In telecommunication systems different processes consisting of requests have to be served. Various scheduling disciplines are applied for overload control, prioritizing the different processes, efficient use of the caches and for ensuring performance characteristics. The aim of this project is a performance analysis of a multi-processor system under a round robin discipline. In the round robin discipline the requests receive consecutively a fixed quantum of service in a cyclic manner. As limiting case, where the quanta tend to zero, the processor sharing discipline is obtained.

Firstly, we analyze a multi-queue multi-processor system where the requests at the head of the queues are served under processor sharing (head of the line multi-processor sharing). The stability of the system depends strongly on the input streams, as some processors may idle although work load is present in the system. For a general stationary input, necessary as well as sufficient stability conditions for the different queues and for the whole system are derived, which are also tight within this class.

Secondly, we analyze a multi-processor system under processor sharing with Poisson arrivals. For the case of exponential as well as deterministic service times representations for the moments of the sojourn times of the requests are derived. Thus higher moments of the sojourn time in a multi-processor system under processor sharing are computable in a non-phase-type model for the first time. By means of these results, an approximation for the moments of the sojourn time in case of generally distributed service times is given.