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James F. Kurose, Keith W. Ross
Computer Networks And The Internet
Question:2 | ISBN:9780132856201 | Edition: 6


Equation 1.1 gives a formula for the end-to-end delay of sending one packet

of length L over N links of transmission rate R. Generalize this formula for sending P such packets back-to-back over the N links.



Consider the given data

           N = Total number of links

           R = Transmission rate

           L = Packet length

           P = packets that tramnsmit over the N link

The following is the formula of back-to-back delay of sending P packets, each of length L over N links of transmisson rateR=d_{back-to-back}=PN\left ( \frac{L}{R} \right )

0 2


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first packet's delay N\frac{L}{R}  but, consecutive packet's delay would be \frac{L}{R} , because they are not at the beginnig. They are at the router just before the final host. When a packet comes to final destination, at the same time next packet come to the router previous packet left. Then formula would be N\frac{L}{R}+(P-1)\frac{L}{R}  . First term for the first packet and second term is for remaining packets.


Yes this is the correct formula,  N\frac{L}{R}+(P-1)\frac{L}{R}


N*L/R  the first packet reaches the destination.

N*L/R +L/R  the second packet reaches the destination.

N*L/R +L/R+L/R the third packet reaches the destination.

After  N*L/R + (P-1)*L/R  reaches the Pth packet the destination.

More simplyfied

N*L/R + (P-1)*L/R = (N+P-1)*L/R

Post the discussion to improve the above solution.