### Blocks that Model Multiple Servers

You can use the N-Server and Infinite
Server blocks to model a bank of identical servers operating
in parallel. The N-Server block lets you specify the
number of servers using a parameter, while the Infinite Server block
models a bank of infinitely many servers.

To model multiple servers that are not identical to each other,
you must use multiple blocks. For example, to model a pair of servers
whose service times do not share the same distribution, use a pair
of Single Server blocks rather than a single N-Server block.
The example in Select the First Available Server illustrates
the use of multiple Single Server blocks with a switch.

### Model an M/M/5 Queuing System

The example below (open modelmodel) shows
a system with infinite storage capacity and five identical servers.
In the notation, the M stands for Markovian; M/M/5 means that the
system has exponentially distributed interarrival and service times,
and five servers.

The plot below shows the waiting time in
the queuing system.

You can compare the empirical values shown in the plot with
the theoretical value, E[S], of the mean system time for an M/M/m
queuing system with an arrival rate of λ=1/2 and a service rate
of μ=1/5. Using expressions in [2], the computation
is as follows.

$$\begin{array}{l}\rho =\frac{\lambda}{m\mu}=\frac{(1/2)}{5(1/5)}=\frac{1}{2}\hfill \\ {\pi}_{0}={\left[1+{\displaystyle \sum _{n=1}^{m-1}\frac{{(m\rho )}^{n}}{n!}+\frac{{(m\rho )}^{m}}{m!}\frac{1}{1-\rho}}\right]}^{-1}\approx 0.0801\hfill \\ E[S]=\frac{1}{\mu}+\frac{1}{\mu}\frac{{(m\rho )}^{m}}{m!}\frac{{\pi}_{0}}{m{(1-\rho )}^{2}}\approx 5.26\hfill \end{array}$$

Zooming in the plot shows that the empirical
value is close to 5.26.