Message delay analysis for a TDMA scheme operating under a preemptive priority discipline

A TDMA (time-division multiple-access) access-control scheme operating under a preemptive message-based priority discipline is considered and analyzed. The system considered is general, so that an arbitrary number of slots can be allocated to different stations, on a uniformly (equally) spaced basis, in each frame. Under the assumptions of a Poisson message arrival stream and random message lengths governed by a general distribution, it is shown how the Laplace-Stieltjes transform of the actual message waiting time and the delay distributions can easily be obtained, for each priority class, at each of the network stations. Using these results, explicit formulas for any moment of the message delay for any priority class can be obtained. In particular, expressions for the first two moments of the message waiting time and for the average delay of class-k messages are derived