By Nov 13, we've got up Flow and Congestion Control, and Scheduling, and you can have had a look at problems up to P4 here.
I'll note that multicast circuit routing iis easy, because multicast IP routing is stateful (routers know where host members are) so the tree building algorithms that apply to IP multicast should work fine for circuits too,
The use of randomness in mobile is really mainly to prevent oscillation between base stations when a node is moving on a path between several choices - i.e. sticky random like the telephone trunk routing discussed.
Deriving Erlang is not too tricky - its just a random walk - see wikipedia for a good intro.
Deriviing Padheye's TCP throughput equation in full is a bit more complex - for those interested, see the original paper - the main thing is to draw the time sequence diagram of packets being sent, acks arriving, and the state variables, then, when there's a loss (indicated by duplicate acks or timeout), then the window halves or you trigger slow start. then just count the area under the curve. The one extra term in Padhye's equuation covers the case where the sender is rate limited by a "too small" advertised receive wiindow so they can't fill the "bandwidth*delay" product's worth of bottleneck capacity.
Flow control when end point is physical - fairly straightforward to extend the feedback from an output device like a printer if it has monitoring of page rate (or jams) (or input device, like a scanner), through the operating system, to the API to TCP (or similar) end-to-end protocol.
For consideration of batteries as a resource, no special reason to treat them differently than memory, CPU, except for human preference (risk of running battery flat before reaching next charging point might be a preference in the API for smart batteries/phones/cars) - see software defined batteries work at Microsoft (with Tesla)
Finally, this year we are not covering Control Theory itself due to lack of space/time in the course. However it is now covered in more detail in another Part II course (next term) - see Computer Systems Modeling.
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