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A router buffer of infinite size has queuing delay Let L be the size of packets coming to the router and R be the rate(bits/sec) at which packets are sent out of the queue.
What is the average routing delay if N packets arrive simultaneously every NL/R seconds.

  1.   Zero
  2.   (L(N-1)) / 2R
  3.   L/R
  4.   none

//is routing delay and queing delay same thing??

1 Answer

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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

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