Processor Scheduling

<p>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.</p>
<p>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.</p>
<p>Secondly, we analyze systems where requests are served under the state-dependent processor sharing discipline with Poisson arrivals, in particular with multi-processor system under processor sharing. For general service time distributions we found expressions for the Laplace-Stieltjes Transform of the conditional sojourn times (being the basis for numerical algorithms) as well as tight insensitive upper bounds for their moments. For special cases, including 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, approximations for the moments of the conditional sojourn times in case of generally distributed service times are given. In case of a two server system for particular service time distributions we were able to derive explicite expressions for the Laplace Stieltjes Transform and the variance of the conditional sojourn times.</p>