DES meaning in Maths ?

A discrete-event simulation (DES) models the operation of a system as a (discrete) sequence of events in time. Each event occurs at a particular instant in time and marks a change of state in the system. Between consecutive events, no change in the system is assumed to occur; thus the simulation time can directly jump to the occurrence time of the next event, which is called next-event time progression.

In addition to next-event time progression, there is also an alternative approach, called fixed-increment time progression, where time is broken up into small time slices and the system state is updated according to the set of events/activities happening in the time slice. Because not every time slice has to be simulated, a next-event time simulation can typically run much faster than a corresponding fixed-increment time simulation.

Both forms of DES contrast with continuous simulation in which the system state is changed continuously over time on the basis of a set of differential equations defining the rates of change of state variables.