1,409 research outputs found
Queues and risk processes with dependencies
We study the generalization of the G/G/1 queue obtained by relaxing the
assumption of independence between inter-arrival times and service
requirements. The analysis is carried out for the class of multivariate matrix
exponential distributions introduced in [12]. In this setting, we obtain the
steady state waiting time distribution and we show that the classical relation
between the steady state waiting time and the workload distributions re- mains
valid when the independence assumption is relaxed. We also prove duality
results with the ruin functions in an ordinary and a delayed ruin process.
These extend several known dualities between queueing and risk models in the
independent case. Finally we show that there exist stochastic order relations
between the waiting times under various instances of correlation
A tandem queue with server slow-down and blocking
We consider two variants of a two-station tandem network with blocking. In both variants the first server ceases to work when the queue length at the second station hits a `blocking threshold'. In addition, in variant the first server decreases its service rate when the second queue exceeds a `slow-down threshold', which is smaller than the blocking level. In both variants the arrival process is Poisson and the service times at both stations are exponentially distributed. Note, however, that in case of slow-downs, server works at a high rate, a slow rate, or not at all, depending on whether the second queue is below or above the slow-down threshold or at the blocking threshold, respectively. For variant , i.e., only blocking, we concentrate on the geometric decay rate of the number of jobs in the first buffer and prove that for increasing blocking thresholds the sequence of decay rates decreases monotonically and at least geometrically fast to , where is the load at server . The methods used in the proof also allow us to clarify the asymptotic queue length distribution at the second station. Then we generalize the analysis to variant , i.e., slow-down and blocking, and establish analogous results. \u
The Embedding Capacity of Information Flows Under Renewal Traffic
Given two independent point processes and a certain rule for matching points
between them, what is the fraction of matched points over infinitely long
streams? In many application contexts, e.g., secure networking, a meaningful
matching rule is that of a maximum causal delay, and the problem is related to
embedding a flow of packets in cover traffic such that no traffic analysis can
detect it. We study the best undetectable embedding policy and the
corresponding maximum flow rate ---that we call the embedding capacity--- under
the assumption that the cover traffic can be modeled as arbitrary renewal
processes. We find that computing the embedding capacity requires the inversion
of very structured linear systems that, for a broad range of renewal models
encountered in practice, admits a fully analytical expression in terms of the
renewal function of the processes. Our main theoretical contribution is a
simple closed form of such relationship. This result enables us to explore
properties of the embedding capacity, obtaining closed-form solutions for
selected distribution families and a suite of sufficient conditions on the
capacity ordering. We evaluate our solution on real network traces, which shows
a noticeable match for tight delay constraints. A gap between the predicted and
the actual embedding capacities appears for looser constraints, and further
investigation reveals that it is caused by inaccuracy of the renewal traffic
model rather than of the solution itself.Comment: Sumbitted to IEEE Trans. on Information Theory on March 10, 201
How wireless queues benefit from motion: an analysis of the continuum between zero and infinite mobility
This paper considers the time evolution of a queue that is embedded in a
Poisson point process of moving wireless interferers. The queue is driven by an
external arrival process and is subject to a time-varying service process that
is a function of the SINR that it sees. Static configurations of interferers
result in an infinite queue workload with positive probability. In contrast, a
generic stability condition is established for the queue in the case where
interferers possess any non-zero mobility that results in displacements that
are both independent across interferers and oblivious to interferer positions.
The proof leverages the mixing property of the Poisson point process. The
effect of an increase in mobility on queueing metrics is also studied. Convex
ordering tools are used to establish that faster moving interferers result in a
queue workload that is smaller for the increasing-convex stochastic order. As a
corollary, mean workload and mean delay decrease as network mobility increases.
This stochastic ordering as a function of mobility is explained by establishing
positive correlations between SINR level-crossing events at different time
points, and by determining the autocorrelation function for interference and
observing that it decreases with increasing mobility. System behaviour is
empirically analyzed using discrete-event simulation and the performance of
various mobility models is evaluated using heavy-traffic approximations.Comment: Preliminary version appeared in WiOPT 2020. New version with
revision
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