Single Server Queue system: M$/$U$/1$

For a single$-$server queue, customers arrive one at a time and served one at a time $($the $1^{st}$ customer arrives at time $0$ to find the system empty and idle$)$

Inter$-$arrival times have exponential distribution with arrival rate $=0\mathrm{.}5$ customer$/$minute

Service times have a continuous uniform distribution between $a=0\mathrm{.}4$ minute and $b=2\mathrm{.}7$ minutes.

You are required to just watch the waiting times in the queue $W{Q}_1,W{Q}_2,$dots,$W{Q}_{400}$

For customer $i,$

a$.S_i$ : time in service for customer $i$

b$.A_i$ : inter$-$arrival time between customers i and $i-1$

c$.W{Q}_i=$max$(W{Q}_{i-1}+S_{i-\text{I}}-A_i,0)$

Remember:

To generate inter$-$arrival times from the expo distribution:

$A_i=-(\frac{1}{})ln(1-U)$

And to generate service times from the uniform distribution:

$S_i=a+(b-a)U$

Calculate the steady state expected mean wait time in queue $=E(W{Q}_{})=\frac{\text{V}\text{a}\text{r}(S_i)+(E(S_i){)}^2}{2(1-E(S_i))}$

Where: service time