Assignment:
Bank tellers—Consider a banking system involving two inside tellers and two drivein tellers. Arrivals to the banking system are either for the drive-in tellers or for the inside tellers. The time between arrivals to the drive-in tellers is exponentially distributed with a mean of 1 min. The drive-in tellers have limited waiting space. Queuing space is available for only three cars waiting for the first teller and four cars waiting for the second teller. The service time of the first drive-in teller is normally distributed with a mean of 2 min and a standard deviation of 0.25. The service time of the second drive-in teller is uniformly distributed between 1 and 3 min. If a car arrives when the queues of both drive-in tellers are full, the customer balks and seeks service from one of the inside bank tellers. However, the inside bank system opens 1 h after the drive-in bank, and it takes between 0.5 and 1 min to park and walk inside the bank. Customers who seek the services of the inside tellers directly arrive through a different process, with the time between arrivals exponentially distributed with a mean of 1.5 min. However, they join the same queue as those balking from the drive-in tellers. A single queue is used for both inside tellers. A maximum of seven customers can wait in this single queue. Customers arriving when seven are in the inside queue leave. The service times for the two inside tellers are triangularly distributed between 1 and 4 min with a mode of 3 min. Simulate the operation of the bank for an 8 h period (7 h for the inside tellers). Assess the performance of the current system.
Provide complete and step by step solution for the question and show calculations and use formulas.