Please solve using excel

2. M/M/1 Queue with Reneging: consider a first-in-first-out M/M/1 queue where customers can decide to leave the system (renege) while waiting in the queue. We model the customer's "patience" as follows: if the time spent by the customer waiting in the queue exceeds the patience, she abandons the queue. We assume the customers never leave the system as soon as they started to get their service. (a) Assume the mean of service duration is 15 minutes for each customer, and the customer's arrival rate to the system is 4 customers per hour. Also, let the patience time for all customers be p minutes. Simulate the above system for p=120,p=60, and p=. Note that p= simply means that customers never leave the system before getting their service. (b) Based on the simulation results in part (a), answer the following questions for each setting (p=120,60,). (b1) What is the average waiting time in the queue for each customer? (b2) What is the average total time in the system (sojourn time) for each customer? (b3) What is the average number of customers in the system? (b4) Report the percentage of time the system is empty, i.e., the server is idle. (b5) Verify whether the PK formula and Little's law are consistent with your simulation results. (c) Consider the system you simulated in part (b) with p= but add this modification: the queue has a finite buffer (capacity) of size 9 , so at any time, maximum 10 customers can be present in the system. In this system, we assume a customer who faces a full system will leave (balk) and never come back. Simulate this new system and report the average number of customers in the system. Compare the new system with your results in part (b) with p=120