Queuing theory - 2018

Question 1: Arrival rate and service rate at a service centre follow Poisson distribution with mean 25 per hour and 40 per hour respectively. A person doesn't join such system if there is at least one person waiting for the service in addition to the one getting served.

a) What is the probability that this person will join the system?                                                 3 marks

b) Management wants that the probability of such persons joining the system be 0.9. What should be the mean service rate?                                                                                                                  5 marks

Answer can be seen at

https://drive.google.com/file/d/1G0zr5SHv3izAZqeDulpNQ0KLpyS1B1M7/view?usp=sharing