and Lower Case Should Be Used for Short Title of Paper Discrete and Impulsive Systems

DYNAMICS OF COMPUTER COMMUNICATION NETWORKS AND OPTIMAL CONTROL

N.U.Ahmed

School of Information Technology and Engineering and Department of Mathematics, University of Ottawa, Ottawa,Canada

Abstract. In this talk we develop several continuous time dynamic models for computer communication net works. In our previous work [1] we have developed discrete time discrete state models for packet switched networks. Recently [2] we have developed the so called fluid model for the same system which is continuous in time and state. This is based on the token bucket control mechanism: a traffic shaping mechanism used at the network access point. We have suggested several different dynamic models with or without buffers, with or without priorities, with or without capacity constraints. The mathematical model turns out to be a system of nonlinear differential equations with discontinuous right hand side. We formulate this as differential inclusions and prove the existence of solutions and viability of the admissible domain of operation. This is a class of nonstandard systems. We prove the existence and regularity properties of solutions for these systems and discuss control and optimization. There is no Pontryagin type minimum principle available for systems with discontinuous vector fields. This needs an entirely new theoretical development. We present some numerical results for the discrete time models only. We shall also discuss stochastic versions of these models and the associated mathematical problems.

1 References

[1] N.U.Ahmed, Q. Wang and L.O. Barbosa, A Systems Approach to Modeling the Token Bucket Algorithm in Computer Networks, International Journal of Communication Systems, (to appear).

[2] N.U. Ahmed, K.L. Teo, Dynamic Models for Computer Communication Network and Their Mathematical Analysis, Journal of ” Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS), ( to Appear).