Packet Switching

Congestion

A relevant example is air plane ticket overbooking. If an air plane has a capacity of 100 seats, and the probability of of a passenger showing up to their flight is 80%, then you can overbook ticket sales due to the probability of passengers not showing up

If 110 tickets are sold, the probability of more than 100 passengers is 0.0058%
If 115 tickets are sold, the probability goes up to 1.94%
If 120 tickets are sold, the probability is 15.17%
If 130 tickets are sold, the probability is 78.12%

Performance

Throughput: Rate (bits/time) at which bits are transferred between sender/receiver

Instantaneous: Receiving rate at any instant of time
Average: Receiving rate over a longer period of time

How fast a node (host or router) is transmitting depends on

How fast the sender is sending
How fast the link is transmitting

End-to-end throughput is constrained by rate of bottleneck link (the link of the minimum rate on an end-to-end path). The weakest link in the chain (of nodes) determines the throughput of the entire link.

Delay and Loss

Packets queue in a router buffer (Store and Forward)

They are delayed while waiting in the buffer for it's turn
Slowed down while the queue keeps growing (congestion)
Dropped (lost) if no free space in a full buffer

There is four sources of nodal delay:

Node processing: Decoding the incoming electronic signal and accounting for distortion (e.g. wireless signal distortion), and verifying the correctness of the packet, and determining the output link. Usually very small (10^{-6} secs)
Queuing: Time waiting at the output link for transmission. Amount depends on the congestion of the network.
Transmission: L/R, L = Packet length, R = Link bandwidth
Propagation: m/s m = Physical distance of link (e.g. 100m wire), s = propagation speed of link (e.g. speed of electricity)

The entire delay is the sum of all of these figures

Measuring queuing delay

Traffic intensity is a measure of congestion.

 \frac{L \times a}{R}

a: Average packet arrive rate (packets/s) L: Packet length/size (bits/packet) R: Link bandwidth/rate (bps)

If this figure is 0, the delay on average is very small If this figure is 1, the delay is large If this figure is > 1, then more work arriving than serviced (severe congestion)

Note: There is a field called traffic engineering, and an important rule for this field is to not let the traffic intensity exceed 1.

Example: Delay

Consider only transmission delay and propagation delay. S sends 1 packet of length L to D over a single link of rate R and distance m. s is the speed of the link

L = 1 kb R = 100 kb/s m = 100 km s = 2\times10^8 m/s

d_{prop} = m/s = 10^5/(2\times 10^8) = 5 \times 10^{-4}

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