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Since this is clearly homework, can you please show what you've attempted so far, so we can provide advice and direction? I'm not comfortable providing answers to homework questions.
EDIT: it's important to understand the approach to this question because you're likely required to use the methods you were taught in class, but there's several ways to accomplish this, either in Base SAS, IML or SAS/OR procs. Posting a solution in a different approach than you need isn't going to be helpful to you.
The problem: A petrol station opens at 8pm and closes at 11pm. All through the evening, the inter-arrival time of customers has an exponential distribution with mean 1.3 minutes. Until 9.30pm customers are served inside the shop, with a service time that has an exponential distribution with mean 1 minute. Customers who arrive after 9.30pm are served through a hatch, with a service time that has an exponential distribution with mean 1.55 minutes.
(i) Simulate the arrivals at the petrol station throughout the 3-hour period (it is acceptable to simulate more than required, then discard those who arrive after 11pm). Simulate the corresponding service-times, and calculate the total waiting and service times for each customer. Explain carefully the meaning of each value you calculate.
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