Optimal Price and Delay Differentiation in Large-Scale Queueing Systems

2018 ◽  
Vol 64 (5) ◽  
pp. 2427-2444 ◽  
Author(s):  
Costis Maglaras ◽  
John Yao ◽  
Assaf Zeevi
Keyword(s):  
Large Scale ◽  
Queueing Systems ◽  
Optimal Price

scholarly journals Randomized longest-queue-first scheduling for large-scale buffered systems

2015 ◽  
Vol 47 (04) ◽  
pp. 1015-1038 ◽  
Author(s):  
A. B. Dieker ◽  
T. Suk
Keyword(s):  
Limit Theorems ◽  
Large Scale ◽  
Scheduling Algorithm ◽  
Queueing Systems ◽  
Mean Field ◽  
Diffusion Approximations ◽  
Mean Field Limit ◽  
Multi Scale ◽  
Noteworthy Feature ◽  
Longest Queue First

We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling (LQF) algorithm by establishing new mean-field limit theorems as the number of buffers n → ∞. We achieve this by allowing the number of sampled buffers d = d(n) to depend on the number of buffers n, which yields an asymptotic 'decoupling' of the queue length processes. We show through simulation experiments that the resulting approximation is accurate even for moderate values of n and d(n). To the best of the authors' knowledge, this is the first derivation of diffusion approximations for a queueing system in the large-buffer mean-field regime. Another noteworthy feature of our scaling idea is that the randomized LQF algorithm emulates the LQF algorithm, yet is computationally more attractive. The analysis of the system performance as a function of d(n) is facilitated by the multi-scale nature in our limit theorems: the various processes we study have different space scalings. This allows us to show the trade-off between performance and complexity of the randomized LQF scheduling algorithm.

scholarly journals Product-Form Solutions for Integrated Services Packet Networks and Cloud Computing Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Wanyang Dai
Keyword(s):  
Cloud Computing ◽  
Queueing Networks ◽  
Large Scale ◽  
Stochastic Dynamics ◽  
Queueing Systems ◽  
Product Form ◽  
Backbone Networks ◽  
Iterative Solutions ◽  
Computing Centers ◽  
Local Edge

We iteratively derive the product-form solutions of stationary distributions for a type of preemptive priority multiclass queueing networks with multiserver stations. This type of queueing systems can typically be used to model the stochastic dynamics of some large scale backbone networks with multiprocessor shared-memory switches or local (edge) cloud computing centers with parallel-server pools. The queueing networks are Markovian with exponential interarrival and service time distributions. The obtained iterative solutions can be used to conduct performance analysis or as comparison criteria for approximation and simulation studies. Numerical comparisons with existing Brownian approximating model (BAM) related to general interarrival and service times are provided to show the effectiveness of our current designed algorithm and our previous derived BAM. Furthermore, based on the iterative solutions, we can also give some analysis concerning network stability for some cases of these queueing systems, which provides some insight for more general study.

Optimal Wine Pricing for Restaurants

2015 ◽  
Vol 10 (2) ◽  
pp. 204-224 ◽  
Author(s):  
Guillaume Coqueret
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Hedonic Models ◽  
Pricing Models ◽  
Optimal Price ◽  
Optimization Program ◽  
Initial Cost ◽  
Dominant Characteristic ◽  
Jel Classifications

AbstractWe present a simple static way of optimizing the prices of bottles of wine for restaurants with a given cellar. In contrast to classical assortment pricing models, we posit that the cellar (i.e., inventory) is given and is not taken as a variable entering the optimization program. In our model, the optimal price is driven mainly by a rating parameter after the effect of initial cost is removed. This parameter plays the role of a dominant characteristic in hedonic models, even though the levels of stocks may also be determinant when they are very low. We provide a numerical sensitivity analysis of prices to various parameters and study a realistic large-scale example based on two wine lists with 50 bottles each. Finally, several extensions are discussed. (JEL Classifications: C61, L11, L83)

scholarly journals Randomized longest-queue-first scheduling for large-scale buffered systems

2015 ◽  
Vol 47 (4) ◽  
pp. 1015-1038 ◽  
Author(s):  
A. B. Dieker ◽  
T. Suk
Keyword(s):  
Limit Theorems ◽  
Large Scale ◽  
Scheduling Algorithm ◽  
Queueing Systems ◽  
Mean Field ◽  
Diffusion Approximations ◽  
Mean Field Limit ◽  
Multi Scale ◽  
Noteworthy Feature ◽  
Longest Queue First

We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling (LQF) algorithm by establishing new mean-field limit theorems as the number of buffers n → ∞. We achieve this by allowing the number of sampled buffers d = d(n) to depend on the number of buffers n, which yields an asymptotic 'decoupling' of the queue length processes. We show through simulation experiments that the resulting approximation is accurate even for moderate values of n and d(n). To the best of the authors' knowledge, this is the first derivation of diffusion approximations for a queueing system in the large-buffer mean-field regime. Another noteworthy feature of our scaling idea is that the randomized LQF algorithm emulates the LQF algorithm, yet is computationally more attractive. The analysis of the system performance as a function of d(n) is facilitated by the multi-scale nature in our limit theorems: the various processes we study have different space scalings. This allows us to show the trade-off between performance and complexity of the randomized LQF scheduling algorithm.

Some comments about observations and image processing of comet 29P/Schwassmann-Wachmann 1

1999 ◽  
Vol 173 ◽  
pp. 243-248
Author(s):  
D. Kubáček ◽  
A. Galád ◽  
A. Pravda
Keyword(s):  
Image Processing ◽  
Large Scale ◽  
Harvard College ◽  
Oak Ridge ◽  
Large Scale Structures ◽  
Short Period Comet ◽  
Short Period ◽  
Scale Structures ◽  
Harvard College Observatory ◽  
Period Comet

AbstractUnusual short-period comet 29P/Schwassmann-Wachmann 1 inspired many observers to explain its unpredictable outbursts. In this paper large scale structures and features from the inner part of the coma in time periods around outbursts are studied. CCD images were taken at Whipple Observatory, Mt. Hopkins, in 1989 and at Astronomical Observatory, Modra, from 1995 to 1998. Photographic plates of the comet were taken at Harvard College Observatory, Oak Ridge, from 1974 to 1982. The latter were digitized at first to apply the same techniques of image processing for optimizing the visibility of features in the coma during outbursts. Outbursts and coma structures show various shapes.

Evolution of Large-Scale Coronal Structures

1994 ◽  
Vol 144 ◽  
pp. 29-33
Author(s):  
P. Ambrož
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Large Scale ◽  
Coronal Magnetic Field ◽  
Source Surface ◽  
Solar Cycles ◽  
Characteristic Relationship ◽  
The Magnetic Field ◽  
Coronal Structures

AbstractThe large-scale coronal structures observed during the sporadically visible solar eclipses were compared with the numerically extrapolated field-line structures of coronal magnetic field. A characteristic relationship between the observed structures of coronal plasma and the magnetic field line configurations was determined. The long-term evolution of large scale coronal structures inferred from photospheric magnetic observations in the course of 11- and 22-year solar cycles is described.Some known parameters, such as the source surface radius, or coronal rotation rate are discussed and actually interpreted. A relation between the large-scale photospheric magnetic field evolution and the coronal structure rearrangement is demonstrated.

Large-scale Motion of Solar Filaments

2000 ◽  
Vol 179 ◽  
pp. 205-208
Author(s):  
Pavel Ambrož ◽  
Alfred Schroll
Keyword(s):  
Magnetic Flux ◽  
Proper Motion ◽  
Time Scale ◽  
Large Scale ◽  
Accuracy Of Measurements ◽  
Solar Filaments ◽  
General Movement ◽  
Scale Motion ◽  
Velocity Scatter

AbstractPrecise measurements of heliographic position of solar filaments were used for determination of the proper motion of solar filaments on the time-scale of days. The filaments have a tendency to make a shaking or waving of the external structure and to make a general movement of whole filament body, coinciding with the transport of the magnetic flux in the photosphere. The velocity scatter of individual measured points is about one order higher than the accuracy of measurements.

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