Queueing theory question

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In summary, a bank with two counters handles service A and service B differently. People in the queue have a turn for one of those services, but all are queued in the same queue. The model for this kind of situation is not clear to the author. He looks for help on the internet and finds that queueing theory is relevant to his problem. He finds a software package to help with the simulation, determines steady-state and transient conditions, and determines waiting times for the people in the queue.
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Jorge07
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Hi all, I'm a software developer and i am working on a project which use queueing theory. I was reading some stuff about that but I could not find anything related to my problem or I didn't know how to search it. For example If a bank customer service have 2 counters. The first counter have the ability to handle the service A and B. The second counter only the service A. People in the queue have a turn for one of those services, but all are queued in the same queue. I could not find a model for that kind of situation. It is like a service priority but what i found is queue with priorities with all the servers handling both services. Can anyone point me to the right way? Thansk

Counters (servers)
C1 can handle A or B
C2 can handle one A

People in the queue
P1 needs Service A
P2 needs Service B
P3 needs Service B
P4 needs Service A
P5 needs Service B
... and so on

I need to estimate the waiting time for each person in the queue
 
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If you were looking for an "approximate/ballpark" answer for how long someone would be queued before getting served,you could determine how long one counter handled the queue and then determine how long two counters of the same type (ie offers both A and B services) handles the queuefiguring your answer would be somewhere in between.

Then you could apply some weighted average based on average time to perform service A vs average time to perform service B and the percentage of A and B requestors you expect to get.

This is how I'd approach it from a programming point of view.

There may be better methods that other folks will know about.
 
  • #4
I've ended up by weighting the servers. Supose you have a service speed M and it is the same for both departments A and B. Now, the department A will run 50% faster than M and service B will run 50% slower than M. In other words, I divided the counters (servers) in halfs, so queue A will run at 3/2 of M speed and queue B will run at 1/2 of M speed. This approach gives me the ability to treat both queue times with independency of each other. That is enough for my needs. I know this is not the better way to do it but I have no advanced knowledge about math and statistics to research more. Neither the time :) Thank you all guys to help me on this issue.
 

What is queueing theory?

Queueing theory is a branch of mathematics and statistics that deals with the study of waiting lines, or queues. It involves analyzing and modeling the behavior of queues in order to optimize system performance and improve efficiency.

What are the applications of queueing theory?

Queueing theory has a wide range of applications in various fields such as telecommunications, transportation, healthcare, finance, and manufacturing. It can be used to improve customer service, reduce waiting times, and increase overall system efficiency.

What are the key components of queueing systems?

The key components of queueing systems include arrival rate (how often customers arrive), service rate (how fast customers can be served), queue capacity (the maximum number of customers that can be waiting in line), and queue discipline (the order in which customers are served).

How can queueing theory be used to optimize system performance?

Queueing theory can be used to determine the optimal number of servers, the best queueing discipline, and the ideal queue capacity for a system. It can also help identify potential bottlenecks and predict waiting times under different scenarios.

Are there any limitations to queueing theory?

While queueing theory can provide valuable insights and solutions, it is based on certain simplifying assumptions and may not always accurately reflect real-world situations. Additionally, it does not take into account human behavior and emotions, which can impact queueing systems.

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