Assignment 1 (10%)

A supermarket has p checkouts and customers must choose one, forming a queue if it is already occupied. Customers always choose the shortest queue. The time between each new customer arriving at the checkouts has an exponential distribution with mean \mu minutes. The time it takes for a checkout operator to process a customer has an independent exponential distribution with mean \lambda minutes.

Write an R function to simulate the supermarket queues at each checkout, taking the arguments mu, lambda, p and n, and returning the total number of customers waiting to be served, n minutes after the supermarket opens. The argument p should have default value 3, while n should have default value 720 (the number of minutes in a 12 hour day). The other arguments should have no default values. Your function should be named remaining_customers.

Your code should be as efficient as possible. Arguments should be checked for range and class.

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Due: 21 March 2025
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