TY - GEN A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - A sample path relation for the sojourn times in G/G/1-PS systems and its applications N2 - For the general G/G/1 processor sharing (PS) system a sample path result for the sojourn times in a busy period is proved, which yields a relation between the sojourn times under PS and FCFS discipline. In particular, the result provides a formula for the mean sojourn time in G/D/1-PS in terms of the mean sojourn time in the corresponding G/D/1-FCFS, generalizing known results for GI/M/1 and M/GI/1. Extensions of the formula provide the basis for a two-moment approximation of the mean sojourn time in G/GI/1-PS in terms of a related G/D/1-FCFS. T3 - ZIB-Report - 03-18 KW - G/G/1 KW - G/GI/1 KW - G/D/1 KW - G/M/1 KW - processor sharing KW - sojourn time KW - waiting time KW - busy period KW - sample path KW - first come first served KW - two-moment ap Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7401 ER - 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 -