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 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.

Stability condition for a single-server retrial queue

1993 ◽  
Vol 25 (03) ◽  
pp. 690-701 ◽  
Author(s):  
Huei-Mei Liang ◽  
V. G. Kulkarni
Keyword(s):  
Stability Condition ◽  
Service Time ◽  
Retrial Queue ◽  
Arrival Rate ◽  
Retrial Queues ◽  
Single Server ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
The Mean ◽  
The Stability

A single-server retrial queue consists of a primary queue, an orbit and a single server. Assume the primary queue capacity is 1 and the orbit capacity is infinite. Customers can arrive at the primary queue either from outside the system or from the orbit. If the server is busy, the arriving customer joins the orbit and conducts a retrial later. Otherwise, he receives service and leaves the system. We investigate the stability condition for a single-server retrial queue. Let λ be the arrival rate and 1/μ be the mean service time. It has been proved that λ / μ < 1 is a sufficient stability condition for the M/G /1/1 retrial queue with exponential retrial times. We give a counterexample to show that this stability condition is not valid for general single-server retrial queues. Next we show that λ /μ < 1 is a sufficient stability condition for the stability of a single-server retrial queue when the interarrival times and retrial times are finite mixtures of Erlangs.

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.

Stability condition for a single-server retrial queue

1993 ◽  
Vol 25 (3) ◽  
pp. 690-701 ◽  
Author(s):  
Huei-Mei Liang ◽  
V. G. Kulkarni
Keyword(s):  
Stability Condition ◽  
Service Time ◽  
Retrial Queue ◽  
Arrival Rate ◽  
Retrial Queues ◽  
Single Server ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
The Mean ◽  
The Stability

A single-server retrial queue consists of a primary queue, an orbit and a single server. Assume the primary queue capacity is 1 and the orbit capacity is infinite. Customers can arrive at the primary queue either from outside the system or from the orbit. If the server is busy, the arriving customer joins the orbit and conducts a retrial later. Otherwise, he receives service and leaves the system.We investigate the stability condition for a single-server retrial queue. Let λ be the arrival rate and 1/μ be the mean service time. It has been proved that λ/μ < 1 is a sufficient stability condition for the M/G/1/1 retrial queue with exponential retrial times. We give a counterexample to show that this stability condition is not valid for general single-server retrial queues. Next we show that λ /μ < 1 is a sufficient stability condition for the stability of a single-server retrial queue when the interarrival times and retrial times are finite mixtures of Erlangs.

scholarly journals A BIOLOGICALLY INSPIRED FLUID MODEL OF THE CYCLIC SERVICE SYSTEM

2020 ◽  
Vol 25 (4) ◽  
pp. 505-521
Author(s):  
Aliya Kantarbayeva ◽  
Almaz Mustafin
Keyword(s):  
Service System ◽  
Fluid Model ◽  
Arrival Rate ◽  
Random Order ◽  
Biologically Inspired ◽  
Queue Discipline ◽  
Cyclic Service ◽  
The Mean ◽  
Multichannel Service ◽  
Enzyme Molecules

A deterministic fluid model in the form of nonlinear ordinary differential equations is developed to provide the description for a multichannel service system with service-in-random-order queue discipline, abandonment and re-entry, where servers are treated like enzyme molecules. The parametric analysis of the model’s fixed point is given, particularly, how the arrival rate of new customers affects the steady-state demand. It is also shown that the model implies a saturating clearing function (yield vs. demand) of the Karmarkar type providing the mean service time is much shorter than the characteristic waiting time.

scholarly journals Peningkatan Pelayanan di Poli Kebidanan dan Kandungan RSUD Saiful Anwar dengan Menggunakan Simulasi Antrian

2010 ◽  
Vol 3 (1) ◽  
pp. 85
Author(s):  
Ilyas Mas'udin
Keyword(s):  
System Design ◽  
Waiting Time ◽  
Service Time ◽  
Service System ◽  
Initial Condition ◽  
Trial And Error ◽  
Time Data ◽  
Service System Design ◽  
Kolmogorov Smirnov ◽  
The Mean

This research have aim to reduce waiting time of patient in pregnant division at RSUD Saiful Anwar Malang. First step, collecting the time between arrival data and service time data at each division. These data were tested using Kolmogorov-Smirnov to find a kind of distribution and the parameter of the data. Them making service system design based on the initial condition using ARENA and run to find the mean of waiting time from the beginning design, using trial and error then tried some new altematives design to minimize waiting time.

scholarly journals Quality Control in 3D Printing: Accuracy Analysis of 3D-Printed Models of Patient-Specific Anatomy

Materials ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1021
Author(s):  
Bernhard Dorweiler ◽  
Pia Elisabeth Baqué ◽  
Rayan Chaban ◽  
Ahmed Ghazy ◽  
Oroa Salem
Keyword(s):  
Wall Thickness ◽  
Large Scale ◽  
Fused Deposition Modeling ◽  
Vascular Anatomy ◽  
3D Models ◽  
Patient Specific ◽  
Stl File ◽  
Fused Deposition ◽  
3D Printed ◽  
The Mean

As comparative data on the precision of 3D-printed anatomical models are sparse, the aim of this study was to evaluate the accuracy of 3D-printed models of vascular anatomy generated by two commonly used printing technologies. Thirty-five 3D models of large (aortic, wall thickness of 2 mm, n = 30) and small (coronary, wall thickness of 1.25 mm, n = 5) vessels printed with fused deposition modeling (FDM) (rigid, n = 20) and PolyJet (flexible, n = 15) technology were subjected to high-resolution CT scans. From the resulting DICOM (Digital Imaging and Communications in Medicine) dataset, an STL file was generated and wall thickness as well as surface congruency were compared with the original STL file using dedicated 3D engineering software. The mean wall thickness for the large-scale aortic models was 2.11 µm (+5%), and 1.26 µm (+0.8%) for the coronary models, resulting in an overall mean wall thickness of +5% for all 35 3D models when compared to the original STL file. The mean surface deviation was found to be +120 µm for all models, with +100 µm for the aortic and +180 µm for the coronary 3D models, respectively. Both printing technologies were found to conform with the currently set standards of accuracy (<1 mm), demonstrating that accurate 3D models of large and small vessel anatomy can be generated by both FDM and PolyJet printing technology using rigid and flexible polymers.

scholarly journals Relationship between large-scale ionospheric field-aligned currents and electron/ion precipitations: DMSP observations

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Chao Xiong ◽  
Claudia Stolle ◽  
Patrick Alken ◽  
Jan Rauberg
Keyword(s):  
Time Distribution ◽  
Large Scale ◽  
Particle Flux ◽  
Particle Energy ◽  
Lower Latitude ◽  
Particle Precipitation ◽  
Data Set ◽  
The Mean ◽  
Two Parameters ◽  
Meteorological Satellite

Abstract In this study, we have derived field-aligned currents (FACs) from magnetometers onboard the Defense Meteorological Satellite Project (DMSP) satellites. The magnetic latitude versus local time distribution of FACs from DMSP shows comparable dependences with previous findings on the intensity and orientation of interplanetary magnetic field (IMF) By and Bz components, which confirms the reliability of DMSP FAC data set. With simultaneous measurements of precipitating particles from DMSP, we further investigate the relation between large-scale FACs and precipitating particles. Our result shows that precipitation electron and ion fluxes both increase in magnitude and extend to lower latitude for enhanced southward IMF Bz, which is similar to the behavior of FACs. Under weak northward and southward Bz conditions, the locations of the R2 current maxima, at both dusk and dawn sides and in both hemispheres, are found to be close to the maxima of the particle energy fluxes; while for the same IMF conditions, R1 currents are displaced further to the respective particle flux peaks. Largest displacement (about 3.5°) is found between the downward R1 current and ion flux peak at the dawn side. Our results suggest that there exists systematic differences in locations of electron/ion precipitation and large-scale upward/downward FACs. As outlined by the statistical mean of these two parameters, the FAC peaks enclose the particle energy flux peaks in an auroral band at both dusk and dawn sides. Our comparisons also found that particle precipitation at dawn and dusk and in both hemispheres maximizes near the mean R2 current peaks. The particle precipitation flux maxima closer to the R1 current peaks are lower in magnitude. This is opposite to the known feature that R1 currents are on average stronger than R2 currents.

scholarly journals Improved Visual Localization via Graph Filtering

2021 ◽  
Vol 7 (2) ◽  
pp. 20
Author(s):  
Carlos Lassance ◽  
Yasir Latif ◽  
Ravi Garg ◽  
Vincent Gripon ◽  
Ian Reid
Keyword(s):  
Image Retrieval ◽  
Large Scale ◽  
Visual Localization ◽  
Localization Accuracy ◽  
Additional Information ◽  
Feature Representations ◽  
The Mean ◽  
Classical Image ◽  
Vision Based Localization ◽  
Improve Reliability

Vision-based localization is the problem of inferring the pose of the camera given a single image. One commonly used approach relies on image retrieval where the query input is compared against a database of localized support examples and its pose is inferred with the help of the retrieved items. This assumes that images taken from the same places consist of the same landmarks and thus would have similar feature representations. These representations can learn to be robust to different variations in capture conditions like time of the day or weather. In this work, we introduce a framework which aims at enhancing the performance of such retrieval-based localization methods. It consists in taking into account additional information available, such as GPS coordinates or temporal proximity in the acquisition of the images. More precisely, our method consists in constructing a graph based on this additional information that is later used to improve reliability of the retrieval process by filtering the feature representations of support and/or query images. We show that the proposed method is able to significantly improve the localization accuracy on two large scale datasets, as well as the mean average precision in classical image retrieval scenarios.

Sign in / Sign up

Export Citation Format

Share Document