I have corrected an error in my page about the availability and
efficiency, the utilization is equal to the arrival rate divided by
the servive rate, not the inverse..
And here is the part that i have corrected:
As you have noticed, i have finally arrived to the following
mathematical model of our Jackson network that model an Enterprise
T = Ni /A = (Nn + Ns + Nc) /A
= (((A/Ss)/n) / (1 -((A/Ss)/n)) + (A/Sn) / (1 -(A/Sn))
+ (A/Sc) / (1 -(A/Sc))) / A
T: is the average response time..
So read it carefully an you will notice that this mathematical
model also can simulate and predict an intranet website behavior
or an internet website..
First look at the first factor ((A/Ss)/n) / (1 -((A/Ss)/n))
is equal to (A/((Ss x n) - A) in our mathematical model,
as you have noticed as n (number of servers) grows
this will make the denominator grow and this will make
(A/((Ss x n) - A) smaller, that's good for the response time...
Now let's look at the other factors in this mathematical
IF the system is an Intranet, and for example the local
area network Sn is faster than the multiserver, that means:
We have Sn >> Ss, and that means => Sn /A >> Ss /A => that the
Knee in the server side can be reached more quickly than the
Knee in the network node of our Jackson network, so that
the bottleneck becomes the server node.
In the other hand if:
Ss >> Sn => Ss /A >> Sn / A => the Knee in the M/M/1 network
node can be reached more quickly, so that the network node in
the Jackson network becomes the bottleneck.
Please read more on my page:
Amine Moulay Ramdane.