In a packet switching network, packets are routed from source to destination…
2005
In a packet switching network, packets are routed from source to destination along a single path having two intermediate nodes. If the message size is 24 bytes and each packet contains a header of 3 bytes, then the optimum packet size is:
Answer: D. 9 — Given: Message size M = 24 bytes Header size h = 3 bytes Two intermediate nodes ⇒ path has three links (k = 3) Let the payload size be s bytes. Number of…
- A.
4
- B.
6
- C.
7
- D.
9
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Correct answer: D
Given:
Message size M = 24 bytes
Header size h = 3 bytes
Two intermediate nodes ⇒ path has three links (k = 3)
Let the payload size be s bytes. Number of packets p = M/s. In a store-and-forward network with pipelining, total transmission time is proportional to (p + k − 1)·(s + h) = (M/s + 2)·(s + h).
To minimize with respect to s, consider the variable part f(s) = (M·h)/s + 2s (constants omitted). Differentiate and set to zero:
f'(s) = −M·h / s² + 2 = 0 ⇒ s² = M·h / 2
s = sqrt(M·h / 2) = sqrt(24·3 / 2) = sqrt(36) = 6 bytes
Therefore: optimal payload = 6 bytes; adding the 3-byte header gives optimal packet size = 6 + 3 = 9 bytes.