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 - Advances in Applied Probability 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. Y1 - 2010 U6 - https://doi.org/10.1239/aap/1269611152 VL - 42 IS - 1 SP - 246 EP - 267 ER - TY - JOUR A1 - Brandt, Manfred A1 - Brandt, Andreas T1 - Additive functionals with application to sojourn times in infinite-server and processor sharing systems JF - Queueing 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 $M/GI(n)/\infty$. Y1 - 2012 U6 - https://doi.org/10.1007/s11134-012-9282-1 VL - 70 IS - 4 SP - 369 EP - 409 ER - TY - JOUR A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - Workload and busy period for M/GI/1 with a general impatience mechanism JF - Queueing Systems 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. Y1 - 2013 U6 - https://doi.org/10.1007/s11134-013-9373-7 VL - 75 IS - 2-4 SP - 189 EP - 209 ER - TY - JOUR A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - On the stability of the multi-queue multi-server processor sharing with limited service JF - Queueing Syst. Y1 - 2007 VL - 56 SP - 1 EP - 8 ER - TY - JOUR A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - On the sojourn times for many-queue head-of-the-line processor-sharing systems with permanent customers JF - Math. Methods Oper. Res. Y1 - 1998 VL - 47 SP - 181 EP - 220 ER - TY - JOUR A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - On the two-class $M/M/1$ system under preemptive resume and impatience of the prioritized customers JF - Queueing Syst. Y1 - 2004 VL - 47 SP - 147 EP - 168 ER - TY - JOUR A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - Asymptotic results and a Markovian approximation for the $M(n)/M(n)/s+GI$ system JF - Queueing Syst. Y1 - 2002 VL - 41 SP - 73 EP - 94 ER - TY - JOUR A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - Waiting times for $M/M$ systems under state-dependent processor sharing JF - Queueing Syst. Y1 - 2008 VL - 59 SP - 297 EP - 319 ER - TY - JOUR A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - On the moments of overflow and freed carried traffic for the $GI/M/C/0$ system JF - Methodol. Comput. Appl. Probab. Y1 - 2002 VL - 4 SP - 69 EP - 82 ER - TY - JOUR A1 - Brandt, Andreas A1 - Brandt, Manfred T1 - A sample path relation for the sojourn times in $G/G/1-PS$ systems and its applications JF - Queueing Syst. Y1 - 2006 VL - 52 SP - 281 EP - 286 ER - 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 -