Message delay analysis for TDMA schemes using contiguous-slot assignments

Under a TDMA (time-division multiple-access) scheme, a station shares a multiple-access communications channel by transmitting its messages during its dedicated time slots. An exact result concerning the queue-sizer and message delay analysis of TDMA systems in which a station is allocated multiple consecutive slots per frame is presented. The generating function of the system queue-size for a general independent arrival message process is obtained. Messages consist of a random number of packets, following a geometric distribution. An exact result for the generating function of the message delay for various common message arrival processes and light bounds for the mean message queue-size and delay are then derived. The results are compared to previously derived approximations. It is also proved that a slot allocation scheme which distributes station slots uniformly over the frame yields a message-delay lower bound. The results also apply to the analysis of time-shared reservation schemes