1,571 research outputs found
Queues and risk models with simultaneous arrivals
We focus on a particular connection between queueing and risk models in a
multi-dimensional setting. We first consider the joint workload process in a
queueing model with parallel queues and simultaneous arrivals at the queues.
For the case that the service times are ordered (from largest in the first
queue to smallest in the last queue) we obtain the Laplace-Stieltjes transform
of the joint stationary workload distribution. Using a multivariate duality
argument between queueing and risk models, this also gives the Laplace
transform of the survival probability of all books in a multivariate risk model
with simultaneous claim arrivals and the same ordering between claim sizes.
Other features of the paper include a stochastic decomposition result for the
workload vector, and an outline how the two-dimensional risk model with a
general two-dimensional claim size distribution (hence without ordering of
claim sizes) is related to a known Riemann boundary value problem
Shot-noise queueing models
We provide a survey of so-called shot-noise queues: queueing models with the special feature that the server speed is proportional to the amount of work it faces. Several results are derived for the workload in an M/G/1 shot-noise queue and some of its variants. Furthermore, we give some attention to queues with general workload-dependent service speed. We also discuss linear stochastic fluid networks, and queues in which the input process is a shot-noise process
The achievable region method in the optimal control of queueing systems : formulations, bounds and policies
Cover title.Includes bibliographical references (p. 44-48).Supported in part by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118Dimitris Bertsimas
The achievable region method in the optimal control of queueing systems : formulations, bounds and policies
Cover title.Includes bibliographical references (p. 44-48).Supported in part by a Presidential Young Investigator Award, with matching funds from Draper Laboratory. DDM-9158118Dimitris Bertsimas
Fluid queues and mountain processes
This paper is devoted to the analysis of a fluid queue with a buffer content that varies linearly during periods that are governed by a three-state semi-Markov process. Two cases are being distinguished: (i) two upward slopes and one downward slope, and (ii) one upward slope and two downward slopes. In both cases, at least one of the period distributions is allowed to be completely general. We obtain exact results for the buffer content distribution, the busy period distribution and the distribution of the maximal buffer content during a busy period. The results are obtained by establishing relations between the fluid queues and ordinary queues with instantaneous input, and by using level crossing theory
Two parallel insurance lines with simultaneous arrivals and risks correlated with inter-arrival times
We investigate an insurance risk model that consists of two reserves which
receive income at fixed rates. Claims are being requested at random epochs from
each reserve and the interclaim times are generally distributed. The two
reserves are coupled in the sense that at a claim arrival epoch, claims are
being requested from both reserves and the amounts requested are correlated. In
addition, the claim amounts are correlated with the time elapsed since the
previous claim arrival. We focus on the probability that this bivariate reserve
process survives indefinitely. The infinite- horizon survival problem is shown
to be related to the problem of determining the equilibrium distribution of a
random walk with vector-valued increments with reflecting boundary. This
reflected random walk is actually the waiting time process in a queueing system
dual to the bivariate ruin process. Under assumptions on the arrival process
and the claim amounts, and using Wiener-Hopf factor- ization with one
parameter, we explicitly determine the Laplace-Stieltjes transform of the
survival function, c.q., the two-dimensional equilibrium waiting time
distribution. Finally, the bivariate transforms are evaluated for some
examples, including for proportional reinsurance, and the bivariate ruin
functions are numerically calculated using an efficient inversion scheme.Comment: 24 pages, 6 figure
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