
A natural extension of a DTMC occurs when time is treated as
a continuous parameter. In this section, we consider continuoustime,
discretestate stochastic processes but limit our attention
to the case where the Markovian property holds; that is, the
future realization of a system depends only on the current state
and the random events that proceed from it.This is call a Continuous
Time Markov Chain (CTMC). Some times we use the term Markov
Process for this kind of system.
It happens that the Markov property is only satisfied in a
continuoustime stochastic process if all activity durations
are exponentially distributed. Although this may sound somewhat
restrictive, many practical situations can be modeled as CTMC
and many powerful analytical results can be obtained. A primary
example is an M/M/s queueing system in
which customer arrivals and service times follow an exponential
distribution. Because it is possible to compute the steadystate
probabilities for such systems, it is also possible to compute
many performancerelated statistics such as the average wait
and the average number of customers in the queue. In addition,
many critical design and operational questions can be answered
with little computational effort.
