Optimal Flow Control Of M/G/1/∞ Queue With R Players

In computer and communication networks, queue game has received attention widely, for example someone applies Nash equilibrium and queue system into communication networks, derives the existence of equilibrium using fixed-point theorems and so on. But it wasn't studied completely. Basing on it, the aim of this paper is to study optimal flow control of four queues, think of two typical performance objectives (non-cooperative optimization and cooperative optimization), and show some characters of two solutions.Firstly, introduction provides phylogeny of classical games theory, background of the paper, the solutions to non-cooperative game and cooperative game, and queue game.Secondly, we introduce some basic concepts, such as flow control, M/M/1/∞queue system. First, M/M/1/∞queue with r players is defined, two classical game models are proposed, namely r-person non-cooperative game model and r-person cooperative game model, the solutions to the two games are given and the uniqueness of them are proved.Thirdly, some basic concepts are introduced, such as M/M/n/∞queue system, queue length, mean waiting time and mean sojourn time. M/M/n/∞queue with r players is defined, the solution to r-person non-cooper- -ative game is mainly studied, the uniqueness is proved. In addition, we study the solution to r-person cooperative game.Lastly, we introduce M/Ek/1/∞queue system, M/G/1/∞queue system. Optimal flow control of these two queue systems are studied, and some properties of the solutions are given.