TY - JOUR A1 - Brandt, Manfred A1 - Brandt, Andreas T1 - On sojourn times in $M/GI$ systems under state-dependent processor sharing JF - Queueing Syst. Y1 - 2010 VL - 64 SP - 167 EP - 201 ER - TY - JOUR A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - Insensitive bounds for the moments of the sojourn times in $M/GI$ systems under state-dependent processor sharing JF - Adv. Appl. Probab. Y1 - 2010 VL - 42 SP - 246 EP - 267 ER - TY - JOUR A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - Individual overflow and freed carried traffics for a link with trunk reservation JF - Telecommunication Syst. Y1 - 2005 VL - 29 SP - 283 EP - 308 ER - TY - CHAP A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - On the computation of the probability of a system failure T2 - Proc. ESREL’99 10th European Conf. on Safety and Reliability, G.I. Schuëller, P. Kafka (eds.), Balkema Rotterdam Y1 - 1999 SP - 457 EP - 461 CY - München-Garching ER - TY - CHAP A1 - Brandt, Andreas A1 - Brandt, Manfred A1 - Spahl, G. A1 - Weber, D. T1 - Modelling and optimization of call distribution systems T2 - Proc. 15th Int. Teletraffic Cong. (ITC 15) Y1 - 1997 SP - 133 EP - 144 CY - Washington D.C., USA ER - TY - JOUR A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - Approximation for overflow moments of a multiservice link with trunk reservation JF - Perform. Eval. Y1 - 2001 VL - 43 SP - 259 EP - 268 ER - TY - JOUR A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - On the $M(n)/M(n)/s$ queue with impatient calls JF - Perform. Eval. Y1 - 1999 VL - 35 SP - 1 EP - 18 ER - TY - GEN A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - Workload and busy period for M/GI/1 with a general impatience mechanism N2 - The paper deals with the workload and busy period for the M/GI/1 system under FCFS discipline, where the customers may become impatient during their waiting for service with generally distributed maximal waiting times and also during their service with generally distributed maximal service times depending on the time waited for service. This general impatience mechanism, originally introduced by Kovalenko (1961) and considered by Daley (1965), too, covers the special cases of impatience on waiting times as well as impatience on sojourn times, for which Boxma et al. (2010), (2011) gave new results and outlined special cases recently. Our unified approach bases on the vector process of workload and busy time. Explicit representations for the LSTs of workload and busy period are given in case of phase-type distributed impatience. T3 - ZIB-Report - 11-43 KW - impatient customers KW - workload KW - busy period KW - waiting time dependent service Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14304 SN - 1438-0064 ER - TY - GEN A1 - Manfred, Brandt A1 - Andreas, Brandt T1 - On sojourn times for an infinite-server system in random environment and its application to processor sharing systems N2 - We deal with an infinite-server system where the service speed is governed by a stationary and ergodic process with countably many states. Applying a random time transformation such that the service speed becomes one, the sojourn time of a class of virtual requests with given required service time is equal in distribution to an additive functional defined via a stationary version of the time-changed process. Thus bounds for the expectation of functions of additive functionals yield bounds for the expectation of functions of virtual sojourn times, in particular bounds for fractional moments and the distribution function. Interpreting the $GI(n)/GI(n)/\infty$ system or equivalently the $GI(n)/GI$ system under state-dependent processor sharing as an infinite-server system with random states given by the number $n$ of requests in the system provides results for sojourn times of virtual requests. In case of $M(n)/GI(n)/\infty$, the sojourn times of arriving and added requests are equal in distribution to sojourn times of virtual requests in modified systems, which yields many results for the sojourn times of arriving and added requests. In case of integer moments, the bounds generalize earlier results for $M/GI(n)/\infty$. In particular, the mean sojourn times of arriving and added requests in $M(n)/GI(n)/\infty$ are proportional to the required service time, generalizing Cohen's famous result for $M/GI(n)/\infty$. T3 - ZIB-Report - 11-28 KW - infinite-server KW - random environment KW - time transformation KW - sojourn times KW - state-dependent processor sharing Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-13190 ER - TY - CHAP A1 - Brandt, Andreas A1 - Brandt, Manfred A1 - Rugel, S. A1 - Weber, D. T1 - Admission control for realtime traffic T2 - Proc. IEEE Wireless Communications & Networking Conference WCNC 2005 Y1 - 2005 CY - New Orleans, USA ER -