Scenario To begin this problem, let us first recall the queue length of a basic G/G/1...

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Scenario To begin this problem, let us first recall the queue length of a basic G/G/1 queuing system from module one: E[L] = p2CV+CV P 2 As usual, the right-hand side of the multiplication sign is the conversion factor to adjust for the in- terarrival and service time distributions where "M" represents the exponential distribution (with) a mean and standard deviation equal to each other), "G" represents the general distribution (where the mean and standard deviation do not necessarily equal each other), and "D" represents a de- terministic/constant rate (with a standard deviation equal to zero). Remember that CV is the squared coefficient of variation for the interarrival times: CV2 = E[A]2 Of course the CV term is defined analogously for service time. Now for our problem. To regulate merging traffic onto a freeway, the transportation department installed a traffic light signal on an on-ramp. When vehicles are present, the signal lets one vehicle into the expressway precisely every E[T] 12 seconds here we use "precisely" to indicate the service time is constant. Vehicles wait in a single queue in the merging lane. Assume the times between consecutive vehicle arrivals to the on-ramp lane are exponentially distributed with a mean of E [A] = 15 seconds. Questions 1. Calculate the input parameters A and (in vehicles per minute). " 2. What is the probability of finding no vehicles in the merging lane, Po? 3. How would you characterize the traffic light queue (M/M/1, G/G/1, etc.)? What is the average number of vehicles in the lane (in line plus at the light) waiting to merge into the freeway? 4. Using your answer from above, calculate the waiting time (seconds) for a vehicle to completely merge into the freeway. Scenario To begin this problem, let us first recall the queue length of a basic G/G/1 queuing system from module one: E[L] = p2CV+CV P 2 As usual, the right-hand side of the multiplication sign is the conversion factor to adjust for the in- terarrival and service time distributions where "M" represents the exponential distribution (with) a mean and standard deviation equal to each other), "G" represents the general distribution (where the mean and standard deviation do not necessarily equal each other), and "D" represents a de- terministic/constant rate (with a standard deviation equal to zero). Remember that CV is the squared coefficient of variation for the interarrival times: CV2 = E[A]2 Of course the CV term is defined analogously for service time. Now for our problem. To regulate merging traffic onto a freeway, the transportation department installed a traffic light signal on an on-ramp. When vehicles are present, the signal lets one vehicle into the expressway precisely every E[T] 12 seconds here we use "precisely" to indicate the service time is constant. Vehicles wait in a single queue in the merging lane. Assume the times between consecutive vehicle arrivals to the on-ramp lane are exponentially distributed with a mean of E [A] = 15 seconds. Questions 1. Calculate the input parameters A and (in vehicles per minute). " 2. What is the probability of finding no vehicles in the merging lane, Po? 3. How would you characterize the traffic light queue (M/M/1, G/G/1, etc.)? What is the average number of vehicles in the lane (in line plus at the light) waiting to merge into the freeway? 4. Using your answer from above, calculate the waiting time (seconds) for a vehicle to completely merge into the freeway.