Performance metrics

T_t = L/B (size and rate, not distance). T_p = d/v (distance, v = 2 × 10⁸ m/s). Nodal delay = processing + queuing + T_t + T_p. N packets over h equal links: (N + h − 1)·T_t + h·T_p; unequal links: the slowest sets the spacing. RTT = 2·T_p; BDP = B × T_p; a = T_p/T_t; send-and-wait U = 1/(1 + 2a). Circuit total = setup + M/R + h·T_p; packets pipeline but pay headers; optimal p ≈ √(MH/(h − 1)).

From 1.3.1 Bandwidth, data rate, throughput and transmission delay

• Bandwidth / data rate B = link capacity in bps (decimal prefixes).
• T_t = L / B (L in bits) — independent of distance.
• Throughput = bits delivered / time ≤ min link rate on the path (bottleneck).

From 1.3.2 Propagation, queuing and processing delay; multi-hop pipelining

• T_p = d / v, v = 2 × 10⁸ m/s default; independent of size and rate.
• Nodal delay = d_proc + d_queue + T_t + T_p.
• One packet, h equal links: h·T_t + h·T_p.
• N packets, h equal links: (N + h − 1)·T_t + h·T_p (+ (h − 1)·d_proc).
• Unequal links: first packet ΣT_t + ΣT_p, then + (N − 1) × max T_t.
• Traffic intensity L·a/R → 1: queues explode.

From 1.3.3 RTT, bandwidth-delay product, utilisation and a = Tp/Tt

• RTT = 2·T_p for tiny signals (add T_t / queuing if stated).
• BDP = B × T_p bits in flight; B × RTT before any reply.
• a = T_p / T_t.
• Send-and-wait: U = T_t/(T_t + 2T_p) = 1/(1 + 2a); throughput = U·B.
• To keep the link busy: about 1 + 2a units in flight.

From 1.3.4 Circuit vs packet switching: delay numericals

• Circuit: setup + M/R + h·T_p.
• Message switching: h·(M + H)/B + h·T_p.
• Packet switching: (⌈M/p⌉ + h − 1)·(p + H)/B + h·T_p.
• Optimal p ≈ √(M·H/(h − 1)); in MCQs evaluate each option.

1. NAT · 1 mark

   A 1250-byte packet on a 10 Mbps link, 400 km long (v = 2 × 10⁸ m/s). Time until the last bit arrives, in ms?

   Write your answer before opening the key.

2. NAT · 2 marks

   20 packets, each T_t = 0.5 ms, over 5 equal links, T_p = 0.2 ms per link. Total in ms?

   Write your answer before opening the key.

3. NAT · 2 marks

   B = 2 Mbps, T_p = 15 ms, units of 1500 bytes, send-and-wait. Utilisation (3 decimals)?

   Write your answer before opening the key.

4. MCQ · 1 mark

   Which quantity is unchanged when a link is made twice as long?

   1. Propagation delay
   2. Transmission delay
   3. a = T_p/T_t
   4. Bandwidth-delay product
5. NAT · 1 mark

   Bandwidth-delay product (in bytes) of a 400 Mbps link with T_p = 2 ms?

   Write your answer before opening the key.

6. MSQ · 1 mark

   Which are true?

   1. End-to-end throughput ≤ the slowest link rate.
   2. Circuit total time includes M/R once, not h times.
   3. Message switching beats packet switching on multi-hop paths.
   4. RTT for a tiny signal on one link is 2·T_p.
7. NAT · 2 marks

   Circuit: setup 100 ms, file 5 × 10⁵ bits on a circuit of 250 kbps, 3 links with T_p = 10 ms. Total in seconds?

   Write your answer before opening the key.

8. NAT · 1 mark

   How many units must be in flight to keep a link with a = 4.5 fully busy (whole number)?

   Write your answer before opening the key.

9. MCQ · 1 mark

   Two hosts are separated by 3 routers. How many links does the path have?

   1. 2
   2. 3
   3. 4
   4. 6