this is for holding javascript data
Aldo Nassigh edited subsection_Two_Major_Results_Given__.tex
almost 9 years ago
Commit id: 3e10c99dd921321b9270ca45ee23c3a8ec606f23
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\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, 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 and manner, the queue is rapidly disposed
of. in this case of amd 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.