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Problem # 2 (40 points) The Blue and White (B&W) Cab Company owns two taxis. The taxi service operates 24 hours per day and seven days per week. Calls arrive at the dispatching office according to a Poisson distribution with a mean of 10 calls per hour. The length of each ride (time to pick up a customer plus taking the customer to his/her destination) is known to be exponential with a mean of 12 minutes. Because of the high demand on the cab service, B& W limits the waiting list at the dispatching office to 3 customers. Once the limit is reached, future customers are advised to seek service elsewhere because of potential long wait. The B& W Cab Company can be modeled as a queueing system where the customers are people using the taxi service and the servers are the taxis (a) (5 points) Use Kendall's notation to define the queueing system corresponding the B& W Cab Company. (b) (5 points) Determine the arrival rate, service rate per server, and provide the time unit used to represent the rates. Also, draw the state transition diagram including transition rates. (c) (10 points) Compute the steady state probabilities. (d) (5 points) Determine the average number of busy taxis (e) (5 points) Determine the probability that a calling customer receives service immediately (i.e., he/she is not rejected and does not have to be placed in the waiting list). (f) (5 points) Determine the probability that a calling customer is rejected. (g) (5 points) Determine the average number of customers in the waiting list