Suppose that jobs arrive at a single server queueing system according to a

nonhomogeneous Poisson process whose rate is initially $4$ per hour, increases

steadily until it hits $19$ per hour after $5$ hours, and then decreases steadily

until it hits $4$ per hour after an additional $5$ hours. The rate then repeats

indefinitely in this fashion, that is $(t+10)=(t).$ Suppose that the service

distribution is exponential with rate $25$ per hour. Suppose also that whenever

the server completes a service and finds no jobs waiting he goes on break for a

$($Please write in hand and provide the R code!!!!!!$)$ time that is uniformly distributed on $(0,0\mathrm{.}3).$ If upon returning from his break

there are no jobs waiting, then he goes on another break. Use simulation to

estimate the expected amount of time that the serve is on break in the first

$100$ hours of operation. Do $500$ simulation runs.