Timing optimal control and reliability of uncertain data transmission systems with interval parameters

Abstract

This paper presents an investigation of the timing optimal control and timing reliability of data transmission systems of which the launch time, transmission time, and reception time are uncertain. The time series model of uncertain data transmission systems is established by using max-plus algebra. We introduce the parametric vector-valued function of uncertain data transmission systems and the non-negative solution of max-plus linear equations. We determine, on the one hand, the minimum value of the reception time (the earliest reception time) of the data and the corresponding optimal solutions under the constraints for which the transmission time is valued in given intervals and the launch time is non-negative. On the other hand, we establish the maximum value of the launch time (the latest launch time) of the data and the corresponding optimal solutions under the constraints for which the reception time is limited in some intervals. We define reliable intervals of uncertain data transmission systems such that the data can be received within the required time and the influence of transport delays can be avoided as long as they are launched at any time during such intervals. The tolerance solution intervals of interval systems of max-plus linear equations is introduced to establish the existing criterion of reliable intervals, and an effective algorithm for finding the largest reliable interval is developed.