Proceedings of INFOCOM, Tel Aviv
Sarkar S, Tassiulas L (2000c) Layered bandwidth allocation for multicasting of hierarchically encoded sources. In: Proceedings of INFOCOM
Sarkar S, Tassiulas L (2001) Back pressure based multicast scheduling for fair bandwidth allocation. In: Proceedings of INFOCOM, Alaska
Sarkar S, Tassiulas L (2002) Fair allocation of utilities in multirate multicast networks: a framework for unifying diverse fairness objective. IEEE Trans Automat Contr 47(6):931–944
Scarf H (1973) The Computation of economic equilibria. Yale University Press, New Haven
Shapiro JK, Towsley D, Kurose J (2000) Optimization-based congestion control for multicast communications. In: Proceedings of IEEE INFOCOM, Tel Aviv
Simon CP, Blume L (1994) Mathematics for Economists. W. W. Norton, New York
Stoenescu TM, Teneketzis D (2002) A pricing methodology for resource allocation and routing in integrated-service networks with quality of service requirements. Math Methods Oper Res (MMOR) 56(2)
Thomas P, Tenektezis D, MacKie-Mason JK (2002) A market - based approach to optimal resource allocation in integrated - services connection- oriented networks. Oper Res 50(5)
Turletti T, Bolot JC (1994) Issues with multicast video distribution in heterogeneous packet networks. In: Packet Video Workshop
Tzeng HY, Siu KY (1997) On max-min fair congestion for multicast ABR service in ATM. IEEE J Select Areas Commun 15(3)
van der Laan G, Talman A (1979) A restart algorithm for computing fixed points without an extra dimension. Math Programm 17:74–84
van der Laan G, Talman A (1983) Interpretation of the variable dimension fixed point algorithm with an artificial level. Math Oper Res 8:86–99
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Stoenescu, T.M., Liu, M. & Teneketzis, D. Multirate multicast service provisioning II: a tâtonnement process for rate allocation. Math Meth Oper Res 65, 389–415 (2007). https://doi.org/10.1007/s00186-006-0118-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00186-006-0118-9