1,164 research outputs found
Symmetric groups and conjugacy classes
Let S_n be the symmetric group on n-letters. Fix n>5. Given any nontrivial
, we prove that the product of
the conjugacy classes and is never a conjugacy
class. Furthermore, if n is not even and is not a multiple of three, then
is the union of at least three distinct conjugacy
classes. We also describe the elements in the case when
is the union of exactly two distinct conjugacy
classes.Comment: 7 page
A Lindley-type equation arising from a carousel problem
In this paper we consider a system with two carousels operated by one picker.
The items to be picked are randomly located on the carousels and the pick times
follow a phase-type distribution. The picker alternates between the two
carousels, picking one item at a time. Important performance characteristics
are the waiting time of the picker and the throughput of the two carousels. The
waiting time of the picker satisfies an equation very similar to Lindley's
equation for the waiting time in the PH/U/1 queue. Although the latter equation
has no simple solution, we show that the one for the waiting time of the picker
can be solved explicitly. Furthermore, it is well known that the mean waiting
time in the PH/U/1 queue depends on to the complete interarrival time
distribution, but numerical results show that, for the carousel system, the
mean waiting time and throughput are rather insensitive to the pick-time
distribution.Comment: 10 pages, 1 figure, 19 reference
Approximate performance analysis of generalized join the shortest queue routing
In this paper we propose a highly accurate approximate performance analysis
of a heterogeneous server system with a processor sharing service discipline
and a general job-size distribution under a generalized join the shortest queue
(GJSQ) routing protocol. The GJSQ routing protocol is a natural extension of
the well-known join the shortest queue routing policy that takes into account
the non-identical service rates in addition to the number of jobs at each
server. The performance metrics that are of interest here are the equilibrium
distribution and the mean and standard deviation of the number of jobs at each
server. We show that the latter metrics are near-insensitive to the job-size
distribution using simulation experiments. By applying a single queue
approximation we model each server as a single server queue with a
state-dependent arrival process, independent of other servers in the system,
and derive the distribution of the number of jobs at the server. These
state-dependent arrival rates are intended to capture the inherent correlation
between servers in the original system and behave in a rather atypical way.Comment: 16 pages, 5 figures -- version 2 incorporates minor textual change
Analytic properties of two-carousel systems
We present analytic results for warehouse systems involving pairs of
carousels. Specifically, for various picking strategies, we show that the
sojourn time of the picker satisfies an integral equation that is a contraction
mapping. As a result, numerical approximations for performance measures such as
the throughput of the system are extremely accurate and converge fast (e.g.\
within 5 iterations) to their real values. We present simulation results
validating our results and examining more complicated strategies for pairs of
carousels.Comment: 28 pages, 17 figure
On the accuracy of phase-type approximations of heavy-tailed risk models
Numerical evaluation of ruin probabilities in the classical risk model is an
important problem. If claim sizes are heavy-tailed, then such evaluations are
challenging. To overcome this, an attractive way is to approximate the claim
sizes with a phase-type distribution. What is not clear though is how many
phases are enough in order to achieve a specific accuracy in the approximation
of the ruin probability. The goals of this paper are to investigate the number
of phases required so that we can achieve a pre-specified accuracy for the ruin
probability and to provide error bounds. Also, in the special case of a
completely monotone claim size distribution we develop an algorithm to estimate
the ruin probability by approximating the excess claim size distribution with a
hyperexponential one. Finally, we compare our approximation with the heavy
traffic and heavy tail approximations.Comment: 24 pages, 13 figures, 8 tables, 38 reference
Corrected phase-type approximations of heavy-tailed queueing models in a Markovian environment
Significant correlations between arrivals of load-generating events make the
numerical evaluation of the workload of a system a challenging problem. In this
paper, we construct highly accurate approximations of the workload distribution
of the MAP/G/1 queue that capture the tail behavior of the exact workload
distribution and provide a bounded relative error. Motivated by statistical
analysis, we consider the service times as a mixture of a phase-type and a
heavy-tailed distribution. With the aid of perturbation analysis, we derive our
approximations as a sum of the workload distribution of the MAP/PH/1 queue and
a heavy-tailed component that depends on the perturbation parameter. We refer
to our approximations as corrected phase-type approximations, and we exhibit
their performance with a numerical study.Comment: Received the Marcel Neuts Student Paper Award at the 8th
International Conference on Matrix Analytic Methods in Stochastic Models 201
Do energy efficiency measures really reduce household energy consumption? A difference-in-difference analysis
This study investigates the impact of energy efficiency measures installed through the Carbon Emission Reduction Target (CERT) and the Community Energy Saving Programme (CESP) on domestic gas and total energy consumptions. The recently released National Energy Efficiency Data-Framework (NEED) database is used to examine the changes in domestic gas and total energy consumptions for the dwellings in the sample relative to the changes in gas and total energy consumptions for a comparable control group in the year after installation. The results obtained from this difference-in-difference analysis confirm that observed energy consumption decreases significantly in dwellings following upgrades such as cavity wall insulation, loft insulation and a new efficient boiler. The single most effective energy efficiency measure when installed alone is found to be cavity wall insulation, reducing annual gas consumption by 10.5 % and annual total energy consumption by 8.0 % in the year following installation. Comparing bundles of different energy efficiency measures, we find that dwellings retrofitted with both cavity wall insulation and a new efficient boiler experience the largest reductions in annual gas and total energy consumptions of 13.3 and 13.5 %, respectively. This is followed by a mean annual reduction of 11.9 and 10.5 % in gas and total energy consumptions for dwellings with all three energy efficiency measures installed in the same year. Contrary to expectations, installing cavity wall insulation on its own is found to be more effective in reducing measured energy consumption than combining loft insulation and a new efficient boiler.This is the final version of the article. It was first available from Springer via http://dx.doi.org/10.1007/s12053-015-9418-
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