16,174 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
Computationally Efficient Simulation of Queues: The R Package queuecomputer
Large networks of queueing systems model important real-world systems such as
MapReduce clusters, web-servers, hospitals, call centers and airport passenger
terminals. To model such systems accurately, we must infer queueing parameters
from data. Unfortunately, for many queueing networks there is no clear way to
proceed with parameter inference from data. Approximate Bayesian computation
could offer a straightforward way to infer parameters for such networks if we
could simulate data quickly enough.
We present a computationally efficient method for simulating from a very
general set of queueing networks with the R package queuecomputer. Remarkable
speedups of more than 2 orders of magnitude are observed relative to the
popular DES packages simmer and simpy. We replicate output from these packages
to validate the package.
The package is modular and integrates well with the popular R package dplyr.
Complex queueing networks with tandem, parallel and fork/join topologies can
easily be built with these two packages together. We show how to use this
package with two examples: a call center and an airport terminal.Comment: Updated for queuecomputer_0.8.
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
Some aspects of queueing and storage processes : a thesis in partial fulfilment of the requirements for the degree of Master of Science in Statistics at Massey University
In this study the nature of systems consisting of a single queue are first considered. Attention is then drawn to an analogy between such systems and storage systems.
A development of the single queue viz queues with feedback is considered after first considering feedback processes in general. The behaviour of queues, some with feedback loops, combined into networks is then considered. Finally, the application of such networks to the analysis of interconnected reservoir systems is considered and the conclusion drawn that such analytic methods complement the more recently developed mathematical programming methods by providing analytic solutions for
sub systems behaviour and thus guiding the development of a system model
Stochastic decomposition in discrete-time queues with generalized vacations and applications
For several specific queueing models with a vacation policy, the stationary system occupancy at the beginning of a rantdom slot is distributed as the sum of two independent random variables. One of these variables is the stationary number of customers in an equivalent queueing system with no vacations. For models in continuous time with Poissonian arrivals, this result is well-known, and referred to as stochastic decomposition, with proof provided by Fuhrmann and Cooper. For models in discrete time, this result received less attention, with no proof available to date. In this paper, we first establish a proof of the decomposition result in discrete time. When compared to the proof in continuous time, conditions for the proof in discrete time are somewhat more general. Second, we explore four different examples: non-preemptive proirity systems, slot-bound priority systems, polling systems, and fiber delay line (FDL) buffer systems. The first two examples are known results from literature that are given here as an illustration. The third is a new example, and the last one (FDL buffer systems) shows new results. It is shown that in some cases the queueing analysis can be considerably simplified using this property
Control of Robotic Mobility-On-Demand Systems: a Queueing-Theoretical Perspective
In this paper we present and analyze a queueing-theoretical model for
autonomous mobility-on-demand (MOD) systems where robotic, self-driving
vehicles transport customers within an urban environment and rebalance
themselves to ensure acceptable quality of service throughout the entire
network. We cast an autonomous MOD system within a closed Jackson network model
with passenger loss. It is shown that an optimal rebalancing algorithm
minimizing the number of (autonomously) rebalancing vehicles and keeping
vehicles availabilities balanced throughout the network can be found by solving
a linear program. The theoretical insights are used to design a robust,
real-time rebalancing algorithm, which is applied to a case study of New York
City. The case study shows that the current taxi demand in Manhattan can be met
with about 8,000 robotic vehicles (roughly 60% of the size of the current taxi
fleet). Finally, we extend our queueing-theoretical setup to include congestion
effects, and we study the impact of autonomously rebalancing vehicles on
overall congestion. Collectively, this paper provides a rigorous approach to
the problem of system-wide coordination of autonomously driving vehicles, and
provides one of the first characterizations of the sustainability benefits of
robotic transportation networks.Comment: 10 pages, To appear at RSS 201
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