Question

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 50,000 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 25,000 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 sorting 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 21,000 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. 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 "0".

Answer 1

Without applying Queueing model this can be just clarified by following rationales:

• Since the landing rate is higher than the administration rate in 6 pm to 6 am space the most noteworthy no of holding up will be in this opening as it were.
• Likewise the most elevated no of holding up taxi will be at end of 6 am as the landing rate and serving rate is steady all through.
• Presently the distinction between administration rate and entry rate is 15000 every hour ,for the vacancy of 6pm to 8 pm, till 8pm the holding up line will wind up 30 vans (as every van convey 1000).
• Additionally for the time of 8 pm to 6am the distinction in the administration rate and landing rate is 9000 so the holding up line will increment by 9 vans for each hour.
• Henceforth in the time of 6pm to 6 am, at time of 6 am all out no. of vans holding on to be served = 30 + 10 *9 = 120 vans
• Though the all out no of vans in the line will be 121 , in which 120 pausing and 1 getting served at 5:59 am.

The answer is 120 vans.