This problem presents a Ticket booking system.

Customer arrive at a ticket counter for collecting Train ticket.   Customers arrive the counter with exponentially distributed inter-arrival times of mean 7 minutes. Now when a new customer comes to the booth, he/she see the queue, if they feel comfortable then he/she wait before the queue. 75% of them waited in the queue and rest of them will check the line after some time.

Before going to ticket counter they need to go to the Checking Counter for some checking (Like whether they have their id and other necessary document with them or not). If they do not have necessary document then after collecting their document they need to join the queue again. Checking time is uniformly distributed between 3 and 5 minutes.  10% of them leave the counter and rest of them enter for collecting ticket. After enter in the ticket counter each customer needs 5 minutes to collect his or her ticket. We are interested in simulating the system for 50 hours to obtain process utilization.

Find out:

1.      The number of customer enter in the system

2.      The number of customer leave the system by collecting ticket

3.      The number of customer leave the system without collecting ticket