A food-truck has one cashier and one cook. Customers first wait in line to ‘plac

Question

A food-truck has one cashier and one cook. Customers first wait in line to ‘place the order and pay the cashier’, and then enter a ‘pick-up’ line to get the food that is being prepared by the cook. Currently, the cashier can take an order and handle the money transaction in an average of 1 minutes. The cook can prepare an order in exactly 2 minutes. During an hour, 15 customers arrive on average. The interarrival times are exponentially distributed.

What is the average number of customers in the food-truck?

Explanation / Answer

Average number of customers in food truck is given by = Arrival rate / (Service rate - Arrival rate)

Service rate for cashier is 60 per hour but for cook is 30 per hour. Therefore service rate of system is 30 per hour.

Average number of customers in the system (food truck) is = 15 / (30-15) = 1.

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