Consider a taxi stand where inter-arrival times of the taxis and the customers are both exponential...
Consider a taxi stand where inter-arrival times of the taxis and
the customers are both exponential with means of 0.5 and 1 minutes,
respectively. Stand has 3 spots that taxis can park while waiting
for the arriving customers. Arriving taxis leaves the stand when
all the spots are occupied. Similarly, arriving customers are also
lost when there is no taxi in the stand.
a. Model this system as a birth and death process by defining the
state and the state space, and drawing the rate diagram.
b. Compute the steady-state probabilities.
c. What is the expected number of taxis waiting at the stand in the
long run?
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