Message delay and queue-size analysis for circuit-switched TDMA systems

A multiple-access communications channel which is shared among network stations using a circuit-switched time-division multiple-access (CS-TDMA) scheme is examined. Each station is allocated a fixed number of slots (N) during each frame. The authors carry out queue-size message delay analysis for CS-TDMA systems. They derive the generating function of the queue size and of the waiting time distribution for a discrete-time Geom^[x]/Geom/N queuing system. This result is used to obtain the generating function of the system size for the CS-TDMA scheme. The associated computation requires the solution of (N+1)2^N linear equations. To derive a more computationally effective procedure, tight lower and upper bounds are obtained, requiring the solution of at most 3N linear equations. The authors prove that a slot allocation scheme which distributes station slots uniformly over the frame yields a message delay lower bound. The application of the results to the analysis of demand-assigned CS-TDMA systems is also discussed