(5 points) Use queueing theory. The following systems assume that each server has capacity 1 , and all times are exponential distributions unless otherwise specified. State any other assumptions you make. For each of the following systems, answer the questions: i. Is this a stable system? If not, why not. ii. If it is a stable system, estimate the Utilization of each server. iii. If it is a stable system, estimate the overall Number in System and Time in System (in minutes) a) Serial system: Arrivals 15/hour; ServerA service rate 35 /hour; ServerB service rate 25/ hour. In addition to reporting results on the table below, show equations and calculations in detail. b) Serial system: Arrivals 60/hour; ServerA service time 1.2 minute; ServerB service time 0.6 minutes. In addition to reporting results on the table below, show equations and calculations in detail. c) Parallel system: Arrivals 60/hour; ServerA service time 1.2 minute; ServerB service time 0.6 minutes. Assume a 5050% chance of arriving at server A or B. In addition to reporting results on the table below, show equations and calculations in detail. d) Serial system: Interarrival time is Exponential (6) minutes; ServerA service time Uniform (3,4) minutes; ServerB service time Uniform (4,6) minutes. In addition to reporting results on the table below, show equations and calculations in detail