Question: Customers arrive to a system according to a Poisson process with parameter 1/min. Customer service time is exponentially distributed with parameter 2/min. A single server

Customers arrive to a system according to a Poisson process with parameter 1/min. Customer service time is exponentially distributed with parameter 2/min. A single server serves all customers. Each customer is endowed with a patience level that is uniformly distributed between 0.3 min and 0.6 min. If a customers time of waiting in the queue reaches his/her patience level, then he/she immediately leaves system without waiting for the service any longer. Please compute (1) the 100th customers expected waiting time, (2) the probability that the 100th customer leaves the system after receiving the service, (3) the 100th customers expected time of staying in the system.

Run a Monte Carlo simulation with 1000 replications of the 100th customer values. Please be certain that you model clearly outputs the answers to the questions below.

What is the probability that the 100th customer will be served? (Round your answer to 2 decimal places.)

What is the average wait time of the 100th customer in minutes? (Round your answer to 2 decimal places.)

What is the average time in the system for the 100th customer in minutes? (Time in the system is defined as the time from arrival to departure for the 100th customer.) (Round the proportion to 2 decimal places.)

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