Assignment task: Queueing models
A small take away pizza restaurant operates for 8 hours per day, 5 days a week. Past records show that customers arrive at the restaurant at an average of one every 10 minutes. The restaurant currently employs one staff who serves customers and it takes 6 minutes on average to serve each customer (from the time an order is accepted through to making the pizza and taking payment). Assuming Poisson distribution on the arrival rate of customers and exponential distribution on the service times performed by the staff, answer the following questions: a) Due to limited space, the restaurant management wants to limit the probability of having more than 3 customers in the restaurant to 5% by improving the service rate. Calculate the required service rate to achieve the goal and the customer's waiting time? Use trial and error to find the required service rate, and show the two closest figures above and below your final answer at 2 decimal points b) The restaurant management considers two options to reduce the customers' waiting time: (i) Employing another staff member and splitting the tasks equally between the two staff to reduce the