Abstract The behavior of buffers in computer communication systems is studied under the following conditions: 1. (i) infinite buffer size; 2. (ii) periodic opportunities for service (synchronous transmission); 3. (iii) random server interruptions; 4. (iv) periods during which server is available are i.i.d. random variables with geometric density function; 5. (v) periods during which server is blocked are i.i.d. with arbitrary density function; 6. (vi) numbers of arrivals during consecutive clock time intervals are i.i.d. with arbitrary density function. An expression is derived for the probability generating function of the buffer contents at customer departure times. Previous solutions to this problem are shown to be less general than the one presented here, because of more restrictive assumptions concerning the server interruption process and the arrival process.