[DeTomaso] NPC: Help on Queueing theory wanted

Sean Korb spkorb at gmail.com
Tue May 19 23:31:41 EDT 2015 

I think about this a lot.  Fair Share in Grid Engine allows queue hogs to
run their jobs for a long time, and also allows small jobs to invade which
makes them mad, but the fairshare queue "remembers" and gives the resource
back and then more so.  In theory, everyone remains equally mad.
https://www.nersc.gov/assets/Uploads/submittingjobs.pdf

I think this has the graph(s) you are  looking for though.

http://fy.chalmers.se/~f3aamp/queue.html

sean

On Tue, May 19, 2015 at 1:12 PM, Charles McCall <charlesmccall at gmail.com>
wrote:

>    Hi All
>
>
>    Perhaps the record for the least Pantera content ever? College was a
>    somewhat long time ago, and I took a couple of Statistics courses...
>    one of them had a heavy content of queueing theory, which I
>    particularly liked. Finding mathematical models to try to represent
>    daily occurrences such as lines at the grocery store or traffic jams
>    was pretty neat I thought.
>
>
>    I've long since forgotten all the formulas, but I remember a concept
>    that I am trying to find information but without success. I've googled
>    a moderate amount and apparently can't come up with the correct
>    description to find what I need.
>
>
>    I need a graph that shows the relationship between Capacity Utilization
>    and Waiting Time.
>
>
>    I remember the concept that, oversimplifying a bunch, average waiting
>    time remains basically statistically zero until the utilization of the
>    resource reaches a certain threshold, when it starts to rise, and then
>    above another point it increases exponentially. I'm looking for that
>    graph. Looking at a practical example, we have three cash registers.
>    They are idle 80% of the time, and customers arrive at random
>    intervals. The probability of having more than 3 customers arrive at
>    the same time is pretty remote, so the average wait is zero. But if
>    each cashier is occupied 50% of the time, then the probability of
>    finding an idle cashier with random arrivals is less, and the average
>    wait time begins to increase. At a certain saturation, the probability
>    of finding an idle cashier is basically zero, and if cashiers are 100%
>    saturated, then the length of the wait depends on cycle time and
>    arrival time, but it will be substantial.
>
>
>    Can anyone point me to a graph, with references, showing the average
>    wait time compared to % utilization of the resource? Thanks all!
>
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-- 
Sean Korb spkorb at spkorb.org http://www.spkorb.org
'65,'68 Mustangs,'68 Cougar,'78 R100/7,'60 Metro,'59 A35,'71 Pantera #1382
"The more you drive, the less intelligent you get" --Miller
"Computers are useless.  They can only give you answers." -P. Picasso
-------------- next part --------------
   I think about this a lot.A  Fair Share in Grid Engine allows queue hogs
   to run their jobs for a long time, and also allows small jobs to invade
   which makes them mad, but the fairshare queue "remembers" and gives the
   resource back and then more so.A  In theory, everyone remains equally
   mad.
   [1]https://www.nersc.gov/assets/Uploads/submittingjobs.pdf
   I think this has the graph(s) you areA  looking for though.
   [2]http://fy.chalmers.se/~f3aamp/queue.html
   sean

   On Tue, May 19, 2015 at 1:12 PM, Charles McCall
   <[3]charlesmccall at gmail.com> wrote:

     A  A Hi All
     A  A Perhaps the record for the least Pantera content ever? College
     was a
     A  A somewhat long time ago, and I took a couple of Statistics
     courses...
     A  A one of them had a heavy content of queueing theory, which I
     A  A particularly liked. Finding mathematical models to try to
     represent
     A  A daily occurrences such as lines at the grocery store or traffic
     jams
     A  A was pretty neat I thought.
     A  A I've long since forgotten all the formulas, but I remember a
     concept
     A  A that I am trying to find information but without success. I've
     googled
     A  A a moderate amount and apparently can't come up with the correct
     A  A description to find what I need.
     A  A I need a graph that shows the relationship between Capacity
     Utilization
     A  A and Waiting Time.
     A  A I remember the concept that, oversimplifying a bunch, average
     waiting
     A  A time remains basically statistically zero until the utilization
     of the
     A  A resource reaches a certain threshold, when it starts to rise,
     and then
     A  A above another point it increases exponentially. I'm looking for
     that
     A  A graph. Looking at a practical example, we have three cash
     registers.
     A  A They are idle 80% of the time, and customers arrive at random
     A  A intervals. The probability of having more than 3 customers
     arrive at
     A  A the same time is pretty remote, so the average wait is zero.
     But if
     A  A each cashier is occupied 50% of the time, then the probability
     of
     A  A finding an idle cashier with random arrivals is less, and the
     average
     A  A wait time begins to increase. At a certain saturation, the
     probability
     A  A of finding an idle cashier is basically zero, and if cashiers
     are 100%
     A  A saturated, then the length of the wait depends on cycle time
     and
     A  A arrival time, but it will be substantial.
     A  A Can anyone point me to a graph, with references, showing the
     average
     A  A wait time compared to % utilization of the resource? Thanks
     all!
     _______________________________________________
     Detomaso Forum Managed by POCA
     Posted emails must not exceed 1.5 Megabytes
     DeTomaso mailing list
     [4]DeTomaso at poca.com
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   --
   Sean Korb [6]spkorb at spkorb.org [7]http://www.spkorb.org
   '65,'68 Mustangs,'68 Cougar,'78 R100/7,'60 Metro,'59 A35,'71 Pantera
   #1382
   "The more you drive, the less intelligent you get" --Miller
   "Computers are useless.A  They can only give you answers." -P. Picasso

References

   1. https://www.nersc.gov/assets/Uploads/submittingjobs.pdf
   2. http://fy.chalmers.se/~f3aamp/queue.html
   3. mailto:charlesmccall at gmail.com
   4. mailto:DeTomaso at poca.com
   5. http://poca.com/mailman/listinfo/detomaso_poca.com
   6. mailto:spkorb at spkorb.org
   7. http://www.spkorb.org/

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