Trains pull into a railroad station and must wait for each other
before leaving again in order to let passengers change trains. How
do mathematicians then calculate a railroad timetable that
accurately reflects their comings and goings? One approach is to
use max-plus algebra, a framework used to model Discrete Event
Systems, which are well suited to describe the ordering and timing
of events. This is the first textbook on max-plus algebra,
providing a concise and self-contained introduction to the
topic.
Applications of max-plus algebra abound in the world around us.
Traffic systems, computer communication systems, production lines,
and flows in networks are all based on discrete even systems, and
thus can be conveniently described and analyzed by means of
max-plus algebra.
The book consists of an introduction and thirteen chapters in
three parts. Part One explores the introduction of max-plus algebra
and of system descriptions based upon it. Part Two deals with a
real application, namely the design of timetables for railway
networks. Part Three examines various extensions, such as
stochastic systems and min-max-plus systems. The text is suitable
for last-year undergraduates in mathematics, and each chapter
provides exercises, notes, and a reference section.
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