Three-state Markov model of speech on telephone lines and optimal utilization of communication systems by TASI technique

Abstract

A three-state Markov model of speech on the telephone lines is developed. The model considers the alternate occurrence of the telephone calls and the intercall gaps on the telephone lines. During a phone call there are several talkspurts (speech without break) and pauses (silence without break) in the user's speech. The three types of events, intercall gaps (large gaps) talkspurts and pauses occurring on the telephone lines are assumed to have negative exponential density functions with different transition rate parameters. The steady state probability distribution, average and variance of the number of busy channels and the system utilization are evaluated as a function of call loss fraction ( P 0 f ). The Synchronous Time Division Multiplexing (STDM) system with number of channels in the group equal to 6 and 24 is considered. The model is also applied to Time Assignment Speech Interpolation (TASI) system and the relationships among the number of user terminals, speech Freeze Out Fraction (FOF) and system utilization are obtained for various values of P 0 f . The STDM and TASI systems applied to the group of 6 channels are simulated on the EC-1030 computer to check the validity of the analytical results. The results of this study are portrayed on graphs and may be used as guide lines in the design of TASI systems.