4,903 research outputs found
Two-dimensional fluid queues with temporary assistance
We consider a two-dimensional stochastic fluid model with ON-OFF inputs
and temporary assistance, which is an extension of the same model with
in Mahabhashyam et al. (2008). The rates of change of both buffers are
piecewise constant and dependent on the underlying Markovian phase of the
model, and the rates of change for Buffer 2 are also dependent on the specific
level of Buffer 1. This is because both buffers share a fixed output capacity,
the precise proportion of which depends on Buffer 1. The generalization of the
number of ON-OFF inputs necessitates modifications in the original rules of
output-capacity sharing from Mahabhashyam et al. (2008) and considerably
complicates both the theoretical analysis and the numerical computation of
various performance measures
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
On deciding stability of multiclass queueing networks under buffer priority scheduling policies
One of the basic properties of a queueing network is stability. Roughly
speaking, it is the property that the total number of jobs in the network
remains bounded as a function of time. One of the key questions related to the
stability issue is how to determine the exact conditions under which a given
queueing network operating under a given scheduling policy remains stable.
While there was much initial progress in addressing this question, most of the
results obtained were partial at best and so the complete characterization of
stable queueing networks is still lacking. In this paper, we resolve this open
problem, albeit in a somewhat unexpected way. We show that characterizing
stable queueing networks is an algorithmically undecidable problem for the case
of nonpreemptive static buffer priority scheduling policies and deterministic
interarrival and service times. Thus, no constructive characterization of
stable queueing networks operating under this class of policies is possible.
The result is established for queueing networks with finite and infinite buffer
sizes and possibly zero service times, although we conjecture that it also
holds in the case of models with only infinite buffers and nonzero service
times. Our approach extends an earlier related work [Math. Oper. Res. 27 (2002)
272--293] and uses the so-called counter machine device as a reduction tool.Comment: Published in at http://dx.doi.org/10.1214/09-AAP597 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The effective bandwidth problem revisited
The paper studies a single-server queueing system with autonomous service and
priority classes. Arrival and departure processes are governed by marked
point processes. There are buffers corresponding to priority classes,
and upon arrival a unit of the th priority class occupies a place in the
th buffer. Let , denote the quota for the total
th buffer content. The values 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 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
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