Question

Baylor University w D Finance 3310: Intro О YouTu Question 8 2 pts The National Overnight (NatO) company provides express small package delivery overnight. Airplanes arrive 24 hours a day at the national hub in Dallas where their contents are unloaded onto cargo vans each capable of holding 1,000 packages. The cargo vans transport the packages to the sorting center. The sorting center has a large storage area designed to hold up to 49.000 packages. After being sorted, another fleet of cargo vans transports the packages to the outgoing planes. However, the following information details the receiving process only. During the night (6 p.m. to 6 a.m.), airplanes arrive at a high rate providing a continuous arrival flow of packages with an average rate of 27.000 packages per hour. However, during the day (6 a.m. to 6 p.m.) air landings are less frequent, resulting in an average arrival rate of 5,000 packages per hour. NatO runs two 12-hour shifts at the center: the night shift starts at 8 p.m. and leaves by 8 a.m. The night shift has the largest number of employees and can process up to 18,000 packages per hour. The day shift, on the other hand, is smaller and can process up to 12,000 packages per hour from 8 a.m. to 8 p.m. It is known that the cargo vans typically had to wait to unload at the sorting center during some portions of the night shift. Cargo van drivers were paid $10/hour, benefits included. sorting NatO begins each night with completely empty storage bins at 6 p.m. Cargo vans begin waiting as soon as the storage area is full. What is the maximum number of cargo vans waiting in line at any given during a 24-hour period? Input your answer as a whole integer such as "17"or"9". If capacity is such that no vans ever have to wait then input "O Question S9

Answer 1

Answer:

• 120 vans.

Explanation:

• Without applying Queueing model this can be simply explained by following logics:
  • Since the arrival rate is higher than the service rate in 6 pm to 6 am slot the highest no of waiting will be in this slot only.
  • Also the highest no of waiting cab will be at end of 6 am as the arrival rate and serving rate is constant throughout.
  • Now the difference between service rate and arrival rate is 15000 per hour ,for the time slot of 6pm to 8 pm, till 8pm the waiting line will become 30 vans (as each van carry 1000).
  • Also for the period of 8 pm to 6am the difference in the service rate and arrival rate is 9000 so the waiting line will increase by 9 vans per hour.
  • Hence in the period of 6pm to 6 am, at time of 6 am total no. of vans waiting to be served = 30 + 10 *9 = 120 vans
  • Whereas the total no of vans in the line will be 121 , in which 120 waiting and 1 getting served at 5:59 am.