Problem 2. (18 marks in total) A Company has just set up a call center. Assume two technical representatives are always on duty to take the calls; the time required by either representative to answer a customer's questions has an exponential distribution with a mean of 8 minutes; and that calls arrive according to a Poisson process at a mean rate of 10 per hour. By next year, the mean arrival rate of calls is expected to decline to 5 per hour, which will allow to reduce the number of technical representatives to one then. (a) (8 marks) Assuming that the service rate will be the same as currently next year, determine L,L,,W, and W, for both the current system and next year's system. (b) (3 marks) What fraction of time is the current system empty? How about next year's system? (c) (3 marks) Calculate the utilization factor of the current and next year's system. (d) (2 marks) Under the current system, what is the probability of two calls arriving per hour? (e) (2 marks) Next year, what is the probability that a customer calling in will have to wait 10 minutes or more before his/her question will be answered? Problem 2. (18 marks in total) A Company has just set up a call center. Assume two technical representatives are always on duty to take the calls; the time required by either representative to answer a customer's questions has an exponential distribution with a mean of 8 minutes; and that calls arrive according to a Poisson process at a mean rate of 10 per hour. By next year, the mean arrival rate of calls is expected to decline to 5 per hour, which will allow to reduce the number of technical representatives to one then. (a) (8 marks) Assuming that the service rate will be the same as currently next year, determine L,L,,W, and W, for both the current system and next year's system. (b) (3 marks) What fraction of time is the current system empty? How about next year's system? (c) (3 marks) Calculate the utilization factor of the current and next year's system. (d) (2 marks) Under the current system, what is the probability of two calls arriving per hour? (e) (2 marks) Next year, what is the probability that a customer calling in will have to wait 10 minutes or more before his/her question will be answered