this is for holding javascript data
Aldo Nassigh edited subsection_Two_Major_Results_Given__.tex
almost 9 years ago
Commit id: b22b4b01df4e36f5996fce69825ad85ab83f55b2
deletions | additions
diff --git a/subsection_Two_Major_Results_Given__.tex b/subsection_Two_Major_Results_Given__.tex
index c53ee44..5e9b640 100644
--- a/subsection_Two_Major_Results_Given__.tex
+++ b/subsection_Two_Major_Results_Given__.tex
...
\begin{equation}\label{Tim}
T_w = \frac{L_w}{\lambda} = \frac{\rho}{1-\rho} \cdot \frac{P_w}{\lambda}
\end{equation}
The average time $T_w$ is a non-linear function of the traffic intensity $a$, of the number of servers $c$ and of their ratio $\rho$. We stress here that, as the average server utilization $\rho$
grows, increases getting close to one, the behavior of $T_w$ in dependence of it becomes \textbf{strongly non-linear} with fast divergence.\\ The heuristic explanation of this singularity is related to the stochastic nature of this problem. Under any value of $\rho$, from time to time, a big upsurge of customers can temporarily arise, leading to the formation of a queue. If the average server utilization is low, however, the system reacts in a timely manner, the queue is rapidly disposed of and the impact on the average waiting time is very low. if, on the other hand, the server utilization is already high on average, the time needed to dispose of a temporary large queue can be very long, with material impact on the average waiting time.