In your question Routing Delay seems to be equal to Queing delay because in both the cases packet have to wait to be transmitted.Practically Queing delay is one of the basic delay in network delay after Processing and transmitting delay.Routing delay is generally assumed to be negligible.
Coming to your question
Let initial state of Queue is empty,
and if $N$ packets arrive simultaneously every $\frac{LN}{R}$ seconds.
So first Packet will suffer $0$ delay as it have not to wait for being transmitted.
Second packet $\Rightarrow$ $\frac{L}{R}$ seconds.
Third packet $\Rightarrow$ $\frac{2L}{R}$ seconds.
$\vdots$
$N^{th}$ $\Rightarrow$ $\frac{(N-1)*L}{R}$ seconds
so average Queing delay =$\frac{0+\frac{L}{R}+\frac{2L}{R}+\cdots +\frac{(N-1)L}{R}}{N-1}$
=$\frac{L}{R}*\frac{(N-1)*(N-1)}{2*(N-1)}$.
=$\frac{(N-1)*L}{2R}$
option 2 is right