Suppose a message of size 15000 bytes is transmitted from a source to a destination using IPv4 protocol via two routers as shown in the figure. Each router has a defined maximum transmission unit (MTU) as shown in the figure, including IP header. The number of fragments that will be delivered to the destination is ______ . (Answer in integer)

To determine the total number of fragments delivered to the destination, we follow the IPv4 fragmentation process across each router. By default, the IPv4 header size is $20\text{ bytes}$, and the payload data in any non-terminal fragment must be a multiple of $8\text{ bytes}$.

1. Fragmentation at Router-1:

• MTU $= 5000\text{ bytes}$

• Maximum IP header size $= 20\text{ bytes}$

• Maximum available data payload per fragment $= 5000 - 20 = 4980\text{ bytes}$

• Since the data payload must be a multiple of $8$, the maximum payload per fragment is:

  $$\lfloor 4980 / 8 \rfloor \times 8 = 622 \times 8 = 4976\text{ bytes}$$

• The original message size is $15000\text{ bytes}$. It is split into fragments of data sizes:

  • Fragment 1: $4976\text{ bytes}$

  • Fragment 2: $4976\text{ bytes}$

  • Fragment 3: $4976\text{ bytes}$

  • Fragment 4: $15000 - (3 \times 4976) = 15000 - 14928 = 72\text{ bytes}$

Thus, Router-1 produces 4 fragments.

2. Fragmentation at Router-2:

• MTU $= 3000\text{ bytes}$

• Maximum available data payload per fragment $= 3000 - 20 = 2980\text{ bytes}$

• Since the data payload must be a multiple of $8$, the maximum payload per fragment is:

  $$\lfloor 2980 / 8 \rfloor \times 8 = 372 \times 8 = 2976\text{ bytes}$$

Now, each incoming fragment is fragmented further if its total size (payload $+ 20\text{ bytes}$) exceeds $3000\text{ bytes}$:

• Fragment 1 ($4976\text{ bytes}$ payload): exceeds MTU. It is split into:

  • Sub-fragment 1a: $2976\text{ bytes}$

  • Sub-fragment 1b: $4976 - 2976 = 2000\text{ bytes}$

  $\rightarrow 2\text{ fragments}$

• Fragment 2 ($4976\text{ bytes}$ payload): split similarly into $2976\text{ bytes}$ and $2000\text{ bytes}$. $\rightarrow 2\text{ fragments}$

• Fragment 3 ($4976\text{ bytes}$ payload): split similarly into $2976\text{ bytes}$ and $2000\text{ bytes}$. $\rightarrow 2\text{ fragments}$

• Fragment 4 ($72\text{ bytes}$ payload): total size $= 72 + 20 = 92\text{ bytes} \le 3000\text{ bytes}$, so it is not fragmented. $\rightarrow 1\text{ fragment}$

Total fragments delivered to the destination: