A single channel on/off model with transmission control protocol-like control

We model behavior of a TCP-like source transmitting over a single channel to a server that processes work at a constant rate τ. Transmission by the source follows an on/off mechanism. When the overall load in the system is below a critical constant γ, transmission rates increase linearly but when the load exceeds γ, then transmission rates decrease geometrically fast. We study the system by means of an embedded Markov chain, which gives the buffer content at the start of transmissions. Attention is paid to the time necessary to transmit a file of size L and both the tail behavior and expectation of the distribution of file transmission time are considered.