Seaports are important in global supply chains. Their management plays an important part in minimizing waiting time for ships that visit seaports for loading and unloading cargo and port utilization. The Oakland seaport is a busy container seaport on the West coast of America, but it is a bit relaxed in the month of December. Based on the past data, it is observed that 6 ships arrive there, on an average, per day, and it takes 3 hours to unload a ship on an average, with a standard deviation of 4 hours. Determine the following: Minimum number of unlading facilities.Probability (each unloading facility is busy)Probability (each unloading facility is idle)Probability of 2 ships in the system and 4 ships in the systemAverage number of ships in the system, that is, number of ships in the line including the one being unloaded.Average number of ships waiting to be unloaded, that is, number of ships in the line excluding being unloaded.Average time a ship spends in the system, that is, waiting time plus unloading time.Average time a customer spends in the waiting line before reaching the unloading berth.Redo (e) to (g) above if the ship’s unloading time has an Exponential distribution.Based on the statistics computed in (e) to (g) above in Question 1, you (as an expert) realized that too many ships are in the line for service and there have been complaints recently. In view of your knowledge of queuing analysis, you would advise as a consultant to install the state-of-the-arts unloading facility which can unload or load a ship in exactly 3 hours. Redo (e) to (g) above if the ship’s unloading time is exactly 3 hours for each ship.Tabulate (a) to (h) statistics for the three queueing systems.

NOTE: We are allowed to do the first three sub-parts only. The queuing theory was first developed in…

Answered: Minimum number of unlading facilities.…

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 21P

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Seaports are important in global supply chains. Their management plays an important part in minimizing waiting time for ships that visit seaports for loading and unloading cargo and port utilization. The Oakland seaport is a busy container seaport on the West coast of America, but it is a bit relaxed in the month of December. Based on the past data, it is observed that 6 ships arrive there, on an average, per day, and it takes 3 hours to unload a ship on an average, with a standard deviation of 4 hours. Determine the following:

Minimum number of unlading facilities.
Probability (each unloading facility is busy)
Probability (each unloading facility is idle)
Probability of 2 ships in the system and 4 ships in the system
Average number of ships in the system, that is, number of ships in the line including the one being unloaded.
Average number of ships waiting to be unloaded, that is, number of ships in the line excluding being unloaded.
Average time a ship spends in the system, that is, waiting time plus unloading time.
Average time a customer spends in the waiting line before reaching the unloading berth.
Redo (e) to (g) above if the ship’s unloading time has an Exponential distribution.
Based on the statistics computed in (e) to (g) above in Question 1, you (as an expert) realized that too many ships are in the line for service and there have been complaints recently. In view of your knowledge of queuing analysis, you would advise as a consultant to install the state-of-the-arts unloading facility which can unload or load a ship in exactly 3 hours. Redo (e) to (g) above if the ship’s unloading time is exactly 3 hours for each ship.
Tabulate (a) to (h) statistics for the three queueing systems.

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