12,737 research outputs found
Simple and explicit bounds for multi-server queues with (and sometimes better) scaling
We consider the FCFS queue, and prove the first simple and explicit
bounds that scale as (and sometimes better). Here
denotes the corresponding traffic intensity. Conceptually, our results can be
viewed as a multi-server analogue of Kingman's bound. Our main results are
bounds for the tail of the steady-state queue length and the steady-state
probability of delay. The strength of our bounds (e.g. in the form of tail
decay rate) is a function of how many moments of the inter-arrival and service
distributions are assumed finite. More formally, suppose that the inter-arrival
and service times (distributed as random variables and respectively)
have finite th moment for some Let (respectively )
denote (respectively ). Then
our bounds (also for higher moments) are simple and explicit functions of
, and
only. Our bounds scale gracefully even when the number of
servers grows large and the traffic intensity converges to unity
simultaneously, as in the Halfin-Whitt scaling regime. Some of our bounds scale
better than in certain asymptotic regimes. More precisely,
they scale as multiplied by an inverse polynomial in These results formalize the intuition that bounds should be tighter
in light traffic as well as certain heavy-traffic regimes (e.g. with
fixed and large). In these same asymptotic regimes we also prove bounds for
the tail of the steady-state number in service.
Our main proofs proceed by explicitly analyzing the bounding process which
arises in the stochastic comparison bounds of amarnik and Goldberg for
multi-server queues. Along the way we derive several novel results for suprema
of random walks and pooled renewal processes which may be of independent
interest. We also prove several additional bounds using drift arguments (which
have much smaller pre-factors), and make several conjectures which would imply
further related bounds and generalizations
Large deviations analysis for the queue in the Halfin-Whitt regime
We consider the FCFS queue in the Halfin-Whitt heavy traffic
regime. It is known that the normalized sequence of steady-state queue length
distributions is tight and converges weakly to a limiting random variable W.
However, those works only describe W implicitly as the invariant measure of a
complicated diffusion. Although it was proven by Gamarnik and Stolyar that the
tail of W is sub-Gaussian, the actual value of was left open. In subsequent work, Dai and He
conjectured an explicit form for this exponent, which was insensitive to the
higher moments of the service distribution.
We explicitly compute the true large deviations exponent for W when the
abandonment rate is less than the minimum service rate, the first such result
for non-Markovian queues with abandonments. Interestingly, our results resolve
the conjecture of Dai and He in the negative. Our main approach is to extend
the stochastic comparison framework of Gamarnik and Goldberg to the setting of
abandonments, requiring several novel and non-trivial contributions. Our
approach sheds light on several novel ways to think about multi-server queues
with abandonments in the Halfin-Whitt regime, which should hold in considerable
generality and provide new tools for analyzing these systems
Consensus Division in an Arbitrary Ratio
We consider the problem of partitioning a line segment into two subsets, so that n finite measures all have the same ratio of values for the subsets. Letting ? ? [0,1] denote the desired ratio, this generalises the PPA-complete consensus-halving problem, in which ? = 1/2. Stromquist and Woodall [Stromquist and Woodall, 1985] showed that for any ?, there exists a solution using 2n cuts of the segment. They also showed that if ? is irrational, that upper bound is almost optimal. In this work, we elaborate the bounds for rational values ?. For ? = ?/k, we show a lower bound of (k-1)/k ? 2n - O(1) cuts; we also obtain almost matching upper bounds for a large subset of rational ?.
On the computational side, we explore its dependence on the number of cuts available. More specifically,
1) when using the minimal number of cuts for each instance is required, the problem is NP-hard for any ?;
2) for a large subset of rational ? = ?/k, when (k-1)/k ? 2n cuts are available, the problem is in PPA-k under Turing reduction;
3) when 2n cuts are allowed, the problem belongs to PPA for any ?; more generally, the problem belong to PPA-p for any prime p if 2(p-1)??p/2?/?p/2? ? n cuts are available
Performance-based control system design automation via evolutionary computing
This paper develops an evolutionary algorithm (EA) based methodology for computer-aided control system design (CACSD)
automation in both the time and frequency domains under performance satisfactions. The approach is automated by efficient
evolution from plant step response data, bypassing the system identification or linearization stage as required by conventional
designs. Intelligently guided by the evolutionary optimization, control engineers are able to obtain a near-optimal ‘‘off-thecomputer’’
controller by feeding the developed CACSD system with plant I/O data and customer specifications without the need of
a differentiable performance index. A speedup of near-linear pipelineability is also observed for the EA parallelism implemented on
a network of transputers of Parsytec SuperCluster. Validation results against linear and nonlinear physical plants are convincing,
with good closed-loop performance and robustness in the presence of practical constraints and perturbations
Nonlinear system identification and control using state transition algorithm
By transforming identification and control for nonlinear system into
optimization problems, a novel optimization method named state transition
algorithm (STA) is introduced to solve the problems. In the proposed STA, a
solution to a optimization problem is considered as a state, and the updating
of a solution equates to a state transition, which makes it easy to understand
and convenient to implement. First, the STA is applied to identify the optimal
parameters of the estimated system with previously known structure. With the
accurate estimated model, an off-line PID controller is then designed optimally
by using the STA as well. Experimental results have demonstrated the validity
of the methodology, and comparisons to STA with other optimization algorithms
have testified that STA is a promising alternative method for system
identification and control due to its stronger search ability, faster
convergence rate and more stable performance.Comment: 20 pages, 18 figure
Generalizing Minimal Supergravity
In Grand Unified Theories (GUTs), the Standard Model (SM) gauge couplings
need not be unified at the GUT scale due to the high-dimensional operators.
Considering gravity mediated supersymmetry breaking, we study for the first
time the generic gauge coupling relations at the GUT scale, and the general
gaugino mass relations which are valid from the GUT scale to the electroweak
scale at one loop. We define the index k for these relations, which can be
calculated in GUTs and can be determined at the Large Hadron Collider and the
future International Linear Collider. Thus, we give a concrete definition of
the GUT scale in these theories, and suggest a new way to test general GUTs at
future experiments. We also discuss five special scenarios with interesting
possibilities. With our generic formulae, we present all the GUT-scale gauge
coupling relations and all the gaugino mass relations in the SU(5) and SO(10)
models, and calculate the corresponding indices k. Especially, the index k is
5/3 in the traditional SU(5) and SO(10) models that have been studied
extensively so far. Furthermore, we discuss the field theory realization of the
U(1) flux effects on the SM gauge kinetic functions in F-theory GUTs, and
calculate their indices k as well.Comment: RevTex4, 14 pages, 4 tables, references added, version in PL
Is ChatGPT a game changer for geocoding -- a benchmark for geocoding address parsing techniques
The remarkable success of GPT models across various tasks, including toponymy
recognition motivates us to assess the performance of the GPT-3 model in the
geocoding address parsing task. To ensure that the evaluation more accurately
mirrors performance in real-world scenarios with diverse user input qualities
and resolve the pressing need for a 'gold standard' evaluation dataset for
geocoding systems, we introduce a benchmark dataset of low-quality address
descriptions synthesized based on human input patterns mining from actual input
logs of a geocoding system in production. This dataset has 21 different input
errors and variations; contains over 239,000 address records that are uniquely
selected from streets across all U.S. 50 states and D.C.; and consists of three
subsets to be used as training, validation, and testing sets. Building on this,
we train and gauge the performance of the GPT-3 model in extracting address
components, contrasting its performance with transformer-based and LSTM-based
models. The evaluation results indicate that Bidirectional LSTM-CRF model has
achieved the best performance over these transformer-based models and GPT-3
model. Transformer-based models demonstrate very comparable results compared to
the Bidirectional LSTM-CRF model. The GPT-3 model, though trailing in
performance, showcases potential in the address parsing task with few-shot
examples, exhibiting room for improvement with additional fine-tuning. We open
source the code and data of this presented benchmark so that researchers can
utilize it for future model development or extend it to evaluate similar tasks,
such as document geocoding
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