> Does it mean that transmission delay is determined by router?
The delay is determined by the media characteristics. Remember that most media is serial -- that is, one bit is sent at a time*. A 10Mbps link means that you can transmit 10 million bits per second, or 1 bit every 100 ns. So a 100 byte message would take
100 bytes * 8 bits * 100 ns = 80 µs (microseconds)
To be sent on the link.
(* Note that this is a simplified example. In real life, encoding methods and phase changes are used to increase the amount of information sent per bit.)