Parallel processing of random sequences with priority

Abstract

Dedicated to B. Gyires on his 70 anniversary §1. Introduction and main results. We continue our work [1]. Let A_N denote the set {1,2,…,N} fand

$$\matrix{ {{{\rm{f}}_{\rm{1}}}^{(1)},{{\rm{f}}_2}^{(1)}, \ldots } \cr {{{\rm{f}}_{\rm{1}}}^{(2)},{{\rm{f}}_2}^{(2)}, \ldots } \cr \vdots \cr {{{\rm{f}}_{\rm{1}}}^{({\rm{r}})},{{\rm{f}}_2}^{({\rm{r}})}, \ldots } \cr }$$

an infinite sequence of infinite sequences, the elements of which belong to A_N We process the elements in the sequences according to the following rules: