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How can I determine the number of packets waiting in a queue for a each and every individual relay nodes? That is suppose there are 2 nodes A and B in a given Network topology. Assuming that we assigned the queue length=50packets for each. Let a number of packets are sent to those two nodes. Here my question is how can I know the number of packets that are waiting in a queue in each nodes so that the next packet should have to be sent to a less queued node? Is there any mathematical formula to determine this?

for a node moving packet from receiving port to giving it out to link to next node,

Given

L: packet length (bits)

R: link bandwidth or rate (bps)

if packets arrive in bursts but periodically, for example, suppose n packets arrive simultaneously every (L/R)n seconds. Then the first packet transmitted has no queuing delay; the second packet transmitted has a queuing delay of L/R seconds; and more generally, the nth packet transmitted has a queuing delay of (n -1)L/R seconds.

Generally moving packet from the receiving port of a node A to the out going port of node A to the link going out to node B has four types of delay (total delay) in one way trip

physical distance

---(in)-A-(out)----------------------------------------------B

total delay = node processing delay + queuing delay + transmission delay + propagation delay

node processing delay-: time to access check error bit or determine which port or link to go to after receiving from the in part of node A

queuing delay-: time to wait at the output port of node A before moving on to the link to node B

transmission delay-: time require to transmit bit of packet from output port of node A to the link to node B

td=L/R

propagation delay-: time require to propagate along the physical medium from Node A to B

pd = distance(length of physical link in meters) / propagation speed of the medium (m/s)

propagation speed of the common cable like coaxial- 2x10^8m/s

propagation speed of wireless medium - 3x10^8m/s - speed of light

To learn more see (chapter 1)

Computer Networking: A Top Down Approach 6th edition Jim Kurose, Keith Ross Addison-Wesley March 2012

Olawale E. Olasupo Thanks for your explanations. And my big issue here is how can I know the number of packets that are waiting in a queue in each nodes so that the next packet should have to be sent to a less queued node? Is there any mathematical formula to determine this?

if it is in a simulation software (e.g NS2) you may have to consult the documentation to know the theory behind this or how to do it.

However you can use general queue theory (e.g Markov Birth-Death process) see textbook for more:

Average Number of Packet in the System (L):

L=λ/(μ-λ)

therefore,

Average Queue Length (Lq) ------- using Markov queue theory, this is the formula

L_q=λ^2/μ(μ-λ)

λ is arrival rate (packet per time)

μ is service (link) rate (served packet per time)

Olawale E. Olasupo Thanks, I tried to refer the ns2 documentation but no explanation about this is there. Esp from where can I get arrival rate and service rate values if you have worked with them?