Calculating Waiting Time with Weighted Servers in Queueing Theory

[Jorge07]

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

 

[FactChecker]

Most queueing problems of anything but the simplest networks require simulations to analyse. There are several software packages available to help build queueing simulations. See https://en.wikipedia.org/wiki/Queueing_theory#Software_for_simulation.2Fanalysis . Once you have a simulation, you can determine steady-state conditions and transient behavior under a variety of conditions.

 

[jedishrfu]

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.

 

[Jorge07]

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.