Question 5 A post office has a counter for customer drive-through to pay the bill. The design of the drive- through lane allows for unlimited queue length. The arrival and service rate are Poisson distributed with A= 40 customers per hour arriving on average and u =50 customers per hour can be served on average. a. Compute the average number of arrivals. (2 Marks) b. Compute the average time a customer wait. (2 Marks) c. Compute the average number of arrivals in the system. (2 Marks) d. Compute the average time a customer is in the system. (2 Marks) e. Compute the probability that less than or equal to 2 customers are in the system. (3 Marks) f. Due to the covid-19 pandemic, the unlimited queuing length has been modified to limited queuing length to control the number of cars waiting. The queue length has been limited to 4 cars only with A= 40 and p =50. Compute (a) and (b). (4 Marks) (Total : 15 Marks) Question 5 A post office has a counter for customer drive-through to pay the bill. The design of the drive- through lane allows for unlimited queue length. The arrival and service rate are Poisson distributed with A= 40 customers per hour arriving on average and u =50 customers per hour can be served on average. a. Compute the average number of arrivals. (2 Marks) b. Compute the average time a customer wait. (2 Marks) c. Compute the average number of arrivals in the system. (2 Marks) d. Compute the average time a customer is in the system. (2 Marks) e. Compute the probability that less than or equal to 2 customers are in the system. (3 Marks) f. Due to the covid-19 pandemic, the unlimited queuing length has been modified to limited queuing length to control the number of cars waiting. The queue length has been limited to 4 cars only with A= 40 and p =50. Compute (a) and (b). (4 Marks) (Total : 15 Marks)