Asp Forum - An important mathematical deduction...

Ramine

3/16/2016 9:03:00 PM

Hello,

I will clear something on my mathematical calculations

Since i have mathematically modeled a queuing network
in Tandem of ecommerce websites..

I have to tell you something important..

Here is the network of the ecommerce websites:

A -> M/G/c database servers queue -> M/M/1 Network queue -> M/M/1 Client
-> A

So as you have noticed the queues are interconnected in Tandem,
so this is good, but notice with me that the last queue
that is the M/M/1 Client is usually slower than the M/G/c
database servers queue that has an hyper-exponential service
and it is usually even slower than the M/M/1 Network queue,
so my mathematical calculations have showed that the arrival
rate A to the network is limited by the slowest queue that is
in my example the M/M/1 Client queue, so since the
M/G/c data servers queue is the fastest, so no need to optimize
and to speed more the M/G/c data servers queue by adding more servers ,
and that is a very important thing to know, because this mathematical
deduction is infered from an operational law of queuing theory states
that: The rate of the jobs leaving any stable node must equal its
arrival rate and it is infered from the the Knee of the M/M/1 queue that
is equal to 50%, so the best way to optimize and to speed this network
is by adding more bandwidth on the slowest queue node like
the Client node or the Network node, so be smart and don't forget
this advise.

Also i have said that:

Now i hope you have read my previous post titled:

"And here is how to do a simulation of the ecommerce websites"

Why i have done this mathematical calculations ?

To show you what permit exactly mathematical queuing theory ,
it permit to do a better QoS , and of course that's easy to
understand, but it permit also like in the Amdahl law of parallel
computing to model the ecommerce websites and to know how much the
ecommerce websites can handle of throughput and loads by
taking into account the Knee of the Network queue and the Client
queue, and it allows us to change theorically the characteristics
of the M/G/c queue of the database servers and the Network queue
and the Client queue to be able to do calculations before
adding empirically more servers or more bandwidth , so
that's optimization and that's good for your pocket.

But i have come to an interesting post...because
this modeling of an ecommerce website with mathematical
Queing theory or simulation is not sufficient, because
it's necessary also to know how to limit the number of
connected internet users on the webserver to be able to
control the waiting time of the internet users to not go
beyond a not acceptable waiting time, and it's
important to give more priority to the write transactions
because that's critical for your pocket, because it makes
a company make more money, so my idea to realize
this requirement, is to use a FIFO synchonization semaphore
for each kind of database transactions such us read , write and delete ,
and you have to do a calculation of the time that
the internet users are waiting by computing it, if the time
go beyond an acceptable waiting time you will simply not process
those internet users and tell them to try to reexecute there
transactions again after a certain time... so, this requirement
and my solution that i have added is the right tool to make
a better QoS and to make your ecommerce website succeed.

Here is the book that i have read about capacity planning
with mathematical queuing theory, you have to read it:

Performance by Design: Computer Capacity Planning By Example

http://www.amazon.com/Performance-Design-Computer-Capacity-Planning/dp/...

But the researcher in this book is using Queing with Multiple-Class
Models to model an ecommerce website, but i have not used his method
because i have modeled the M/G/c database servers with an
hyper-exponential service and i have approximate it with
an M/M/c queue , please take a look at my two previous posts that
have been corrected and that are titled:

"Here is the mathematical calculations of a queuing network"

and

" I have come to an interesting post"

To understand more my mathematical modeling of ecommerce websites etc.

Thank you,
Amine Moulay Ramdane.

comp.programming

An important mathematical deduction...

Ramine

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