Message Delays in FDMA and TDMA Communication Channels

Message delays under a Time Division Multiple Access (TDMA) scheme and the corresponding Frequency Division Multiple Access (FDMA) scheme are studied and compared. Under a TDMA scheme, a network station is assigned a number of slots for each time frame. Under the corresponding FDMA scheme, this station is allocated a separate frequency band for which the ratio between its width and the channel bandwidth is equal to the corresponding time portion allocated by the TDMA scheme. The distribution of the message delay difference under the corresponding TDMA and FDMA schemes, for any message arrival stream, any service ordering discipline and at any time, is derived. This distribution is shown to be equal to that of a simple random variable associated with the message arrival stream. Message delays under a TDMA scheme are shown to be always lower than those under the corresponding FDMA scheme, but the difference value is lower than the time frame duration. Station-buffer queue sizes under both schemes are shown to be essentially the same.