Packet delay under the golden ratio weighted TDM policy in a multiple-access channel

Consider n transmission stations sharing a single communication channel. Packets arrive at the stations according to n independent renewal processes, possibly with different rates. The transmitters are assumed to be able to store an unlimited number of packets in their buffers. The stations transmit packets during time slots allocated to them according to a given {\em conflict-free distributed protocol.} The cost criterion according to which protocols are evaluated is the long-run weighted average buffer occupancies. (The average waiting time is a special case of such a weighting.) A lower bound to the cost criterion under time division multiplexing (TDM) protocols is given, and the costs of two protocols are analyzed. The first protocol is the {\em random-control} policy, and the second is the {\em golden ratio} policy which is shown to achieve a cost close to the lower bound for realistic parameters.