Intuition The ONE core ideaA network cannot give everyone their own private wire, so data must share a mesh of intermediate boxes called switches, and each switch must decide which outgoing wire to shove data onto next. Everything in the switching topic is just three different answers to one question: when do we pick the path, and how much memory does each switch keep to do it?
Before you can appreciate those three answers, you need to be fluent in the small alphabet of symbols and pictures the parent note throws at you. This page builds every single one of them from nothing, in an order where each idea leans on the one before it.
Everything happens on a graph : dots joined by lines.
Definition Node, link, switch
A node is a dot in the network — a computer, a phone, or a switch.
A link is a wire (or fibre, or radio channel) joining two nodes. It carries bits from one end to the other.
A switch (also called a router ) is a special node in the middle whose only job is to take bits arriving on one link and send them out on another link.
Why do we even need switches? Look at the next figure.
Intuition The wire-count explosionIf you have n n n − 1
wires = 2 n ( n − 1 )
Let us read every symbol in that tiny formula, because it is the reader's first taste of the notation style used everywhere below.
Definition The symbols in2 n ( n − 1 )
n number of nodes (a plain counting number: 2, 3, 4, …).n − 1 except yourself " — you don't wire a node to itself.n ( n − 1 ) ordered pair.÷ 2 twice (A→B and B→A), so halve it.
Worked example Feel the explosion
n = 5 2 5 ⋅ 4 = 10 n = 100 2 100 ⋅ 99 = 4950 n = 1000 2 1000 ⋅ 999 = 499 , 500
Doubling the users roughly quadruples the wires. This is why we accept sharing through switches instead — the whole topic exists to manage that sharing.
Computers speak in bits — the smallest piece of information, a single 0 or 1.
L L how many bits are in the thing you want to send.
Picture a train: L number of carriages .
Worked example Bytes to bitsA "1 MB file" means 1 = 8 × 1 0 6 1 0 6 L = 8 , 000 , 000
R R how many bits the wire can push out per second , written bps.
Picture the width of a hose: a fat hose (R
Mnemonic Mbps means mega-bits, not mega-bytes"1 Mbps" = 1 0 6 not bytes. Mixing these up is the #1 exam slip. Bits use a lowercase "b".
This is the most important pair of pictures on the page. The parent note's entire delay algebra is built from just these two ideas, and beginners constantly confuse them.
Definition Transmission delay =R L squeeze all the bits out of the sending node onto the wire .
L R Units check: bits/second bits = seconds
Picture: how long it takes the whole train to leave the station platform — nose to tail.
this tool? Why divide?
We divide because "time = amount ÷ rate." You have L R L / R train's length , not the distance travelled.
Definition Propagation delayt p t p one single bit to travel the length of one wire , limited by the speed of the signal (near light speed) — nothing to do with how many bits there are.
Picture: how long the front of the train takes to travel from station A to station B.
Common mistake Transmission vs propagation — the classic mix-upFeels right: "a longer file takes longer to arrive, and a longer wire takes longer, so they're the same kind of delay."
The fix: they are independent. L / R file size and wire speed (loading the train). t p distance (the journey). A short file on a slow satellite link is propagation -dominated; a huge file on a fast short cable is transmission -dominated. You add them, never merge them.
d d how many wires the data crosses from source to destination.
Picture: the number of road segments between two towns; if you pass through 2 switches, that's d = 3
Now we can see why d
Propagation total is always d t p every segment.Transmission total depends on the switching style — that difference is the whole topic (see §7).
Definition Store-and-forwardStore-and-forward means a switch must fully receive an entire packet (store it) before it starts sending it onward (forward). It cannot pass along a half-received packet.
Intuition Why this makes each hop costR L L / R every hop. Across d d ⋅ R L d not store-and-forward after setup) does not . Full details live in Store-and-Forward and Network Delays .
Recall Quick check: why does circuit switching escape the× d L / R only once .
Two last ideas the parent leans on for circuit and virtual-circuit switching.
S S before any data flows , sending a request hop-by-hop to build a path (reserve a channel, or install labels). Circuit and virtual circuits pay S 0 phone ahead and book the whole road before you drive.
Definition Per-connection state / a table entry"State " means information a switch remembers about connections. A switch keeps a small table; each row maps something coming in to a link going out . Circuit and virtual circuits store per-connection rows; datagram stores only per-destination routes computed by Routing Algorithms .
When circuit switching "reserves a channel," it does so by slicing the wire. That slicing is multiplexing , covered in Multiplexing — TDM, FDM .
Definition A channel / time-slot / frequency-band
TDM (time-division): give the connection repeating time slots — it owns the wire for a slice of every second.FDM (frequency-division): give the connection its own frequency band — like its own radio station on the same cable.
Picture: TDM = taking turns on one lane; FDM = separate lanes side by side.
Switch forwards in to out
Wire count n times n minus 1 over 2
Transmission delay L over R
R bits per second: link rate
Circuit and virtual circuit
Per connection state table
Cover the right side and answer out loud. If any line stumps you, re-read its section above before starting the main topic.
Why can't we give every pair of nodes its own wire? It costs 2 n ( n − 1 ) n 2 n
What is a switch's one job? Take bits arriving on one link and forward them out an appropriate link toward the destination.
What does L The message size, measured in bits .
What does R The link rate (bandwidth), in bits per second .
What is transmission delay and its formula? Time to push all bits onto the wire, R L
What is propagation delay t p Time for one bit to travel the length of one wire; depends on distance, not on L
How do transmission and propagation differ? L / R t p
What does d The number of links (hops) along the path.
What is store-and-forward and why does it matter? A switch fully receives a packet before forwarding, so each hop costs R L d ⋅ R L
Why does circuit switching not multiply R L d After setup the path is a continuous pipe with no buffering, so L / R
What is S Setup time to build a path; circuit and virtual-circuit switching pay it, datagram does not.
What is "per-connection state"? A table a switch remembers, mapping an incoming connection to an outgoing link.
What are TDM and FDM? Ways to slice one wire — TDM by time slots, FDM by frequency bands.
Recall Ready to continue?If you nailed all thirteen, head back to Switching — circuit, packet, virtual circuit — the three formulas will now read like plain English.
