  After sketching the basic principles of renewal theory we discuss the
classical Poisson process and offer two other processes, namely the renewal
process of Mittag-Leffler type and the renewal process of Wright type, so named
by us because special functions of Mittag-Leffler and of Wright type appear in
the definition of the relevant waiting times. We compare these three processes
with each other, furthermore consider corresponding renewal processes with
reward and numerically their long-time behaviour.
