6,517 research outputs found
Exclusive Queueing Process with Discrete Time
In a recent study [C Arita, Phys. Rev. E 80, 051119 (2009)], an extension of
the M/M/1 queueing process with the excluded-volume effect as in the totally
asymmetric simple exclusion process (TASEP) was introduced. In this paper, we
consider its discrete-time version. The update scheme we take is the parallel
one. A stationary-state solution is obtained in a slightly arranged matrix
product form of the discrete-time open TASEP with the parallel update. We find
the phase diagram for the existence of the stationary state. The critical line
which separates the parameter space into the regions with and without the
stationary state can be written in terms of the stationary current of the open
TASEP. We calculate the average length of the system and the average number of
particles
A Fixed-Point Algorithm for Closed Queueing Networks
In this paper we propose a new efficient iterative scheme for solving closed queueing networks with phase-type service time distributions. The method is especially efficient and accurate in case of large numbers of nodes and large customer populations. We present the method, put it in perspective, and validate it through a large number of test scenarios. In most cases, the method provides accuracies within 5% relative error (in comparison to discrete-event simulation)
When Backpressure Meets Predictive Scheduling
Motivated by the increasing popularity of learning and predicting human user
behavior in communication and computing systems, in this paper, we investigate
the fundamental benefit of predictive scheduling, i.e., predicting and
pre-serving arrivals, in controlled queueing systems. Based on a lookahead
window prediction model, we first establish a novel equivalence between the
predictive queueing system with a \emph{fully-efficient} scheduling scheme and
an equivalent queueing system without prediction. This connection allows us to
analytically demonstrate that predictive scheduling necessarily improves system
delay performance and can drive it to zero with increasing prediction power. We
then propose the \textsf{Predictive Backpressure (PBP)} algorithm for achieving
optimal utility performance in such predictive systems. \textsf{PBP}
efficiently incorporates prediction into stochastic system control and avoids
the great complication due to the exponential state space growth in the
prediction window size. We show that \textsf{PBP} can achieve a utility
performance that is within of the optimal, for any ,
while guaranteeing that the system delay distribution is a
\emph{shifted-to-the-left} version of that under the original Backpressure
algorithm. Hence, the average packet delay under \textsf{PBP} is strictly
better than that under Backpressure, and vanishes with increasing prediction
window size. This implies that the resulting utility-delay tradeoff with
predictive scheduling beats the known optimal tradeoff for systems without prediction
Packet loss characteristics for M/G/1/N queueing systems
In this contribution we investigate higher-order loss characteristics for M/G/1/N queueing systems. We focus on the lengths of the loss and non-loss periods as well as on the number of arrivals during these periods. For the analysis, we extend the Markovian state of the queueing system with the time and number of admitted arrivals since the instant where the last loss occurred. By combining transform and matrix techniques, expressions for the various moments of these loss characteristics are found. The approach also yields expressions for the loss probability and the conditional loss probability. Some numerical examples then illustrate our results
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