TY - GEN A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - A Note on the Stability of the Many-Queue Head-of-the Line Processor-Sharing System with Permanent Customers N2 - We consider a single server system consisting of $n$ queues with different types of customers 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). By means of Loynes' monotonicity method a stationary work load process is constructed and using sample path analysis general stability conditions are derived. They allow to decide which queues are stable and moreover to compute the fraction of processor capacity devoted to the permanent customers. In case of a stable system the constructed stationary state process is the only one and for any initial state the system converges pathwise to the steady state. T3 - ZIB-Report - SC-96-55 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-2659 ER - TY - GEN A1 - Brandt, Manfred T1 - Approximations for the Distribution Function of the Sum of iid Random Variables with Compact Support in R+ N2 - In this paper a unified approach to central and decentral approximations of the distribution function $F(x,n)$ of the sum of $n$ iid random variables with compact support in $I\!\!R_+$ is given. This approach yields direct Edgeworth expansion (especially the Central limit theorem) and indirect Edgeworth expansion (Theorem of Bahadur-Rao, large deviation results) within a unified framework. An approximative inversion of the LST of $F(x,n)$ (approximation of the complex inversion integral over a line by an integral over a proper bounded arc with a proper integrand) allows to get these approximations and moreover explicit error bounds. T3 - ZIB-Report - SC-95-33 Y1 - 1995 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-1990 ER -