Customers are arriving at a bank office according to a Poisson process at a mean rate of
Question:
Customers are arriving at a bank office according to a Poisson process at a mean rate of 10 per hour. Currently, two officers are available. Each officer can serve a customer with an exponential service time with a mean of 12 minutes. It also has been noticed that if there are already 4 customers in the office (including the customers being served), then any additional arriving customers leave and take their business elsewhere. The profit made from each customer is assumed as $5.
a. Define state variable properly and give the state space to model this system as a birth and death process.
b. Find the steady-state probabilities.
c. What is the expected number of customers in the system (including the one being served) in the shop?
d. What is the expected amount of time spent in the system for a customer?
e. What is the hourly profit?
f. What is the probability that both officers are busy?
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman