[DeTomaso] NPC: Help on Queueing theory wanted

[Charles McCall]

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!

-------------- next part --------------
   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!