  P-time event graphs are discrete event systems suitable for modeling
processes in which tasks must be executed in predefined time windows. Their
dynamics can be represented by systems of linear dynamical inequalities in the
max-plus algebra and its dual, the min-plus algebra, referred to as max-plus
linear-dual inequalities (LDIs). We define a new class of models called
switched LDIs (SLDIs), which allow to switch between different modes of
operations, each corresponding to an LDI, according to an infinite sequence of
modes called schedule. In this paper, we focus on the analysis of SLDIs when
the schedule is fixed and periodic. We show that SLDIs can model single-robot
multi-product processing networks, in which every product has different
processing requirements and corresponds to a specific mode of operation. Based
on the analysis of SLDIs, we propose an algorithm to compute minimum and
maximum cycle times for these processes that improves the time complexity of
other existing approaches.
