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 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.

scholarly journals Mean Waiting Time in Large-Scale and Critically Loaded Power of d Load Balancing Systems

2021 ◽  
Vol 5 (2) ◽  
pp. 1-34
Author(s):  
Tim Hellemans ◽  
Benny Van Houdt
Keyword(s):  
Load Balancing ◽  
Waiting Time ◽  
Large Scale ◽  
Mean Field ◽  
Arrival Rate ◽  
Mean Field Limit ◽  
Mean Waiting Time ◽  
Constant Rate ◽  
Finite Set ◽  
The Mean

Mean field models are a popular tool used to analyse load balancing policies. In some exceptional cases the waiting time distribution of the mean field limit has an explicit form. In other cases it can be computed as the solution of a set of differential equations. In this paper we study the limit of the mean waiting time E[Wλ] as the arrival rate λ approaches 1 for a number of load balancing policies in a large-scale system of homogeneous servers which finish work at a constant rate equal to one and exponential job sizes with mean 1 (i.e. when the system gets close to instability). As E[Wλ] diverges to infinity, we scale with -log(1-λ) and present a method to compute the limit limλ-> 1- -E[Wλ]/l(1-λ). We show that this limit has a surprisingly simple form for the load balancing algorithms considered. More specifically, we present a general result that holds for any policy for which the associated differential equation satisfies a list of assumptions. For the well-known LL(d) policy which assigns an incoming job to a server with the least work left among d randomly selected servers these assumptions are trivially verified. For this policy we prove the limit is given by 1/d-1. We further show that the LL(d,K) policy, which assigns batches of K jobs to the K least loaded servers among d randomly selected servers, satisfies the assumptions and the limit is equal to K/d-K. For a policy which applies LL(di) with probability pi, we show that the limit is given by 1/ ∑i pi di - 1. We further indicate that our main result can also be used for load balancers with redundancy or memory. In addition, we propose an alternate scaling -l(pλ) instead of -l(1-λ), where pλ is adapted to the policy at hand, such that limλ-> 1- -E[Wλ]/l(1-λ)=limλ-> 1- -E[Wλ]/l(pλ), where the limit limλ-> 0+ -E[Wλ]/l(pλ) is well defined and non-zero (contrary to limλ-> 0+ -E[Wλ]/l(1-λ)). This allows to obtain relatively flat curves for -E[Wλ]/l(pλ) for λ ∈ [0,1] which indicates that the low and high load limits can be used as an approximation when λ is close to one or zero. Our results rely on the earlier proven ansatz which asserts that for certain load balancing policies the workload distribution of any finite set of queues becomes independent of one another as the number of servers tends to infinity.

scholarly journals Finite-temperature critical behavior of long-range quantum Ising models

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Eduardo Gonzalez Lazo ◽  
Markus Heyl ◽  
Marcello Dalmonte ◽  
Adriano Angelone
Keyword(s):  
Long Range ◽  
Critical Exponents ◽  
Ground State ◽  
Large Scale ◽  
Mean Field ◽  
Universality Class ◽  
Ising Models ◽  
Ferromagnetic Phase ◽  
Nonzero Temperature ◽  
Mean Field Limit

We study the phase diagram and critical properties of quantum Ising chains with long-range ferromagnetic interactions decaying in a power-law fashion with exponent \alphaα, in regimes of direct interest for current trapped ion experiments. Using large-scale path integral Monte Carlo simulations, we investigate both the ground-state and the nonzero-temperature regimes. We identify the phase boundary of the ferromagnetic phase and obtain accurate estimates for the ferromagnetic-paramagnetic transition temperatures. We further determine the critical exponents of the respective transitions. Our results are in agreement with existing predictions for interaction exponents \alpha<1α>1 up to small deviations in some critical exponents. We also address the elusive regime \alpha < 1α<1, where we find that the universality class of both the ground-state and nonzero-temperature transition is consistent with the mean-field limit at \alpha = 0α=0. Our work not only contributes to the understanding of the equilibrium properties of long-range interacting quantum Ising models, but can also be important for addressing fundamental dynamical aspects, such as issues concerning the open question of thermalization in such models.

scholarly journals Public Awareness: What Climate Change Scientists Should Consider

2020 ◽  
Vol 12 (20) ◽  
pp. 8369
Author(s):  
Mohammad Rahimi
Keyword(s):  
Climate Change ◽  
Social Media ◽  
Large Scale ◽  
Public Awareness ◽  
Connected Network ◽  
Multi Scale ◽  
Valuable Addition ◽  
Scientific Approach ◽  
Design Solutions ◽  
Mitigate Climate Change

In this Opinion, the importance of public awareness to design solutions to mitigate climate change issues is highlighted. A large-scale acknowledgment of the climate change consequences has great potential to build social momentum. Momentum, in turn, builds motivation and demand, which can be leveraged to develop a multi-scale strategy to tackle the issue. The pursuit of public awareness is a valuable addition to the scientific approach to addressing climate change issues. The Opinion is concluded by providing strategies on how to effectively raise public awareness on climate change-related topics through an integrated, well-connected network of mavens (e.g., scientists) and connectors (e.g., social media influencers).

Efficient Schedule of Energy-Constrained UAV Using Crowdsourced Buses in Last-Mile Parcel Delivery

2021 ◽  
Vol 5 (1) ◽  
pp. 1-23
Author(s):  
Yan Pan ◽  
Shining Li ◽  
Qianwu Chen ◽  
Nan Zhang ◽  
Tao Cheng ◽  
...  
Keyword(s):  
Traffic Congestion ◽  
Large Scale ◽  
Load Capacity ◽  
Scheduling Algorithm ◽  
Cost Effective ◽  
Promising Alternative ◽  
Logistics Industry ◽  
Last Mile ◽  
Delivery Scheduling ◽  
Schedule Approach

Stimulated by the dramatical service demand in the logistics industry, logistics trucks employed in last-mile parcel delivery bring critical public concerns, such as heavy cost burden, traffic congestion and air pollution. Unmanned Aerial Vehicles (UAVs) are a promising alternative tool in last-mile delivery, which is however limited by insufficient flight range and load capacity. This paper presents an innovative energy-limited logistics UAV schedule approach using crowdsourced buses. Specifically, when one UAV delivers a parcel, it first lands on a crowdsourced social bus to parcel destination, gets recharged by the wireless recharger deployed on the bus, and then flies from the bus to the parcel destination. This novel approach not only increases the delivery range and load capacity of battery-limited UAVs, but is also much more cost-effective and environment-friendly than traditional methods. New challenges therefore emerge as the buses with spatiotemporal mobility become the bottleneck during delivery. By landing on buses, an Energy-Neutral Flight Principle and a delivery scheduling algorithm are proposed for the UAVs. Using the Energy-Neutral Flight Principle, each UAV can plan a flying path without depleting energy given buses with uncertain velocities. Besides, the delivery scheduling algorithm optimizes the delivery time and number of delivered parcels given warehouse location, logistics UAVs, parcel locations and buses. Comprehensive evaluations using a large-scale bus dataset demonstrate the superiority of the innovative logistics UAV schedule approach.

scholarly journals Diffusion approximations for randomly arriving expert opinions in a financial market with Gaussian drift

2021 ◽  
Vol 58 (1) ◽  
pp. 197-216 ◽  
Author(s):  
Jörn Sass ◽  
Dorothee Westphal ◽  
Ralf Wunderlich
Keyword(s):  
Stock Returns ◽  
Financial Market ◽  
Discrete Time ◽  
High Frequency ◽  
Utility Maximization ◽  
Limit Theorems ◽  
Approximate Solutions ◽  
Diffusion Approximations ◽  
Expert Opinions ◽  
Arrival Intensity

AbstractThis paper investigates a financial market where stock returns depend on an unobservable Gaussian mean reverting drift process. Information on the drift is obtained from returns and randomly arriving discrete-time expert opinions. Drift estimates are based on Kalman filter techniques. We study the asymptotic behavior of the filter for high-frequency experts with variances that grow linearly with the arrival intensity. The derived limit theorems state that the information provided by discrete-time expert opinions is asymptotically the same as that from observing a certain diffusion process. These diffusion approximations are extremely helpful for deriving simplified approximate solutions of utility maximization problems.

scholarly journals The Microscopic Derivation and Well-Posedness of the Stochastic Keller–Segel Equation

2020 ◽  
Vol 31 (1) ◽  
Author(s):  
Hui Huang ◽  
Jinniao Qiu
Keyword(s):  
Existence Of Solutions ◽  
Particle System ◽  
Mean Field ◽  
Field Limit ◽  
Mean Field Limit ◽  
Unique Existence ◽  
Interacting Particle ◽  
Microscopic Derivation ◽  
The Mean ◽  
Limit Result

AbstractIn this paper, we propose and study a stochastic aggregation–diffusion equation of the Keller–Segel (KS) type for modeling the chemotaxis in dimensions $$d=2,3$$ d = 2 , 3 . Unlike the classical deterministic KS system, which only allows for idiosyncratic noises, the stochastic KS equation is derived from an interacting particle system subject to both idiosyncratic and common noises. Both the unique existence of solutions to the stochastic KS equation and the mean-field limit result are addressed.

scholarly journals A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games

2021 ◽  
Author(s):  
Stefano Almi ◽  
Marco Morandotti ◽  
Francesco Solombrino
Keyword(s):  
Mean Field ◽  
Evolutionary Games ◽  
Type Systems ◽  
Convergence Result ◽  
Performance Criterion ◽  
Mean Field Limit ◽  
Spatially Inhomogeneous ◽  
Convergence Results ◽  
Special Cases ◽  
Lagrangian Scheme

AbstractA multi-step Lagrangian scheme at discrete times is proposed for the approximation of a nonlinear continuity equation arising as a mean-field limit of spatially inhomogeneous evolutionary games, describing the evolution of a system of spatially distributed agents with strategies, or labels, whose payoff depends also on the current position of the agents. The scheme is Lagrangian, as it traces the evolution of position and labels along characteristics, and is a multi-step scheme, as it develops on the following two stages: First, the distribution of strategies or labels is updated according to a best performance criterion, and then, this is used by the agents to evolve their position. A general convergence result is provided in the space of probability measures. In the special cases of replicator-type systems and reversible Markov chains, variants of the scheme, where the explicit step in the evolution of the labels is replaced by an implicit one, are also considered and convergence results are provided.

scholarly journals Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit

2021 ◽  
Vol 240 (1) ◽  
pp. 383-417
Author(s):  
Nikolai Leopold ◽  
David Mitrouskas ◽  
Robert Seiringer
Keyword(s):  
Mean Field ◽  
Einstein Condensate ◽  
Back Reaction ◽  
Many Body ◽  
Field Limit ◽  
Mean Field Limit ◽  
Phonon Field ◽  
Bose Einstein Condensate ◽  
Weakly Couple ◽  
Bose Einstein

AbstractWe consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.

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