scholarly journals Asymptotic optimality of a greedy randomized algorithm in a large-scale service system with general packing constraints

2014 ◽  
Vol 79 (2) ◽  
pp. 117-143 ◽  
Author(s):  
Alexander L. Stolyar ◽  
Yuan Zhong
Keyword(s):  
Large Scale ◽  
Service System ◽  
Asymptotic Optimality ◽  
Randomized Algorithm

scholarly journals A Service System with Packing Constraints: Greedy Randomized Algorithm Achieving Sublinear in Scale Optimality Gap

2021 ◽  
Author(s):  
Alexander L. Stolyar ◽  
Yuan Zhong
Keyword(s):  
Steady State ◽  
Service System ◽  
Asymptotic Optimality ◽  
Randomized Algorithm ◽  
Service Time Distribution ◽  
Fixed Parameter ◽  
Customer Type ◽  
Basic Objective ◽  
Optimality Gap ◽  
Number Of Customers

A service system with multiple types of arriving customers is considered. There is an infinite number of homogeneous servers. Multiple customers can be placed for simultaneous service into one server, subject to general packing constraints. The service times of different customers are independent even if they are served simultaneously by the same server; the service time distribution depends on the customer type. Each new arriving customer is placed for service immediately into either an occupied server, that is, one already serving other customers, as long as packing constraints are not violated or into an empty server. After service completion, each customer leaves its server and the system. The basic objective is to minimize the number of occupied servers in steady state. We study a greedy random (GRAND) placement (packing) algorithm, introduced in our previous work. This is a simple online algorithm that places each arriving customer uniformly at random into either one of the already occupied servers that can still fit the customer or one of the so-called zero servers, which are empty servers designated to be available to new arrivals. In our previous work, a version of the algorithm, labeled GRAND(aZ), is considered, in which the number of zero servers is aZ with Z being the current total number of customers in the system and positive a being an algorithm parameter. GRAND(aZ) is shown in our previous work to be asymptotically optimal in the following sense: (a) the steady-state optimality gap grows linearly in the system scale r (the mean total number of customers in service), that is, as c(a)r for some positive c(a), and (b) c(a) vanishes as a goes to zero. In this paper, we consider the GRAND(Zp) algorithm, in which the number of zero servers is Zp, where p < 1 is a fixed parameter, sufficiently close to 1. We prove the asymptotic optimality of GRAND(Zp) in the sense that the steady-state optimality gap is sublinear in the system scale r. This is a stronger form of asymptotic optimality than that of GRAND(aZ).

scholarly journals A large-scale service system with packing constraints

2013 ◽  
Vol 41 (1) ◽  
pp. 41-52 ◽  
Author(s):  
Alexander L. Stolyar ◽  
Yuan Zhong
Keyword(s):  
Large Scale ◽  
Service System

Online peak-aware energy scheduling with untrusted advice

2021 ◽  
Vol 1 (1) ◽  
pp. 59-77
Author(s):  
Russell Lee ◽  
Jessica Maghakian ◽  
Mohammad Hajiesmaili ◽  
Jian Li ◽  
Ramesh Sitaraman ◽  
...  
Keyword(s):  
Competitive Ratio ◽  
Energy Demand ◽  
Large Scale ◽  
Performance Metrics ◽  
Randomized Algorithm ◽  
Deterministic Algorithm ◽  
Pareto Optimal ◽  
Energy Prices ◽  
Worst Case ◽  
Cost Of Energy

This paper studies the online energy scheduling problem in a hybrid model where the cost of energy is proportional to both the volume and peak usage, and where energy can be either locally generated or drawn from the grid. Inspired by recent advances in online algorithms with Machine Learned (ML) advice, we develop parameterized deterministic and randomized algorithms for this problem such that the level of reliance on the advice can be adjusted by a trust parameter. We then analyze the performance of the proposed algorithms using two performance metrics: robustness that measures the competitive ratio as a function of the trust parameter when the advice is inaccurate, and consistency for competitive ratio when the advice is accurate. Since the competitive ratio is analyzed in two different regimes, we further investigate the Pareto optimality of the proposed algorithms. Our results show that the proposed deterministic algorithm is Pareto-optimal, in the sense that no other online deterministic algorithms can dominate the robustness and consistency of our algorithm. Furthermore, we show that the proposed randomized algorithm dominates the Pareto-optimal deterministic algorithm. Our large-scale empirical evaluations using real traces of energy demand, energy prices, and renewable energy generations highlight that the proposed algorithms outperform worst-case optimized algorithms and fully data-driven algorithms.

Rescue Work and Progress of Analog Seismograms in China

2020 ◽  
Vol 91 (5) ◽  
pp. 2704-2718
Author(s):  
Xuchao Chai ◽  
Qingliang Wang ◽  
Leiyu Mu ◽  
Honglei Wang ◽  
Wenqing Wang ◽  
...  
Keyword(s):  
Large Scale ◽  
Service System ◽  
Distributed Database ◽  
Future Prospects ◽  
Seismic Record ◽  
Rescue Work ◽  
Survey Statistics ◽  
Seismic Records ◽  
China Earthquake ◽  
Funding Support

Abstract Rescue work involving scanning and digitization research on historical analog seismograms nationwide in China was launched in 2017. A series of results have been accomplished. There are more than 13 million analog seismic records existing in China, and about 3 million of them were scanned by December 2019. The Second Monitoring and Application Center of China Earthquake Administration completed the phased construction of the “China Analog Seismic Record Rescue Project” in 2019, which has received a great deal of funding support. Most of the analog seismograms and geophysical records in China will be scanned in the following decade, the corresponding stations and instrument parameters will be also collected during this project to provide retrieval and download service. This article first introduces the survey statistics about scanning and digitalization progress of analog seismic records in China. Second, a management and service system for the storage and query of large scale of seismograms has been established based on distributed database and search engine. Finally, future prospects of the rescue work of analog seismograms are mentioned.

scholarly journals Diffusion-Scale Tightness of Invariant Distributions of a Large-Scale Flexible Service System

2015 ◽  
Vol 47 (01) ◽  
pp. 251-269 ◽  
Author(s):  
A. L. Stolyar
Keyword(s):  
Diffusion Process ◽  
Service Time ◽  
Large Scale ◽  
Service System ◽  
Arrival Rate ◽  
Asymptotic Regime ◽  
Invariant Distributions ◽  
Multiple Customer Classes ◽  
The Mean ◽  
Diffusion Scale

A large-scale service system with multiple customer classes and multiple server pools is considered, with the mean service time depending both on the customer class and server pool. The allowed activities (routeing choices) form a tree (in the graph with vertices being both customer classes and server pools). We study the behavior of the system under a leaf activity priority (LAP) policy, introduced by Stolyar and Yudovina (2012). An asymptotic regime is considered, where the arrival rate of customers and number of servers in each pool tend to ∞ in proportion to a scaling parameter r, while the overall system load remains strictly subcritical. We prove tightness of diffusion-scaled (centered at the equilibrium point and scaled down by r −1/2) invariant distributions. As a consequence, we obtain a limit interchange result: the limit of diffusion-scaled invariant distributions is equal to the invariant distribution of the limiting diffusion process.

scholarly journals Diffusion-Scale Tightness of Invariant Distributions of a Large-Scale Flexible Service System

2015 ◽  
Vol 47 (1) ◽  
pp. 251-269 ◽  
Author(s):  
A. L. Stolyar
Keyword(s):  
Diffusion Process ◽  
Service Time ◽  
Large Scale ◽  
Service System ◽  
Arrival Rate ◽  
Asymptotic Regime ◽  
Invariant Distributions ◽  
Multiple Customer Classes ◽  
The Mean ◽  
Diffusion Scale

A large-scale service system with multiple customer classes and multiple server pools is considered, with the mean service time depending both on the customer class and server pool. The allowed activities (routeing choices) form a tree (in the graph with vertices being both customer classes and server pools). We study the behavior of the system under a leaf activity priority (LAP) policy, introduced by Stolyar and Yudovina (2012). An asymptotic regime is considered, where the arrival rate of customers and number of servers in each pool tend to ∞ in proportion to a scaling parameter r, while the overall system load remains strictly subcritical. We prove tightness of diffusion-scaled (centered at the equilibrium point and scaled down by r−1/2) invariant distributions. As a consequence, we obtain a limit interchange result: the limit of diffusion-scaled invariant distributions is equal to the invariant distribution of the limiting diffusion process.

scholarly journals Asymptotic Optimality of Power-of-d Load Balancing in Large-Scale Systems

2020 ◽  
Vol 45 (4) ◽  
pp. 1535-1571 ◽  
Author(s):  
Debankur Mukherjee ◽  
Sem C. Borst ◽  
Johan S. H. van Leeuwaarden ◽  
Philip A. Whiting
Keyword(s):  
Large Scale ◽  
Asymptotic Optimality ◽  
Diffusion Limit ◽  
Fluid Limit ◽  
Large Scale Systems ◽  
Minimum Number ◽  
Join The Shortest Queue ◽  
The Difference ◽  
Shortest Queue ◽  
And Diffusion

We consider a system of N identical server pools and a single dispatcher in which tasks with unit-exponential service requirements arrive at rate [Formula: see text]. In order to optimize the experienced performance, the dispatcher aims to evenly distribute the tasks across the various server pools. Specifically, when a task arrives, the dispatcher assigns it to the server pool with the minimum number of tasks among d(N) randomly selected server pools. We construct a stochastic coupling to bound the difference in the system occupancy processes between the join-the-shortest-queue (JSQ) policy and a scheme with an arbitrary value of d(N). We use the coupling to derive the fluid limit in case [Formula: see text] and [Formula: see text] as [Formula: see text] along with the associated fixed point. The fluid limit turns out to be insensitive to the exact growth rate of d(N) and coincides with that for the JSQ policy. We further establish that the diffusion limit corresponds to that for the JSQ policy as well, as long as [Formula: see text], and characterize the common limiting diffusion process. These results indicate that the JSQ optimality can be preserved at the fluid and diffusion levels while reducing the overhead by nearly a factor O(N) and O([Formula: see text]), respectively.

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