@article{BrandtBrandt2010, author = {Brandt, Andreas and Brandt, Manfred}, title = {Insensitive bounds for the moments of the sojourn times in \$M/GI\$ systems under state-dependent processor sharing}, volume = {42}, journal = {Adv. Appl. Probab.}, pages = {246 -- 267}, year = {2010}, language = {en} } @article{BrandtBrandt2005, author = {Brandt, Andreas and Brandt, Manfred}, title = {Individual overflow and freed carried traffics for a link with trunk reservation}, volume = {29}, journal = {Telecommunication Syst.}, pages = {283 -- 308}, year = {2005}, language = {en} } @inproceedings{BrandtBrandt1999, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the computation of the probability of a system failure}, booktitle = {Proc. ESREL'99 10th European Conf. on Safety and Reliability, G.I. Schu{\"e}ller, P. Kafka (eds.), Balkema Rotterdam}, address = {M{\"u}nchen-Garching}, pages = {457 -- 461}, year = {1999}, language = {en} } @article{BrandtBrandt2001, author = {Brandt, Andreas and Brandt, Manfred}, title = {Approximation for overflow moments of a multiservice link with trunk reservation}, volume = {43}, journal = {Perform. Eval.}, pages = {259 -- 268}, year = {2001}, language = {en} } @article{BrandtBrandt1999, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the \$M(n)/M(n)/s\$ queue with impatient calls}, volume = {35}, journal = {Perform. Eval.}, pages = {1 -- 18}, year = {1999}, language = {en} } @misc{BrandtBrandt2011, author = {Brandt, Andreas and Brandt, Manfred}, title = {Workload and busy period for M/GI/1 with a general impatience mechanism}, issn = {1438-0064}, doi = {10.1007/s11134-013-9373-7}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14304}, number = {11-43}, year = {2011}, abstract = {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.}, language = {en} } @article{BrandtBrandt1999, author = {Brandt, Andreas and Brandt, Manfred}, title = {A note on the stability of the many-queue head-of-the-line processor-sharing system with permanent customers}, volume = {32}, journal = {Queueing Syst.}, pages = {363 -- 381}, year = {1999}, language = {en} } @article{BrandtBrandt1999, author = {Brandt, Andreas and Brandt, Manfred}, title = {On a two-queue priority system with impatience and its application to a call center}, volume = {1}, journal = {Methodol. Comput. Appl. Probab.}, pages = {191 -- 210}, year = {1999}, language = {en} } @article{BrandtBrandt1994, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the distribution of the number of packets in the fluid flow approximation of packet arrival streams}, volume = {17}, journal = {Queueing Syst.}, pages = {275 -- 315}, year = {1994}, language = {en} } @misc{BrandtBrandt2009, author = {Brandt, Andreas and Brandt, Manfred}, title = {Approximations for the second moments of sojourn times in M/GI systems under state-dependent processor sharing}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11414}, number = {09-25}, year = {2009}, abstract = {We consider a system with Poisson arrivals and general service times, where the requests are served according to the State-Dependent Processor Sharing (SDPS) discipline (Cohen's generalized processor sharing discipline), where each request receives a service capacity which depends on the actual number of requests in the system. For this system, denoted by \$M/GI/SDPS\$, we derive approximations for the squared coefficients of variation of the conditional sojourn time of a request given its service time and of the unconditional sojourn time by means of two-moment fittings of the service times. The approximations are given in terms of the squared coefficients of variation of the conditional and unconditional sojourn time in related \$M/D/SDPS\$ and \$M/M/SDPS\$ systems, respectively. The numerical results presented for \$M/GI/m-PS\$ systems illustrate that the proposed approximations work well.}, language = {en} }