Critical Path Statistics of Max-Plus Linear Systems with Gaussian Noise

James Hook
2013 Journal of Applied Probability  
The critical paths of a max-plus linear system with noise are random variables. In this paper we introduce theedge criticalitieswhich measure how often the critical paths traverse each edge in the precedence graph. We also present theparallel path approximation, a novel method for approximating these new statistics as well as the previously studied max-plus exponent. We show that, for low amplitude noise, the critical paths spend most of their time traversing the deterministic maximally
more » ... cycle and that, as the noise amplitude is increased, the critical paths become more random and their distribution over the edges in the precedence graph approaches a highly uniform measure of maximal entropy.
doi:10.1017/s0021900200009761 fatcat:7uqa4cwro5cabnutrv37upczci