Answer to Question #136026 in Math for Nikhil

Question

In a doctor's clinic patients arrive at the rate of 5 per hour and the doctor has to spend on an average 10 minutes with each patient if the arrival process of the patients is assumed to be Possion

Answer 1

If the arrival process of the patients is assumed to be Possion at the rate of 5 per hour and the time doctor takes to examine any patient is exponential with mean 10 minutes, find the expected total time spent (including the service time) by any patient who visits the doctor.

$\lambda=5/hour, \mu=6/hour$

Average waiting time of a patient before receiving service 

$W=\dfrac{\lambda}{\mu(\mu-\lambda)}=\dfrac{5/hour}{6/hour(6/hour-5/hour)}=$

$=\dfrac{5}{6}hour=50 min$