Take a look at Layer2 traceroute (for cisco).. Cdp should be running btw...
Router# traceroute mac 0000.0201.0601 0000.0201.0201
Source 0000.0201.0601 found on con6[WS-C2950G-24-EI] (2.2.6.6)
con6 (2.2.6.6) :Fa0/1 => Fa0/3
con5 (2.2.5.5 ) : Fa0/3 => Gi0/1
con1 (2.2.1.1 ) : Gi0/1 => Gi0/2
con2 (2.2.2.2 ) : Gi0/2 => Fa0/1
Destination 0000.0201.0201 found on con2[WS-C3550-24] (2.2.2.2)
Layer 2 trace completed
Router#
Router# traceroute mac 0001.0000.0204 0001.0000.0304 detail
Source 0001.0000.0204 found on VAYU[WS-C6509] (2.1.1.10)
1 VAYU / WS-C6509 / 2.1.1.10 :
Gi6/1 [full, 1000M] => Po100 [auto, auto]
2 PANI / WS-C6509 / 2.1.1.12 :
Po100 [auto, auto] => Po110 [auto, auto]
3 BUMI / WS-C6509 / 2.1.1.13 :
Po110 [auto, auto] => Po120 [auto, auto]
4 AGNI / WS-C6509 / 2.1.1.11 :
Po120 [auto, auto] => Gi8/12 [full, 1000M] Destination 0001.0000.0304
found on AGNI[WS-C6509] (2.1.1.11) Layer 2 trace completed.
Router#
With circuit switching, you have a 1-to-1 circuit with some predefined channel capacity which is guaranteed. For it to work, you must first establish a circuit/connection before you send any data, and break the connection after.
With packet switching, it's somewhat like the local post office - you bring the packets, send them, and let the other devices forward them around, to one or many different destinations.
What you mentioned in the first part is called multiplexing. When you establish, for example, a phone call, you get a 1-on-1 connection with the other side, and full channel capacity — 0–3400kHz for voice (at least in some parts of Europe), which only you can use. Since using separate wires is expensive, different multiplexing technologies have appeared, such as TDM, where your channel is "compressed", but you still have a 1-to-1 connection with the same capacity. With FDM, your call is mixed up to higher frequencies, but you still get a 1-to-1 channel, with the same capacity.
Yes, the medium is shared, but you still get the full capacity you have payed for, and a 1-to-1 channel.
As to the second part, circuit switching requires a circuit to be set up (you have to dial a number), and after sending the data/voice, you have to break down (shut down) the connection. When you need to communicate to a a lot of different people/devices, this takes time, since when one connection (call) is active, you cannot use that line for anything else, even if you are still waiting for the other person to answer/recieve the data. If compared to traditional networks, it takes a lot less time to send a 100 letters by post, then calling 100 different people.
Another problem with circuit switched systems is that the channel is used up even when no data is sent through it (noone else can use that channel at that time). If you have an 8-line telephone uplink, and even if all 8 callers are waiting on hold, your channel is still used up. With packet switched networks you can even oversell your connection (due to statistical multiplex) — if you're an ISP and have a 8Mbit/s uplink, you can sell 10, 20, maybe even more 1Mbit/s connections, since it is statistically improbable, that all of the users will use the connection fully at the same time. And even if they do, their connection still works, with lower speed (compared to blocked/dropped calls on circuit switched networks).
Best Answer
Circuit switched: each user needs 1/10 of link, so can reserve only 10 channels on the link, whether they are using it 10% or 100%.
Packet switched: Each user is using the channel 10% of the time, so probability of a given user being active is p = 0.1, and inactive q = 0.9. It's a binomial distribution X ~ B(35, 0.1), so probability Pr(X=k) = C(35, k) pk q(35-k). You need Pr(X>10) which is 1 - Pr(X<=10) which is 1-(Pr(X=0) + Pr(X=1) + ... Pr(X=10)).
I actually get 0.000424, not "less than 0.0004".
Description https://en.wikipedia.org/wiki/Binomial_distribution#Cumulative_distribution_function Calculate it here: https://stattrek.com/online-calculator/binomial.aspx
[EDIT to add] It needs to be said both of those include a great deal of assumption and modelling simplifications. In the case of circuit switching, you can do overbooking (in the way of airlines), especially if you know that the channels are only used a certain percentage and you have enough of them to average well. In the case of packet switching, the model assumes they are independent and evenly distributed; again these are reasonable if the number of hosts is large.