# Real life queue - how to model?

• Osmium
In summary, the conversation discusses two scenarios for people queuing to pick up photos at an event. In Scenario A, people scan their bar-coded docket at one of eight print stations and wait for 40 seconds for their photo to be printed. In Scenario B, people enter a "walking maze" and their docket is scanned at the entry. As they walk, their photo is being printed and ready for them when they reach the end of the maze. The criteria for comparison is the perception of wait time, with a constantly moving line being preferred. Different models, such as Kendall notations and computer simulations, can be used to compare these scenarios and determine the conditions under which Scenario B would result in a stopped line of people.
Osmium
People queuing to pick up photos at an event. They have a bar-coded docket. By scanning the docket, printing is initiated on one of eight printers. Each printer takes 40 seconds to print a photo - the software chooses the least heavily loaded print queue - or uses a round-robin approach if print jobs are zero. Working together the printers can produced a print, on average, every 5 seconds.

Scenario A
Each printer has a bar-code reader. Person walks up to one of eight "print stations" and scans their docket. 40 seconds later they have their print. So this is not spreading the load via software, this is much like a shop queue with people going to the next available print station.

Scenario B
People enter a "walking maze" - a zigzag line estimated to take 40 seconds to walk through. The dockets are scanned at the entry to the maze. At least initially, when the person arrives at the printer line, their print will be ready for them. This gives the illusion of no wait time - they just happen to be walking while waiting.

Criteria: A constantly moving line is "better" than a line which requires people to stop and wait. This is more a people perception thing.

What models can I use to compare these scenarios? The number of printers can vary - so I can use this to increase the flow rate. I'd like to be able to see under what conditions scenario B would result in a stopped line of people. If someone can point me to the sources of information I need, that would be greatly appreciated.

I'm a queuing theory newbie but I learn fast...

I'm, not sure what the question is.
Some things just happen if the circumstances make it likely.
I don't know of a theory which requires things to stand in a line on order for the truth to be known.
I'm quite left leaning but not that bad,

Osmium said:
What models can I use to compare these scenarios?

If you want a theoretical approach, you can begin by picking the appropriate Kendall notations for you scenarios:
http://en.wikipedia.org/wiki/Kendall's_notation

If you can write computer programs, I'd suggest using computer simulations to analyze the problem.

## 1. What is a real life queue and why is it important to model?

A real life queue is a line of people or objects waiting for a service or to be processed. It is important to model because it allows us to understand and predict the behavior of queues in different scenarios, such as traffic flow, customer service, and manufacturing processes. This can help us improve efficiency and reduce wait times.

## 2. What factors are involved in modeling a real life queue?

There are several factors that need to be considered when modeling a real life queue, such as arrival rate, service rate, queue capacity, and the behavior of individuals in the queue. Other factors may include the type of queue system (single or multiple lines), the number of servers, and the arrival and service time distributions.

## 3. How do you determine the arrival rate and service rate for a queue?

The arrival rate is the rate at which individuals or objects enter the queue, while the service rate is the rate at which they are processed or served. These rates can be determined by collecting data from the queue, such as the number of arrivals and departures within a specific time frame. Statistical methods can also be used to estimate these rates based on historical data.

## 4. What are the different types of queue systems?

There are two main types of queue systems: single line and multiple lines. In a single line system, all individuals or objects wait in a single queue and are served by one server in a first-come, first-served manner. In a multiple line system, there are several parallel queues and each queue has its own server. This type of system is often used in supermarkets, where customers can choose which line to join.

## 5. How can queue models be used to optimize processes?

Queue models can be used to simulate and analyze different scenarios in order to identify areas for improvement. For example, by changing the number of servers or adjusting the arrival rate, we can determine the most efficient way to reduce wait times and increase throughput. This can be particularly useful in industries such as transportation, healthcare, and telecommunications, where efficient queue management is crucial for customer satisfaction.

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