Assumed that potential customers will start to balk when they see more than 10 p

Question

Assumed that potential customers will start to balk when they see more than 10 people are already in queuing for the restaurant. Further, it is also assumed that the maximum queue length that a potential customer can tolerate is 40 people. As the capacity of the restaurant when fully occupied is 120 people, we can calculate the probability of 10 people in the queue as the probability when there are 130 people in the system (i.e 120 in the restaurant and 10 or more queuing)

What is the probability that the customers will leave or balk given from the above assumption?
What can be done to reduce queue and avoid customers leaving to go to other competitors?

the arrival rate thus is approximately 120 people per hour and the service rate = 120 people / 8 waitresses = 15 people per waitress

Explanation / Answer

mu=120 people/hr

lambda=15 people/waitress

rho=lamba/mu=15/120=0.125

P(Customer will leave)=P(n>=10)=(Rho)^10=(0.125^10)=9.313226e-10

P(n<10)=0.9

1-rho^10=0.9

rho=0.631

mu=lamba/roh=15/0.631=24

serivce rate should increase from 15 people per waitresess to 24 people per waitressess

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