Optimal Decentralized Flow Control of Markovian Queueing Networks with Multiple Controllers

Abstract A Markovian queueing network model is used to derive decentralized flow control mechanisms in computer communication networks with multiple controllers. Under the network optimization criterion, finding the optimal decentralized flow control that maximizes the average network throughput under an average network delay bound becomes a team decision problem. It is shown that the network optimization problem depends on the parameters of the network only through the conditional estimates of the total arrival and departure rates. Using linear programming, the network optimal control is demonstrated to be a set of window-type mechanisms. Under the user optimization criterion, each individual user maximizes its average throughput subject to a constraint on its average time delay. Finding the optimal decentralized flow control under the individual user's performance results in a multiple objective optimization problem and leads to a game theoretic formulation. Structural results which simplify the problem are presented. It is shown that the user optimization problem depends on the parameters of the network and the action of the other users only through the conditional estimate of the user service rate. The Nash equilibrium solution under the game theoretic formulation is demonstrated to be a set of window-type mechanisms. Finally, the class of decentralized flow control problems with Nash equilibrium solutions is characterized.

[1]  Aurel A. Lazar,et al.  Optimal flow control of a class of queueing networks in equilibrium , 1983 .

[2]  M. Reiser,et al.  A Queueing Network Analysis of Computer Communication Networks with Window Flow Control , 1979, IEEE Trans. Commun..

[3]  D. Yao,et al.  Second-order stochastic properties in queueing systems , 1989, Proc. IEEE.

[4]  J. Little.  A Proof for the Queuing Formula: L = λW , 1961 .

[5]  Sarah Williams,et al.  Computer applications , 1988 .

[6]  Paul R. Milgrom,et al.  Predation, reputation, and entry deterrence☆ , 1982 .

[7]  A. Rubinstein.  Perfect Equilibrium in a Bargaining Model , 1982 .

[8]  Κωνσταντινοσ Κουρκουμπετησ.  RESOLVING CONFLICT AMONG RESOURCE SHARING PROCESSES , 1982 .

[9]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[10]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[11]  Jeffrey M. Jaffe,et al.  Bottleneck Flow Control , 1981, IEEE Trans. Commun..

[12]  M. Bacharach.  Two-person Cooperative Games , 1976 .

[13]  Jr. J. Cruz,et al.  Leader-follower strategies for multilevel systems , 1978 .

[14]  J. Nash.  THE BARGAINING PROBLEM , 1950, Classics in Game Theory.

[15]  Aurel A. Lazar,et al.  An extension to Norton's equivalent , 1989, Queueing Syst. Theory Appl..

[16]  Ted L. Anderson,et al.  On the Application of R -Curves and Maximum Load Toughness to Structures , 1988 .

[17]  Yu-Chi Ho.  Team decision theory and information structures , 1980, Proceedings of the IEEE.

[18]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

[19]  D. Fudenberg,et al.  Sequential Bargaining with Incomplete Information , 1983 .

[20]  Yu-Chi Ho,et al.  Team decision theory and information structures , 1980 .

[21]  Costas Courcoubetis,et al.  A game-theoretic view of two processes using a single resource , 1983 .

[22]  P. R. Kumar.  Optimal mixed strategies in a dynamic game , 1980 .

[23]  John C. Harsanyi,et al.  A Simplified Bargaining Model for the n-Person Cooperative Game , 1963 .

[24]  Aurel A. Lazar,et al.  A Game Theoretic Approach to Decentralized Flow Control of Markovian Queueing Networks , 1987, Performance.

[25]  E. Polak.  Introduction to linear and nonlinear programming , 1973 .

[26]  M.-T.T. Hsiao,et al.  Optimal flow control of multiclass queueing networks with partial information , 1990 .

[27]  J. Sobel,et al.  A Multistage Model of Bargaining , 1983 .