In this paper we discuss modelling and control of discrete-event systems using max-min-plus-scaling systems. We analyse how the basic operations max, min, plus, and scaling occur in the modelling phase and we discuss some general forms for the system. Because of the different/deviating character of the signals in a discrete-event MMPS model, we will discuss concepts such as time-invariance and steady-state behavior. In the design of a model predictive controller for MMPS systems we have to revisit the cost functions in light of the discrete-event nature of the signals. We finalize this paper with the an intuitive case study on an urban railway line, performing both modelling and control.