A software company is developing a new system for handling incoming requests from users. Based on historical data, there is an average arrival rate of 280 requests per hour, and it takes an average time of 9 seconds to handle a single request. To analyse the performance of the system and identify any potential bottlenecks, the company models it as an M/M/1 queue. You are currently logged in as. Amanpreet Kaur. a. (1 mark) Write down the service rate , the arrival rate , and the traffic intensity , for this queue. Include relevant units. b. (1 marks) What is the long term average number of requests in the queue (including any which are currently being handled)? c. ( 2 marks) After a user submits a request, how long will it be before their request finishes being handled? d. (2 marks) In the long-term, what is the probability that the queue is empty? e. (3 marks) The company would like to reduce the average time taken before a request finishes being handled to half of the value you calculated in (c). Assuming the arrival rate is unchanged, what service rate is needed to meet this objective? Show all working. Give your answers to at least 3 decimal places. Include your answers in the document you submit at the end of the exam