R$=55/$hr

Buffer $1$

I$=7$

Registration

T$=2$ min

Buffer $2$

I$=34$

Doctor

T$1=5$ min

T$2=30$ min

We assume a stable system. This implies that average inflow equals average outflow at every stage. In this case you are given inventory numbers I and flow rate R $=55$ patients$/$hr$.$ There are two flow units:

$(1)$ Those that are potential admits: flow rate $=55*10\%=5\mathrm{.}5/$hr$.$

$(2)$ Those that get a simple prescription: flow rate $=55*90\%=49\mathrm{.}5/$hr$.$

To find the average flow times, we use Little's law at each activity for which the flow time is unknown:

$(1)$ Buffer $1$: R $=55/$hr $($both flow units go through there$),$ I $=7,$ so that waiting time in buffer $1=$ T $=$ I$/$R $=7\mathrm{.}6$ minutes.

$(2)$ Registration: flow time T $=2$ min $=2/60$ hr$.$ All flow units flow through this stage. Thus flow rate through this stage is R $=55/$ hr$.$ Average inventory at registration is given by I $=$ RT $=2$ patients.

$(3)$ Buffer $2$: R $=55/$hr $($both flow units go through there$),$ I $=34,$ so that waiting time in buffer $2=$ T $=$ I$/$R $=\mathrm{.}62$ hours $=37\mathrm{.}1$ minutes.

$(4)$ Doctor time: depends on the flow unit:

$4$a: potential admits: T $=30$ minutes

$4$b: prescription folks: T $=\_\_\_\_$ minutes