The effective bandwidth problem revisited

The paper studies a single-server queueing system with autonomous service and $\ell$ priority classes. Arrival and departure processes are governed by marked point processes. There are $\ell$ buffers corresponding to priority classes, and upon arrival a unit of the $k$th priority class occupies a place in the $k$th buffer. Let $N^{(k)}$, $k=1,2,...,\ell$ denote the quota for the total $k$th buffer content. The values $N^{(k)}$ are assumed to be large, and queueing systems both with finite and infinite buffers are studied. In the case of a system with finite buffers, the values $N^{(k)}$ characterize buffer capacities. The paper discusses a circle of problems related to optimization of performance measures associated with overflowing the quota of buffer contents in particular buffers models. Our approach to this problem is new, and the presentation of our results is simple and clear for real applications.Comment: 29 pages, 11pt, Final version, that will be published as is in Stochastic Model

Optimization of polling systems with Bernoulli schedules

Optimization;Polling Systems;Queueing Theory;operations research

Fluid flow models in performance analysis

We review several developments in fluid flow models: feedback fluid models, linear stochastic fluid networks and bandwidth sharing networks. We also mention some promising new research directions

Correction. Brownian models of open processing networks: canonical representation of workload

Due to a printing error the above mentioned article [Annals of Applied Probability 10 (2000) 75--103, doi:10.1214/aoap/1019737665] had numerous equations appearing incorrectly in the print version of this paper. The entire article follows as it should have appeared. IMS apologizes to the author and the readers for this error. A recent paper by Harrison and Van Mieghem explained in general mathematical terms how one forms an ``equivalent workload formulation'' of a Brownian network model. Denoting by $Z(t)$ the state vector of the original Brownian network, one has a lower dimensional state descriptor $W(t)=MZ(t)$ in the equivalent workload formulation, where $M$ can be chosen as any basis matrix for a particular linear space. This paper considers Brownian models for a very general class of open processing networks, and in that context develops a more extensive interpretation of the equivalent workload formulation, thus extending earlier work by Laws on alternate routing problems. A linear program called the static planning problem is introduced to articulate the notion of ``heavy traffic'' for a general open network, and the dual of that linear program is used to define a canonical choice of the basis matrix $M$. To be specific, rows of the canonical $M$ are alternative basic optimal solutions of the dual linear program. If the network data satisfy a natural monotonicity condition, the canonical matrix $M$ is shown to be nonnegative, and another natural condition is identified which ensures that $M$ admits a factorization related to the notion of resource pooling.Comment: Published at http://dx.doi.org/10.1214/105051606000000583 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"