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Analyzing Queuing Systems for Efficiency in Reducing Waiting Time

Queuing theory is applied in various fields to optimize systems and reduce wait times. In this task, data from two systems with different queuing rules was compared. System 1 has separate queues where people choose the shortest line while System 2 has a single queue. Analyzing waiting times for 25 people in each system showed that System 2 with a single queue was more efficient in reducing waiting time.

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Analyzing Queuing Systems for Efficiency in Reducing Waiting Time

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  1. Queues You are in a shop, about to pay for something. Till 1 Till 3 Till 4 Till 2 20 items 8 2 10 items Which till queue would you join? items items Why? 5 10 items 8 items items 7 3 items items 1 item

  2. Queuing theory is an area of maths which has many applications. When you log onto the internet you join a queue for a server. Computer engineers and systems designers study queues to help them make systems work more efficiently. Civil engineers use it for traffic lights and retailers use queuing theory to reduce your wait time. In the following task you will examine data from two queuing systems. Both systems have three service points (checkouts) but the queues have different rules.

  3. System 1 Separate Queues Rule People join whichever queue they think will serve them the quickest. This is normally the shortest queue when they arrive, which means the people are shared out equally between the queues. System 2 Single Queue Rule Everyone waits in one queue, and moves to the first available checkout when it becomes free.

  4. System 2 Single Queue System 1 Separate Queues Waiting times for 25 People Time (mins) 0 1 2 3 4 8 10 Waiting times for 25 People Time (mins) 0 1 2 3 4 5 6 Frequency 5 5 5 3 4 1 2 Frequency 3 2 3 9 3 3 2 Using this data, compare both systems and suggest which you think is most efficient in reducing waiting time.

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