30,062 research outputs found
Learning Algorithms for Minimizing Queue Length Regret
We consider a system consisting of a single transmitter/receiver pair and
channels over which they may communicate. Packets randomly arrive to the
transmitter's queue and wait to be successfully sent to the receiver. The
transmitter may attempt a frame transmission on one channel at a time, where
each frame includes a packet if one is in the queue. For each channel, an
attempted transmission is successful with an unknown probability. The
transmitter's objective is to quickly identify the best channel to minimize the
number of packets in the queue over time slots. To analyze system
performance, we introduce queue length regret, which is the expected difference
between the total queue length of a learning policy and a controller that knows
the rates, a priori. One approach to designing a transmission policy would be
to apply algorithms from the literature that solve the closely-related
stochastic multi-armed bandit problem. These policies would focus on maximizing
the number of successful frame transmissions over time. However, we show that
these methods have queue length regret. On the other hand, we
show that there exists a set of queue-length based policies that can obtain
order optimal queue length regret. We use our theoretical analysis to
devise heuristic methods that are shown to perform well in simulation.Comment: 28 Pages, 11 figure
Transient bayesian inference for short and long-tailed GI/G/1 queueing systems
In this paper, we describe how to make Bayesian inference for the transient behaviour and busy period in a single server system with general and unknown distribution for the service and interarrival time. The dense family of Coxian distributions is used for the service and arrival process to the system. This distribution model is reparametrized such that it is possible to define a non-informative prior which allows for the approximation of heavytailed distributions. Reversible jump Markov chain Monte Carlo methods are used to estimate the predictive distribution of the interarrival and service time. Our procedure for estimating the system measures is based in recent results for known parameters which are frequently implemented by using symbolical packages. Alternatively, we propose a simple numerical technique that can be performed for every MCMC iteration so that we can estimate interesting measures, such as the transient queue length distribution. We illustrate our approach with simulated and real queues
Approximate IPA: Trading Unbiasedness for Simplicity
When Perturbation Analysis (PA) yields unbiased sensitivity estimators for
expected-value performance functions in discrete event dynamic systems, it can
be used for performance optimization of those functions. However, when PA is
known to be unbiased, the complexity of its estimators often does not scale
with the system's size. The purpose of this paper is to suggest an alternative
approach to optimization which balances precision with computing efforts by
trading off complicated, unbiased PA estimators for simple, biased approximate
estimators. Furthermore, we provide guidelines for developing such estimators,
that are largely based on the Stochastic Flow Modeling framework. We suggest
that if the relative error (or bias) is not too large, then optimization
algorithms such as stochastic approximation converge to a (local) minimum just
like in the case where no approximation is used. We apply this approach to an
example of balancing loss with buffer-cost in a finite-buffer queue, and prove
a crucial upper bound on the relative error. This paper presents the initial
study of the proposed approach, and we believe that if the idea gains traction
then it may lead to a significant expansion of the scope of PA in optimization
of discrete event systems.Comment: 8 pages, 8 figure
On a generic class of two-node queueing systems
This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an on–off Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying predominantly on probabilistic argumentation, the steady-state buffer content of both queues is determined (in terms of its Laplace transform). Interpreting the buffer content of the second queue in terms of busy periods of the first queue, the (exact) tail asymptotics of the distribution of the second queue are found. Two regimes can be distinguished: a first in which the state of the first queue (that is, being empty or not) hardly plays a role, and a second in which it explicitly does. This dichotomy can be understood by using large-deviations heuristics
Asymptotic Behavior of the Number of Lost Messages
The goal of the paper is to study asymptotic behavior of the number of lost
messages. Long messages are assumed to be divided into a random number of
packets which are transmitted independently of one another. An error in
transmission of a packet results in the loss of the entire message. Messages
arrive to the finite buffer model and can be lost in two cases as
either at least one of its packets is corrupted or the buffer is overflowed.
With the parameters of the system typical for models of information
transmission in real networks, we obtain theorems on asymptotic behavior of the
number of lost messages. We also study how the loss probability changes if
redundant packets are added. Our asymptotic analysis approach is based on
Tauberian theorems with remainder.Comment: 18 pages, The list of references and citations slightly differ from
these appearing in the journa
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