TY - GEN A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - Insensitivity bounds for the moments of the sojourn times in M/GI systems under state-dependent processor sharing N2 - We consider a system with Poisson arrivals and i.i.d. service times and where the requests are served according to the state-dependent (Cohen's generalized) processor sharing discipline, where each request in the system receives a service capacity which depends on the actual number of requests in the system. For this system we derive asymptotically tight upper bounds for the moments of the conditional sojourn time of a request with given required service time. The bounds generalize corresponding results, recently given for the single-server processor sharing system by Cheung et al. and for the state-dependent processor sharing system with exponential service times by the authors. Analogous results hold for the waiting times. T3 - ZIB-Report - 09-02 KW - state-dependent processor sharing KW - sojourn time KW - moments KW - bounds KW - M/GI/m-PS Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11092 SN - 1438-0064 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 -