@misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {Asymptotic Results and a Markovian Approximation for the M(n)/M(n)/s+GI System}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5801}, number = {00-12}, abstract = {In this paper for the \$M(n)/M(n)/s+GI\$ system, i.e.\ for a \$s\$-server queueing system where the calls in the queue may leave the system due to impatience, we present new asymptotic results for the intensities of calls leaving the system due to impatience and a Markovian system approximation where these results are applied. Furthermore, we present a new proof for the formulae of the conditional density of the virtual waiting time distributions, recently given by Movaghar for the less general \$M(n)/M/s+GI\$ system. Also we obtain new explicit expressions for refined virtual waiting time characteristics as a byproduct.}, language = {en} } @misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the Two-Class M/M/1 System under Preemptive Resume and Impatience of the Prioritized Customers}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6953}, number = {02-28}, abstract = {The paper deals with the two-class priority M/M/1 system, where the prioritized class-1 customers are served under FCFS preemptive resume discipline and may become impatient during their waiting for service with generally distributed maximal waiting times but finite expectation. The class-2 customers have no impatience. The required mean service times may depend on the class of the customer. As the dynamics of class-1 customers are related to the well analyzed M/M/1+GI system, our aim is to derive characteristics for class-2 customers and for the whole system. The solution of the balance equations for the partial probability generating functions of the detailed system state process is given in terms of the weak solution of a family of boundary value problems for ordinary differential equations. By means of this solution formulae for the joint occupancy distribution and for the sojourn and waiting times of class-2 customers are derived generalizing results recently obtained by Choi et al. in case of deterministic maximal waiting times. For deterministic maximal waiting times partially new explicit formulae are given.}, language = {en} } @misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the Moments of the Overflow and Freed Carried Traffic for the GI/M/C/0 System}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6355}, number = {01-09}, abstract = {In circuit switching networks call streams are characterized by their mean and peakedness (two-moment method). The \$GI/M/C/0\$ system is used to model a single link, where the \$GI\$-stream is determined by fitting moments appropriately. For the moments of the overflow traffic of a \$GI/M/C/0\$ system there are efficient numerical algorithms available. However, for the moments of the freed carried traffic, defined as the moments of a virtual link of infinite capacity to which the process of calls accepted by the link (carried arrival process) is virtually directed and where the virtual calls get fresh exponential i.i.d.\ holding times, only complex numerical algorithms are available. This is the reason why the concept of the freed carried traffic is not used rigorously. The main result of this paper is an efficient algorithm for computing the moments of the freed carried traffic, in particular an explicit formula for its peakedness. This result offers a unified handling of both overflow and carried traffics in networks. Furthermore, some refined characteristics for the overflow and freed carried streams are derived.}, language = {en} } @misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {Individual Overflow and Freed Carried Traffics for a Link with Trunk Reservation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-6615}, number = {01-35}, abstract = {Two traffic streams \$\Phi_1\$, \$\Phi_2\$ are offered a link. The calls of \$\Phi_i\$ require exponential holding times with parameter \$\mu\$ and are accepted if less than \$C_i\$ trunks are occupied. Approximating the \$\Phi_i\$ by appropriate renewal processes meeting their first two moments, defined as the moments of the numbers of calls in virtual links of infinite capacity to which the traffic streams as freed traffics are virtually directed and where the calls get fresh exponential i.i.d.\ holding times with parameter \$\mu\$, stable recursive algorithms of complexity \$O(\max(C_1,C_2))\$ are derived for the first two defined as above moments of the individual overflow and freed carried traffics. The results offer a unified handling of both overflow and carried traffics in circuit switching networks with trunk reservation, providing a basis for new two-moment network dimensioning algorithms.}, language = {en} } @misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {A sample path relation for the sojourn times in G/G/1-PS systems and its applications}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7401}, number = {03-18}, abstract = {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.}, language = {en} } @misc{BrandtBrandt, author = {Brandt, Manfred and Brandt, Andreas}, title = {On sojourn times in M/GI systems under state-dependent processor sharing}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11366}, number = {09-22}, abstract = {We consider a system with Poisson arrivals and i.i.d. service times. The requests are served according to the state-dependent processor sharing discipline, where each request receives a service capacity which depends on the actual number of requests in the system. The linear systems of PDEs describing the residual and attained sojourn times coincide for this system, which provides time reversibility including sojourn times for this system, and their minimal non negative solution gives the LST of the sojourn time \$V(\tau)\$ of a request with required service time \$\tau\$. For the case that the service time distribution is exponential in a neighborhood of zero, we derive a linear system of ODEs, whose minimal non negative solution gives the LST of \$V(\tau)\$, and which yields linear systems of ODEs for the moments of \$V(\tau)\$ in the considered neighborhood of zero. Numerical results are presented for the variance of \$V(\tau)\$. In case of an M/GI/2-PS system, the LST of \$V(\tau)\$ is given in terms of the solution of a convolution equation in the considered neighborhood of zero. For bounded from below service times, surprisingly simple expressions for the LST and variance of \$V(\tau)\$ in this neighborhood of zero are derived, which yield in particular the LST and variance of \$V(\tau)\$ in M/D/2-PS.}, language = {en} } @misc{BrandtBrandt, 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}, 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} } @misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {Insensitivity bounds for the moments of the sojourn times in M/GI systems under state-dependent processor sharing}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11092}, number = {09-02}, abstract = {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.}, language = {en} } @misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {Waiting times for M/M systems under generalized processor sharing}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9404}, number = {06-46}, abstract = {We consider a system where the arrivals form a Poisson process and the required service times of the requests are exponentially distributed. According to the generalized processor sharing discipline, each request in the system receives a fraction of the capacity of one processor which depends on the actual number of requests in the system. We derive systems of ordinary differential equations for the LST and for the moments of the conditional waiting time of a request with given required service time as well as a stable and fast recursive algorithm for the LST of the second moment of the conditional waiting time, which in particular yields the second moment of the unconditional waiting time. Moreover, asymptotically tight upper bounds for the moments of the conditional waiting time are given. The presented numerical results for the first two moments of the sojourn times in the \$M/M/m-PS\$ system show that the proposed algorithms work well.}, language = {en} } @misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the stability of the multi-queue multi-server processor sharing with limited service}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9199}, number = {06-25}, abstract = {We consider a multi-queue multi-server system with \$n\$ servers (processors) and \$m\$ queues. At the system there arrives a stationary and ergodic stream of \$m\$ different types of requests with service requirements which are served according to the following \$k\$-limited head of the line processor sharing discipline: The first \$k\$ requests at the head of the \$m\$ queues are served in processor sharing by the \$n\$ processors, where each request may receive at most the capacity of one processor. By means of sample path analysis and Loynes' monotonicity method, a stationary and ergodic state process is constructed, and a necessary as well as a sufficient condition for the stability of the \$m\$ separate queues are given, which are tight within the class of all stationary ergodic inputs. These conditions lead to tight necessary and sufficient conditions for the whole system, also in case of permanent customers, generalizing an earlier result by the authors for the case of \$n\$=\$k\$=1.}, language = {en} } @misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the M(n)/M(m)/s Queue with impatient Calls}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2885}, number = {SC-97-19}, abstract = {The paper is concerned with the analysis of an \$s\$ server queueing system in which the calls become impatient and leave the system if their waiting time exceeds their own patience. The individual patience times are assumed to be i.i.d.\ and arbitrary distributed. The arrival and service rate may depend on the number of calls in the system and in service, respectively. For this system, denoted by \$M(n)/M(m)/s+GI\$, where \$m=\min(n,s)\$ is the number of busy servers in the system, we derive a system of integral equations for the vector of the residual patience times of the waiting calls and their original maximal patience times. By solving these equations explicitly we get the stability condition and, for the steady state of the system, the occupancy distribution and various waiting time distributions. As an application of the \mbox{\$M(n)/M(m)/s+GI\$} system we give a performance analysis of an Automatic Call Distributor system (ACD system) of finite capacity with outbound calls and impatient inbound calls, especially in case of patience times being the minimum of constant and exponentially distributed times.}, language = {en} } @misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the Sojourn Times for Many-Queue Head-of-the-Line Processor-Sharing Systems with Permanent Customers}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2005}, number = {SC-95-34}, abstract = {We consider a single server system consisting of \$n\$ queues with different types of customers (Poisson streams) and \$k\$ permanent customers. The permanent customers and those at the head of the queues are served in processor-sharing by the service facility (head-of-the-line processor-sharing). The stability condition and a pseudo work conservation law will be given for arbitrary service time distributions; for exponential service times a pseudo conservation law for the mean sojourn times can be derived. In case of two queues and exponential service times, the generating function of the stationary distribution satisfies a functional equation being a Riemann-Hilbert problem which can be reduced to a Dirichlet problem for a circle. The solution yields the mean sojourn times as an elliptic integral, which can be computed numerically very efficiently. In case \$n\ge 2\$ a numerical algorithm for computing the performance measures is presented, which is efficient for \$n=2,3\$. Since for \$n\ge 4\$ an exact analytical or/and numerical treatment is too complex a heuristic approximation for the mean sojourn times of the different types of customers is given, which in case of a (complete) symmetric system is exact. The numerical and simulation results show that, over a wide range of parameters, the approximation works well.}, language = {en} } @misc{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {On a Two-Queue Priority System with Impatience and its Application to a Call Center}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3641}, number = {SC-98-21}, abstract = {We consider a \$s\$-server system with two FCFS queues, where the arrival rates at the queues and the service rate may depend on the number \$n\$ of customers being in service or in the first queue, but the service rate is assumed to be constant for \$n>s\$. The customers in the first queue are impatient. If the offered waiting time exceeds a random maximal waiting time \$I\$, then the customer leaves the first queue after time \$I\$. If \$I\$ is less than a given deterministic time then he leaves the system else he transits to the end of the second queue. The customers in the first queue have priority. The service of a customer from the second queue will be started if the first queue is empty and more than a given number of servers become idle. For the model being a generalization of the \$M(n)/M(n)/s\!+\!GI\$ system balance conditions for the density of the stationary state process are derived yielding the stability conditions and the probabilities that precisely \$n\$ customers are in service or in the first queue. For obtaining performance measures for the second queue a system approximation basing on fitting impatience intensities is constructed. The results are applied to the performance analysis of a call center with an integrated voice-mail-server. For an important special case a stochastic decomposition is derived illuminating the connection to the dynamics of the \$M(n)/M(n)/s\!+\!GI\$ system.}, language = {en} } @misc{BrandtBrandt, 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}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2659}, number = {SC-96-55}, abstract = {We consider a single server system consisting of \$n\$ queues with different types of customers and \$k\$ permanent customers. The permanent customers and those at the head of the queues are served in processor-sharing by the service facility (head-of-the-line processor-sharing). By means of Loynes' monotonicity method a stationary work load process is constructed and using sample path analysis general stability conditions are derived. They allow to decide which queues are stable and moreover to compute the fraction of processor capacity devoted to the permanent customers. In case of a stable system the constructed stationary state process is the only one and for any initial state the system converges pathwise to the steady state.}, language = {en} } @misc{BrandtBrandt, 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}, 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} } @misc{ManfredAndreas, author = {Manfred, Brandt and Andreas, Brandt}, title = {On sojourn times for an infinite-server system in random environment and its application to processor sharing systems}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13190}, number = {11-28}, abstract = {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\$.}, language = {en} } @article{BrandtBrandt, author = {Brandt, Manfred and Brandt, Andreas}, title = {Additive functionals with application to sojourn times in infinite-server and processor sharing systems}, series = {Queueing Systems}, volume = {70}, journal = {Queueing Systems}, number = {4}, doi = {10.1007/s11134-012-9282-1}, pages = {369 -- 409}, abstract = {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\$.}, language = {en} } @article{BrandtBrandt, author = {Brandt, Andreas and Brandt, Manfred}, title = {Workload and busy period for M/GI/1 with a general impatience mechanism}, series = {Queueing Systems}, volume = {75}, journal = {Queueing Systems}, number = {2-4}, doi = {10.1007/s11134-013-9373-7}, pages = {189 -- 209}, 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{BrandtBrandt, 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}, series = {Advances in Applied Probability}, volume = {42}, journal = {Advances in Applied Probability}, number = {1}, doi = {10.1239/aap/1269611152}, pages = {246 -- 267}, abstract = {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.}, 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}, series = {Queueing Syst.}, volume = {32}, journal = {Queueing Syst.}, pages = {363 -- 381}, year = {1999}, language = {en} } @inproceedings{BrandtBrandt1999, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the computation of the probability of a system failure}, series = {Proc. ESREL'99 10th European Conf. on Safety and Reliability, G.I. Schu{\"e}ller, P. Kafka (eds.), Balkema Rotterdam}, 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{BrandtBrandt1999, author = {Brandt, Andreas and Brandt, Manfred}, title = {On a two-queue priority system with impatience and its application to a call center}, series = {Methodol. Comput. Appl. Probab.}, volume = {1}, journal = {Methodol. Comput. Appl. Probab.}, pages = {191 -- 210}, year = {1999}, language = {en} } @article{BrandtBrandt1999, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the \$M(n)/M(n)/s\$ queue with impatient calls}, series = {Perform. Eval.}, volume = {35}, journal = {Perform. Eval.}, pages = {1 -- 18}, year = {1999}, language = {en} } @article{BrandtBrandt1998, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the sojourn times for many-queue head-of-the-line processor-sharing systems with permanent customers}, series = {Math. Methods Oper. Res.}, volume = {47}, journal = {Math. Methods Oper. Res.}, pages = {181 -- 220}, year = {1998}, language = {en} } @inproceedings{BrandtBrandtSpahletal.1997, author = {Brandt, Andreas and Brandt, Manfred and Spahl, G. and Weber, D.}, title = {Modelling and optimization of call distribution systems}, series = {Proc. 15th Int. Teletraffic Cong. (ITC 15)}, booktitle = {Proc. 15th Int. Teletraffic Cong. (ITC 15)}, address = {Washington D.C., USA}, pages = {133 -- 144}, year = {1997}, 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}, series = {Queueing Syst.}, volume = {17}, journal = {Queueing Syst.}, pages = {275 -- 315}, year = {1994}, language = {en} } @article{BrandtBrandt2010, author = {Brandt, Manfred and Brandt, Andreas}, title = {On sojourn times in \$M/GI\$ systems under state-dependent processor sharing}, series = {Queueing Syst.}, volume = {64}, journal = {Queueing Syst.}, pages = {167 -- 201}, year = {2010}, language = {en} } @article{BrandtBrandt2008, author = {Brandt, Andreas and Brandt, Manfred}, title = {Waiting times for \$M/M\$ systems under state-dependent processor sharing}, series = {Queueing Syst.}, volume = {59}, journal = {Queueing Syst.}, pages = {297 -- 319}, year = {2008}, language = {en} } @article{BrandtBrandt2007, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the stability of the multi-queue multi-server processor sharing with limited service}, series = {Queueing Syst.}, volume = {56}, journal = {Queueing Syst.}, pages = {1 -- 8}, year = {2007}, language = {en} } @article{BrandtBrandt2006, author = {Brandt, Andreas and Brandt, Manfred}, title = {A sample path relation for the sojourn times in \$G/G/1-PS\$ systems and its applications}, series = {Queueing Syst.}, volume = {52}, journal = {Queueing Syst.}, pages = {281 -- 286}, year = {2006}, language = {en} } @article{BrandtBrandt2005, author = {Brandt, Andreas and Brandt, Manfred}, title = {Individual overflow and freed carried traffics for a link with trunk reservation}, series = {Telecommunication Syst.}, volume = {29}, journal = {Telecommunication Syst.}, pages = {283 -- 308}, year = {2005}, language = {en} } @inproceedings{BrandtBrandtRugeletal.2005, author = {Brandt, Andreas and Brandt, Manfred and Rugel, S. and Weber, D.}, title = {Admission control for realtime traffic}, series = {Proc. IEEE Wireless Communications \& Networking Conference WCNC 2005}, booktitle = {Proc. IEEE Wireless Communications \& Networking Conference WCNC 2005}, address = {New Orleans, USA}, year = {2005}, language = {en} } @article{BrandtBrandt2004, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the two-class \$M/M/1\$ system under preemptive resume and impatience of the prioritized customers}, series = {Queueing Syst.}, volume = {47}, journal = {Queueing Syst.}, pages = {147 -- 168}, year = {2004}, language = {en} } @article{BrandtBrandt2002, author = {Brandt, Andreas and Brandt, Manfred}, title = {On the moments of overflow and freed carried traffic for the \$GI/M/C/0\$ system}, series = {Methodol. Comput. Appl. Probab.}, volume = {4}, journal = {Methodol. Comput. Appl. Probab.}, pages = {69 -- 82}, year = {2002}, language = {en} } @article{BrandtBrandt2002, author = {Brandt, Andreas and Brandt, Manfred}, title = {Asymptotic results and a Markovian approximation for the \$M(n)/M(n)/s+GI\$ system}, series = {Queueing Syst.}, volume = {41}, journal = {Queueing Syst.}, pages = {73 -- 94}, year = {2002}, language = {en} } @article{BrandtBrandt2001, author = {Brandt, Andreas and Brandt, Manfred}, title = {Approximation for overflow moments of a multiservice link with trunk reservation}, series = {Perform. Eval.}, volume = {43}, journal = {Perform. Eval.}, pages = {259 -- 268}, year = {2001}, language = {en} } @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}, series = {Adv. Appl. Probab.}, volume = {42}, journal = {Adv. Appl. Probab.}, pages = {246 -- 267}, year = {2010}, language = {en} } @misc{Brandt, author = {Brandt, Manfred}, title = {Approximations for the Distribution Function of the Sum of iid Random Variables with Compact Support in R+}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1990}, number = {SC-95-33}, abstract = {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.}, language = {en} }