Performance analysis of a telephone system with both patient and
impatient customers
In this paper, the performance of a telephone system in which there
are both patient and impatient customers is studied. Depending on the
waiting time in the buffer, a customer may become impatient and therefore
the call is incomplete. A impatient customer still consumes real processing
time. The impact of impatient customers on the system is much more
remarkable than people would expect.
We formulate this model as a queueing system with a finite buffer.
The status of a customer, i.e. whether patient or impatient, depends on the
waiting time
in the buffer and the service time is different for different type
of customers.
The joint distribution of the numbers of patient and impatient customers
in the system is obtained for the system in equilibrium. Expressions
of many performance measures, including
the average number of
patient customers or impatient customers in the system,
the average length of the service time, the average arrivals during a
service period and the proportion of the "useful"
service time contributing towards
patient customers' service,
can be expressed in terms of the joint probabilities.
The waiting time probabilities and the average waiting time
of a customer in the buffer, and the probability that a customer will
be served as a patient customer are also obtained.
Numerical examples are presented.
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