246 research outputs found
Fixed points for multi-class queues
Burke's theorem can be seen as a fixed-point result for an exponential
single-server queue; when the arrival process is Poisson, the departure process
has the same distribution as the arrival process. We consider extensions of
this result to multi-type queues, in which different types of customer have
different levels of priority. We work with a model of a queueing server which
includes discrete-time and continuous-time M/M/1 queues as well as queues with
exponential or geometric service batches occurring in discrete time or at
points of a Poisson process. The fixed-point results are proved using
interchangeability properties for queues in tandem, which have previously been
established for one-type M/M/1 systems. Some of the fixed-point results have
previously been derived as a consequence of the construction of stationary
distributions for multi-type interacting particle systems, and we explain the
links between the two frameworks. The fixed points have interesting
"clustering" properties for lower-priority customers. An extreme case is an
example of a Brownian queue, in which lower-priority work only occurs at a set
of times of measure 0 (and corresponds to a local time process for the
queue-length process of higher priority work).Comment: 25 page
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"
Self-Evaluation Applied Mathematics 2003-2008 University of Twente
This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008
A game theoretic model of the behavioural gaming that takes place at the EMS - ED interface
This research describes the development and application of a 3-player game theoretic model between two queueing systems and a service that distributes individuals to them. The resultant model is used to explore dynamics between all players. The first aspect of this work is the development of a queueing system with two consecutive waiting spaces where the strategic managerial behaviour corresponds to how individuals use these waiting spaces. Two modelling techniques are deployed: discrete event simulation and Markov chains. The state probabilities of the Markov chain system are used to extract the performance measures of the queueing model (e.g. mean time in each waiting room, mean number of individuals in each room, etc.). A 3-player game theoretic model is subsequently proposed between the two queueing systems and the service that distributes individuals to them. In particular this can be viewed as a 2-player normal-form game where the utilities are determined by a third player with its own strategies and objectives. A backwards induction technique is used to get the utilities of the normal-form game between the two queueing systems. This particular system has many applications, including those in healthcare where it captures the emergent behaviour between the Emergency Medical Service (EMS) and the Emergency Department (ED). The impact of time-target measures on patient well-being is explored in this paper
Recommended from our members
Decomposition of general queueing network models. An investigation into the implementation of hierarchical decomposition schemes of general closed queueing network models using the principle of minimum relative entropy subject to fully decomposable constraints.
Decomposition methods based on the hierarchical partitioning of
the state space of queueing network models offer powerful evaluation
tools for the performance analysis of computer systems and
communication networks. These methods being conventionally
implemented capture the exact solution of separable queueing network
models but their credibility differs when applied to general queueing
networks. This thesis provides a universal information theoretic
framework for the implementation of hierarchical decomposition
schemes, based on the principle of minimum relative entropy given
fully decomposable subset and aggregate utilization, mean queue
length and flow-balance constraints. This principle is used, in
conjuction with asymptotic connections to infinite capacity queues,
to derive new closed form approximations for the conditional and
marginal state probabilities of general queueing network models. The
minimum relative entropy solutions are implemented iteratively at
each decomposition level involving the generalized exponential (GE)
distributional model in approximating the general service and
asymptotic flow processes in the network. It is shown that the
minimum relative entropy joint state probability, subject to mean
queue length and flow-balance constraints, is identical to the exact
product-form solution obtained as if the network was separable. An
investigation into the effect of different couplings of the resource
units on the relative accuracy of the approximation is carried out,
based on an extensive experimentation. The credibility of the method
is demonstrated with some illustrative examples involving
first-come-first-served general queueing networks with single and
multiple servers and favourable comparisons against exact solutions
and other approximations are made
- …