please answer question 2 and use question 1 for reference
1. A two-runway (one runway dedicated to landing, one runway for dedicated to taking off) airport is being designed for propeller-driven aircraft. The time to land an airplane is known to be exponentially distributed with a mean of 1.5 minutes. Assume that the airplanes arrivals are assumed to occur at random with exponentially distributed inter-arrival times. From the above assumptions, it is easy to see that this run-way landing system can be viewed as an M/M/1 queue with average service time of 1.5 minutes. Based on the information above, answer the following questions: (a) Calculate the average waiting times and average numbers of airplanes waiting for landing for various values of arrival rates (from relatively small values to close to the service rate) and plot them as functions of the arrival rate. What arrival rate(s) would you recommend for based on plots? [Feel free to use MS Excel, MATLAB, or other computer tools to answer this part.] (b) What arrival rate can be tolerated if the average waiting time in the sky is not to exceed 3 minutes? (c) Under the arrival rate obtained in (b), what is the average number airplanes waiting in the sky for landing? 2. Repeat (a)(b)(c) of Problem 1 assuming that the airport has two runways for landing and the landing time of an airplane is still exponentially distributed with a mean of 1.5min. [Hint: It will] be difficult to try to derive that arrival rate analytically but you can solve it numerically by, for instance, trial-and-error.] 1. A two-runway (one runway dedicated to landing, one runway for dedicated to taking off) airport is being designed for propeller-driven aircraft. The time to land an airplane is known to be exponentially distributed with a mean of 1.5 minutes. Assume that the airplanes arrivals are assumed to occur at random with exponentially distributed inter-arrival times. From the above assumptions, it is easy to see that this run-way landing system can be viewed as an M/M/1 queue with average service time of 1.5 minutes. Based on the information above, answer the following questions: (a) Calculate the average waiting times and average numbers of airplanes waiting for landing for various values of arrival rates (from relatively small values to close to the service rate) and plot them as functions of the arrival rate. What arrival rate(s) would you recommend for based on plots? [Feel free to use MS Excel, MATLAB, or other computer tools to answer this part.] (b) What arrival rate can be tolerated if the average waiting time in the sky is not to exceed 3 minutes? (c) Under the arrival rate obtained in (b), what is the average number airplanes waiting in the sky for landing? 2. Repeat (a)(b)(c) of Problem 1 assuming that the airport has two runways for landing and the landing time of an airplane is still exponentially distributed with a mean of 1.5min. [Hint: It will] be difficult to try to derive that arrival rate analytically but you can solve it numerically by, for instance, trial-and-error.]
