Fractional Speech Loss and Talker Activity Model for TASI and for Packet-Switched Speech

The cutout fraction in a TASI system is shown to be \phi=\frac{1}{np}\sum_{k=c+1}^n (k-c) n\choose k p^{k}(1-p)^{n-k} where n is the number of sources, c is the number of channels, and p is the probability that a source is issuing a talkspurt at a random time. This result is shown to hold independently of the probability density function of talkspurt duration. The same formula is shown to apply to the fraction of packets lost in a packet-switched link with a transmission capacity of c packets every T p seconds, where T p is the interval between packet generations for an individual source during talkspurt, and where no packet is queued for a time longer than T p . In addition, a simple Markov birth-death model is presented for the random process a(t) representing the number of talkers issuing talkspurts at a given time.