the bank is considering the possibility of installing a network of ATMs in one of its branches.
Question:
the bank is considering the possibility of installing a network of ATMs in one of its branches. Since the influx of the public that will demand this service is unknown, it places a single ATM for a month. Data on customer arrival times, as well as service times, are collected daily. Assuming that the branch is located in a neighborhood where there is no other similar service, the arriving customer prefers to wait to be able to use the ATM, when it is busy. After the appropriate analysis of the data collected, it is estimated that: (i) arrivals follow a 'Poisson process; (ii) the distribution of service time is exponential; (iii) the average time elapsed between two consecutive arrivals is 7.5 minutes; (iv) the average service time is 5 minutes per customer.
Calculate:
a. Average waiting time that each client in the queue must suffer.
b. Average queue size and probability that when going to the ATM there is already someone in the queue
Systems analysis and design in a changing world
ISBN: 978-1423902287
5th edition
Authors: John W. Satzinger, Robert B. Jackson, Stephen D. Burd