TY - GEN A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - On the Sojourn Times for Many-Queue Head-of-the-Line Processor-Sharing Systems with Permanent Customers N2 - We consider a single server system consisting of $n$ queues with different types of customers (Poisson streams) and $k$ permanent customers. The permanent customers and those at the head of the queues are served in processor-sharing by the service facility (head-of-the-line processor-sharing). The stability condition and a pseudo work conservation law will be given for arbitrary service time distributions; for exponential service times a pseudo conservation law for the mean sojourn times can be derived. In case of two queues and exponential service times, the generating function of the stationary distribution satisfies a functional equation being a Riemann-Hilbert problem which can be reduced to a Dirichlet problem for a circle. The solution yields the mean sojourn times as an elliptic integral, which can be computed numerically very efficiently. In case $n\ge 2$ a numerical algorithm for computing the performance measures is presented, which is efficient for $n=2,3$. Since for $n\ge 4$ an exact analytical or/and numerical treatment is too complex a heuristic approximation for the mean sojourn times of the different types of customers is given, which in case of a (complete) symmetric system is exact. The numerical and simulation results show that, over a wide range of parameters, the approximation works well. T3 - ZIB-Report - SC-95-34 Y1 - 1995 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/200 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-2005 ER -