Circuit vs packet switching: delay numericals

1. Send-and-wait utilisation when a = 1?
   Stuck? Peek at 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.

   Read lesson 1.3.3

2. N packets over h equal links: total time?
   Stuck? Peek at 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.

   Read lesson 1.3.2

3. Which switching method has a setup phase and reserved capacity?
   Stuck? Peek at 1.2.1 Circuit switching: setup, reserved resources, teardown

   • Circuit switching: setup → data transfer → teardown.
   • Dedicated path; each link's share (time slot or frequency band) is reserved: circuit rate = R/n.
   • Total time = setup + bits/circuit rate (+ travel time if given).
   • + guaranteed rate, in order, no queues; − setup delay, idle capacity wasted, fragile.

   Read lesson 1.2.1

Should we phone (reserve a path) or post letters (packets) to send a 100,000-bit file across 4 links? Phoning costs a setup but then streams with no store-and-forward. Posting has no setup but every router waits for whole packets, and every packet pays for its header. GATE turns this choice into a two-line calculation — and asks how big the letters should be.

4 links of 1 Mbps, T_p = 1 ms each, a 100,000-bit file. Circuit setup takes 50 ms. Packets carry 1000 data bits + 24 header bits. Guess which finishes first.

Packets: 109.472 ms against 154 ms for the circuit. The 50 ms setup is never earned back, while the packet pipeline loses only 3 extra packet times and the header overhead.

Three formulas side by side

Message of M bits, h equal links of rate B, propagation T_p per link:

Why packets beat whole messages

Message switching makes each router wait for the entire message: h full message-times. Packets let routers work in parallel, costing only (h − 1) extra packet-times — at the price of N headers instead of one.

Choosing the packet size

Smaller packets → better pipelining but more headers. Larger packets → fewer headers but longer per-hop waits. The total (M/p + h − 1)(p + H)/B is minimised near p* = √(M·H / (h − 1)). In exams, simply compute the total for each option offered.

Putting it together

• Circuits pay setup once, then stream without store-and-forward.
• Packets pipeline across hops but pay a header per packet; whole messages wait at every hop.
• There is an optimal packet size balancing pipelining against header overhead.

• For circuit switching do not multiply M/B by h — the bits flow through switches without being stored.
• Packet count is ⌈M/p⌉: a partial last packet still costs a full slot in simple GATE-style counting unless the question sizes it exactly.
• Header bits count in each packet's T_t; forgetting them makes small packets look too good.

"Phone once, talk straight; post many letters, each with an envelope."

Phase 1 is complete: layers, switching, and every delay formula. Our message now has a shape (frames, packets, segments) and a timing model. Next (Phase 2): zoom into a single hop — how does the data link layer move a frame to the next node, notice damaged bits, and share a link that many nodes want to use at once?

1. NAT

   Circuit: setup 20 ms, M = 2 × 10⁵ bits at 1 Mbps, 2 links with T_p = 5 ms. Total in ms?

   Write your answer before opening the key.

2. NAT

   Packets: M = 10⁴ bits split into 1000-bit packets, header 0, 3 links of 1 Mbps, T_p = 0. Total in ms?

   Write your answer before opening the key.

3. NAT

   Same as before but sent as one 10⁴-bit message (message switching). Total in ms?

   Write your answer before opening the key.

4. MCQ

   Why does circuit switching not multiply M/B by the number of links?

   1. Links are faster on circuits
   2. Switches forward bits as they arrive, without storing the whole message
   3. Propagation is zero on circuits
   4. Setup sends the data
5. MSQ

   Making packets very small (with a fixed header per packet):

   1. improves pipelining
   2. increases total header overhead
   3. always minimises delay
   4. can make total delay grow again

• 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.

• circuit vs packet vs message switching delay
• optimal packet size

1. Circuit total time?
   Reveal answer

   setup + M/R + h·T_p.
2. Packet total time (equal links)?
   Reveal answer

   (N + h − 1)(p + H)/B + h·T_p.
3. Optimal packet size?
   Reveal answer

   ≈ √(M·H/(h − 1)).

• Circuit total = setup + M/R_circuit + h·T_p. — bits stream through switches without store-and-forward once the circuit exists.
• Optimal packet size p* ≈ √(M·H/(h − 1)). — equal links, fixed header H per packet, M ≫ p; in MCQs just evaluate each option.