Question: 2 Royal Roman Asterix: Caesar has sent romans to our village to repair the weapons. They will arrive in the next week. Cacofonix: Is it?

2 Royal Roman" Asterix: Caesar has sent romans to

2 Royal Roman" Asterix: Caesar has sent romans to our village to repair the weapons. They will arrive in the next week. Cacofonix: Is it? How many romans are coming? Asterix: You can't count them. Infinite! Cacofonix: Who will serve them? Asterix: We have formed a 'special team comprising Obelix and Getafix. They have equal caliber. These two fellows are capable enough to serve all of them. No third person is required at all. Cacofonix: what is the arrival rate of the romans and the service rate of the special team? Asterix: As per our projection, six romans will arrive in every two hours whereas the special team can provide service to 18 romans in three hours. Cacofonix: What is the probability that no roman will be in the system? Asterix: The probability that no roman will be in the system is 0.6. Cacofonix: Okay. Let the fun begin! Based on the conversation above, assuming the romans' arrivals follow a Poisson distribution and service time follows a negative exponential distribution, answer the following questions a) What is the most appropriate queuing model for this system? b) What is the average number of romans in the system (the number in line +number being served)? c) What is the average time a roman spends in the system (in hours)? d) What is the average number of romans in the queue? e) What is the average time a roman spends waiting in the queue (in hours)? f) What is the utilization factor for the system, (the probability the system is being used)

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