Consider a single$-$server queueing system with any service$-$time distribution and any distribution of interarrival times $($the

GI$/$G$/1$ model$).$ Use only basic definitions and the relationships given in Sec. $17\mathrm{.}2$ to verify the following general relationships:

$($a$)$ L$=$ Lq$+(1-$ Po$).$

$($b$)$ L$=$ Lq$+$ p$.$

$($e$)$ Po $=1-$p$.$