computer networks - queuing delay

Question

Consider the queuing delay in a router buffer (preceding an outbound link). Suppose packet  length is  L  bits and the link  rate is  R  bps, and that N packets arrive to the buffer every LN/R seconds. Find the average queuing delay of the packets. 

Answer 1

N packet arrive to buffer every LN/R second .

1 packet arrive after every L/R second.

Length of the packet is L bit

Bandwidth =R bps

the first packet has no queuing delay as no packet is come then.

for the second packet is has the queuing delay of L/R Second.

For the third packet queuing delay is 2L/R as two packets has come before.

for the Nth packet queuing delay is (N-1)L/R.

so average queuing delay =( L/R +2L/R +3L/R + ...+(N-1)L/R ) / N

                                            = (N*(N-1)L)/(2*R*N)

                                            =(N-1)L/2R