Question: STOCHASTIC MODELING Question 5 (101 A small supermarket has two self-service scanners whore customers can pay for their purchases. Customers arrive at these randomly at

STOCHASTIC MODELING

Question 5 (101 A small supermarket has two self-service scanners whore customers can pay for their purchases. Customers arrive at these randomly at an average rate of 20 per hour and have independent exponentially distributed service times taking, on average, 5 minutes each to complete their purchases. Currently there is a single queue for both scanners but a new manager is considering two further options: (1) relocating one of the scanners to the opposite end of the shop so that there will be separate queues for each machine with customers assumed equally likely to enter either queue; (11) selling one scanner leaving only one to serve all the customers. For the three possible options including the existing setup) calculate, where possible, the proportion of customers who will be served immediately on arrival (that is without joining the queue) and advise the manager appropriately

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