A bank has one drive-in counter. It is estimated that cars arrive according to Poisson distribution at
the rate of 2 every 5 minutes and that there is enough space to accommodate a line of 10 cars. Other
arriving cars can wait outside this space, if necessary. It takes 1.5 minutes on an average to serve a
customer, but the service time actually varies according to an exponential distribution. You are
required to find:
a) The probability of time, the facility remains idle.
b) The expected number of customers waiting but currently not being served at a particular point
of time.
c) The expected time a customer spends in the system
d) The probability that the waiting line will exceed the capacity of the space leading to the drive-
in counter
Mean arrival rate:
Mean service rate:
a)
The probability of time, the facility remains idle:
b)
The expected number of customers waiting:
c)
expected time a customer spends in the system:
min
d)
the probability that n customers waiting in a queue for service:
then probability that the waiting line will exceed 10 cars:
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