84 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
Positive and negative streamers in ambient air: measuring diameter, velocity and dissipated energy
Positive and negative streamers are studied in ambient air at 1 bar; they
emerge from a needle electrode placed 40 mm above a planar electrode. The
amplitudes of the applied voltage pulses range from 5 to 96 kV; most pulses
have rise times of 30 ns or shorter. Diameters, velocities and energies of the
streamers are measured. Two regimes are identified; a low voltage regime where
only positive streamers appear and a high voltage regime where both positive
and negative streamers exist. Below 5 kV, no streamers emerge. In the range
from 5 to 40 kV, positive streamers form, while the negative discharges only
form a glowing cloud at the electrode tip, but no streamers. For 5 to 20 kV,
diameters and velocities of the positive streamers have the minimal values of
d=0.2 mm and v \approx 10^5 m/s. For 20 to 40 kV, their diameters increase by a
factor 6 while the voltage increases only by a factor 2. Above the transition
value of 40 kV, streamers of both polarities form; they strongly resemble each
other, though the positive ones propagate further; their diameters continue to
increase with applied voltage. For 96 kV, positive streamers attain diameters
of 3 mm and velocities of 4*10^6 m/s, negative streamers are about 20 % slower
and thinner. An empirical fit formula for the relation between velocity v and
diameter d is v=0.5 d^2/(mm ns) for both polarities. Streamers of both
polarities dissipate energies of the order of several mJ per streamer while
crossing the gap.Comment: 20 pages, 9 figures, accepted for J. Phys.
Heavy traffic analysis of roving server networks
This paper studies the heavy-traffic (HT) behaviour of queueing networks with a single roving server. External customers arrive at the queues according to independent renewal processes and after completing service, a customer either leaves the system or is routed to another queue. This type of customer routing in queueing networks arises very naturally in many application areas (in production systems, computer- and communication networks, maintenance, etc.). In these networks, the single most important characteristic of the system performance is oftentimes the path time, i.e. the total time spent in the system by an arbitrary customer traversing a specific path. The current paper presents the first HT asymptotic for the path-time distribution in queueing networks with a roving server under general renewal arrivals. In particular, we provide a strong conjecture for the system's behaviour under HT extending the conjecture of Coffman et al. [E.G. Coffman Jr., A.A. Puhalskii, M.I. Reiman 1995 and 1998] to the roving server setting of the current paper. By combining this result with novel light-traffic asymptotics we derive an approximation of the mean path-time for arbitrary values of the load and renewal arrivals. This approximation is not only highly accurate for a wide range of parameter settings, but is also exact in various limiting cases
Inception and propagation of positive streamers in high-purity nitrogen: effects of the voltage rise-rate
Controlling streamer morphology is important for numerous applications. Up to
now, the effect of the voltage rise rate was only studied across a wide range.
Here we show that even slight variations in the voltage rise can have
significant effects. We have studied positive streamer discharges in a 16 cm
point-plane gap in high-purity nitrogen 6.0, created by 25 kV pulses with a
duration of 130 ns. The voltage rise varies by a rise rate from 1.9 kV/ns to
2.7 kV/ns and by the first peak voltage of 22 to 28 kV. A structural link is
found between smaller discharges with a larger inception cloud caused by a
faster rising voltage. This relation is explained by the greater stability of
the inception cloud due to a faster voltage rise, causing a delay in the
destabilisation. Time-resolved measurements show that the inception cloud
propagates slower than an earlier destabilised, more filamentary discharge.
This explains that the discharge with a faster rising voltage pulse ends up to
be shorter. Furthermore, the effect of remaining background ionisation in a
pulse sequence has been studied, showing that channel thickness and branching
rate are locally affected, depending on the covered volume of the previous
discharge.Comment: 16 pages, 9 figure
Positive and negative streamers in ambient air: modeling evolution and velocities
We simulate short positive and negative streamers in air at standard
temperature and pressure. They evolve in homogeneous electric fields or emerge
from needle electrodes with voltages of 10 to 20 kV. The streamer velocity at
given streamer length depends only weakly on the initial ionization seed,
except in the case of negative streamers in homogeneous fields. We characterize
the streamers by length, head radius, head charge and field enhancement. We
show that the velocity of positive streamers is mainly determined by their
radius and in quantitative agreement with recent experimental results both for
radius and velocity. The velocity of negative streamers is dominated by
electron drift in the enhanced field; in the low local fields of the present
simulations, it is little influenced by photo-ionization. Though negative
streamer fronts always move at least with the electron drift velocity in the
local field, this drift motion broadens the streamer head, decreases the field
enhancement and ultimately leads to slower propagation or even extinction of
the negative streamer.Comment: 18 pages, 10 figure
An optimization approach to adaptive multi-dimensional capital management
Firms should keep capital to offer sufficient protection against the risks
they are facing. In the insurance context methods have been developed to
determine the minimum capital level required, but less so in the context of
firms with multiple business lines including allocation. The individual capital
reserve of each line can be represented by means of classical models, such as
the conventional Cram\'{e}r-Lundberg model, but the challenge lies in soundly
modelling the correlations between the business lines. We propose a simple yet
versatile approach that allows for dependence by introducing a common
environmental factor. We present a novel Bayesian approach to calibrate the
latent environmental state distribution based on observations concerning the
claim processes. The calibration approach is adjusted for an environmental
factor that changes over time. The convergence of the calibration procedure
towards the true environmental state is deduced. We then point out how to
determine the optimal initial capital of the different business lines under
specific constraints on the ruin probability of subsets of business lines. Upon
combining the above findings, we have developed an easy-to-implement approach
to capital risk management in a multi-dimensional insurance risk model
Probing photo-ionization: Experiments on positive streamers in pure gasses and mixtures
Positive streamers are thought to propagate by photo-ionization whose
parameters depend on the nitrogen:oxygen ratio. Therefore we study streamers in
nitrogen with 20%, 0.2% and 0.01% oxygen and in pure nitrogen, as well as in
pure oxygen and argon. Our new experimental set-up guarantees contamination of
the pure gases to be well below 1 ppm. Streamers in oxygen are difficult to
measure as they emit considerably less light in the sensitivity range of our
fast ICCD camera than the other gasses. Streamers in pure nitrogen and in all
nitrogen/oxygen mixtures look generally similar, but become somewhat thinner
and branch more with decreasing oxygen content. In pure nitrogen the streamers
can branch so much that they resemble feathers. This feature is even more
pronounced in pure argon, with approximately 10^2 hair tips/cm^3 in the
feathers at 200 mbar; this density could be interpreted as the free electron
density creating avalanches towards the streamer stem. It is remarkable that
the streamer velocity is essentially the same for similar voltage and pressure
in all nitrogen/oxygen mixtures as well as in pure nitrogen, while the oxygen
concentration and therefore the photo-ionization lengths vary by more than five
orders of magnitude. Streamers in argon have essentially the same velocity as
well. The physical similarity of streamers at different pressures is confirmed
in all gases; the minimal diameters are smaller than in earlier measurements.Comment: 28 pages, 14 figures. Major differences with v1: - appendix and
spectra removed - subsection regarding effects of repetition frequency added
- many more smaller change
- …