264 research outputs found
Factorization identities for reflected processes, with applications
We derive factorization identities for a class of preemptive-resume queueing
systems, with batch arrivals and catastrophes that, whenever they occur,
eliminate multiple customers present in the system. These processes are quite
general, as they can be used to approximate Levy processes, diffusion
processes, and certain types of growth-collapse processes; thus, all of the
processes mentioned above also satisfy similar factorization identities. In the
Levy case, our identities simplify to both the well-known Wiener-Hopf
factorization, and another interesting factorization of reflected Levy
processes starting at an arbitrary initial state. We also show how the ideas
can be used to derive transforms for some well-known
state-dependent/inhomogeneous birth-death processes and diffusion processes
A Tandem Fluid Network with L\'evy Input in Heavy Traffic
In this paper we study the stationary workload distribution of a fluid tandem
queue in heavy traffic. We consider different types of L\'evy input, covering
compound Poisson, -stable L\'evy motion (with ), and
Brownian motion. In our analysis we separately deal with L\'evy input processes
with increments that have finite and infinite variance. A distinguishing
feature of this paper is that we do not only consider the usual heavy-traffic
regime, in which the load at one of the nodes goes to unity, but also a regime
in which we simultaneously let the load of both servers tend to one, which, as
it turns out, leads to entirely different heavy-traffic asymptotics. Numerical
experiments indicate that under specific conditions the resulting simultaneous
heavy-traffic approximation significantly outperforms the usual heavy-traffic
approximation
On simple ruin expressions in dependent Sparre Andersen risk models
In this note we provide a simple alternative derivation of an explicit formula of Kwan and Yang [14] for the probability of ruin in a risk model with a certain dependence between general claim inter-occurrence times and subsequent claim sizes of conditionally exponential type. The approach puts the type of formula in a general context, illustrating the potential for similar simple ruin probability expressions in more general risk models with dependence
On simple ruin expressions in dependent Sparre Andersen risk models
In this note we provide a simple alternative probabilistic derivation of an explicit formula of Kwan and Yang (2007) for the probability of ruin in a risk model with a certain dependence between general claim interoccurrence times and subsequent claim sizes of conditionally exponential type. The approach puts the type of formula in a general context, illustrating the potential for similar simple ruin probability expressions in more general risk models with dependence
Queues with random back-offs
We consider a broad class of queueing models with random state-dependent
vacation periods, which arise in the analysis of queue-based back-off
algorithms in wireless random-access networks. In contrast to conventional
models, the vacation periods may be initiated after each service completion,
and can be randomly terminated with certain probabilities that depend on the
queue length. We examine the scaled queue length and delay in a heavy-traffic
regime, and demonstrate a sharp trichotomy, depending on how the activation
rate and vacation probability behave as function of the queue length. In
particular, the effect of the vacation periods may either (i) completely vanish
in heavy-traffic conditions, (ii) contribute an additional term to the queue
lengths and delays of similar magnitude, or even (iii) give rise to an
order-of-magnitude increase. The heavy-traffic asymptotics are obtained by
combining stochastic lower and upper bounds with exact results for some
specific cases. The heavy-traffic trichotomy provides valuable insight in the
impact of the back-off algorithms on the delay performance in wireless
random-access networks
Ruin excursions, the G/G/Infinity queue and tax payments in renewal risk models
In this paper we investigate the number and maximum severity of the ruin excursion of the insurance portfolio reserve process in the Cramer-Lundberg model with and without tax payments. We also provide a relation of the Cramer-Lundberg risk model with the G/G/infinity queue and use it to derive some explicit ruin probability formulae. Finally, the renewal risk model with tax is considered, and an asymptotic identity is derived that in some sense extends the tax identity of the Cramer-Lundberg risk model
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