6,325 research outputs found
More Analysis of Double Hashing for Balanced Allocations
With double hashing, for a key , one generates two hash values and
, and then uses combinations for
to generate multiple hash values in the range from the initial two.
For balanced allocations, keys are hashed into a hash table where each bucket
can hold multiple keys, and each key is placed in the least loaded of
choices. It has been shown previously that asymptotically the performance of
double hashing and fully random hashing is the same in the balanced allocation
paradigm using fluid limit methods. Here we extend a coupling argument used by
Lueker and Molodowitch to show that double hashing and ideal uniform hashing
are asymptotically equivalent in the setting of open address hash tables to the
balanced allocation setting, providing further insight into this phenomenon. We
also discuss the potential for and bottlenecks limiting the use this approach
for other multiple choice hashing schemes.Comment: 13 pages ; current draft ; will be submitted to conference shortl
Unbalanced Allocations
We consider the unbalanced allocation of balls into bins by a
randomized algorithm using the "power of two choices". For each ball, we select
a set of bins at random, then place the ball in the fullest bin within the set.
Applications of this generic algorithm range from cost minimization to
condensed matter physics. In this paper, we analyze the distribution of the bin
loads produced by this algorithm, considering, for example, largest and
smallest loads, loads of subsets of the bins, and the likelihood of bins having
equal loads
A Matrix-Analytic Solution for Randomized Load Balancing Models with Phase-Type Service Times
In this paper, we provide a matrix-analytic solution for randomized load
balancing models (also known as \emph{supermarket models}) with phase-type (PH)
service times. Generalizing the service times to the phase-type distribution
makes the analysis of the supermarket models more difficult and challenging
than that of the exponential service time case which has been extensively
discussed in the literature. We first describe the supermarket model as a
system of differential vector equations, and provide a doubly exponential
solution to the fixed point of the system of differential vector equations.
Then we analyze the exponential convergence of the current location of the
supermarket model to its fixed point. Finally, we present numerical examples to
illustrate our approach and show its effectiveness in analyzing the randomized
load balancing schemes with non-exponential service requirements.Comment: 24 page
Product Development and International Trade
We develop a multi-country, dynamic general equilibrium model of product innovation and international trade to study the creation of comparative advantage through research and development and the evolution of world trade over tune. In our model, firms must incur resource costs to introduce new products and forward-looking potential producers conduct R&D and enter the product market whenever profit opportunities exist Trade has both intra- industry and inter-industry components, and the different incentives that face agents in different countries for investment and savings decisions give rise to Intertemporal trade. We derive results on the dynamics of trade patterns and trade volume, and on the temporal emergence of multinational corporations
Doubly Exponential Solution for Randomized Load Balancing Models with General Service Times
In this paper, we provide a novel and simple approach to study the
supermarket model with general service times. This approach is based on the
supplementary variable method used in analyzing stochastic models extensively.
We organize an infinite-size system of integral-differential equations by means
of the density dependent jump Markov process, and obtain a close-form solution:
doubly exponential structure, for the fixed point satisfying the system of
nonlinear equations, which is always a key in the study of supermarket models.
The fixed point is decomposited into two groups of information under a product
form: the arrival information and the service information. based on this, we
indicate two important observations: the fixed point for the supermarket model
is different from the tail of stationary queue length distribution for the
ordinary M/G/1 queue, and the doubly exponential solution to the fixed point
can extensively exist even if the service time distribution is heavy-tailed.
Furthermore, we analyze the exponential convergence of the current location of
the supermarket model to its fixed point, and study the Lipschitz condition in
the Kurtz Theorem under general service times. Based on these analysis, one can
gain a new understanding how workload probing can help in load balancing jobs
with general service times such as heavy-tailed service.Comment: 40 pages, 4 figure
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