In this work we address the problem of statistically multiplexing a variabl
e number of telephone calls via a limited number of channels. Terminals ope
rate with voice activity and silence detectors, and the speech is encoded t
o a bit rate which is system state dependent. Growing from zero, calls in t
he system are admitted with a maximum bit rate (maximum quality) until the
cutoff fraction of talkspurt (a front end clipping) reaches a certain thres
hold. At this point the voice bit rate of all transmitting terminals is red
uced. If due to traffic fluctuations, the number of calls in progress decre
ases, then all voice terminals are allowed to operate at the maximum bit ra
te again. In order to avoid annoying effects to listeners, both the percent
age of voice information that is lost and the mean number of changes in the
bit rate per mean call holding time are constrained. The first constraint
is strongly dependent on the encoding bit rate, and the second one is contr
olled by using a hysteresis threshold when switching from one bit rate to a
nother. In this work we have used three encoding bit rates, high, medium an
d low. A birth-death Markov process is used to model the system, which prov
ided exact numerical evaluations for the percentage of time the system oper
ates in each encoding bit rate and for the mean number of changes in the bi
t rate. Metrics are defined to measure the percentage of both types of voic
e information that are lost (not transmitted), cutoff or front end clipping
and uniform dropping. Finally, an illustrative example is reported.