scholarly journals Matched Queues with Flexible Customers and Impatient Customers

2022 ◽  
Author(s):  
hengli liu
Keyword(s):  
Performance Measures ◽  
Sharing Economy ◽  
System Stability ◽  
Probability Vector ◽  
Impatient Customers ◽  
Employee Recruitment ◽  
System Parameters ◽  
Qbd Process ◽  
Theoretical Results ◽  
Stationary Probability Vector

Abstract This paper studies a double-ended queue with four Poisson inputs and flexible customers, and its stability is guaranteed by customers’ impatient behavior. We show that such a queue can be expressed as a quasi birth-and-death (QBD) process with infinitely many phases. For this purpose, we provide a detailed analysis for the QBD process, including the system stability, the stationary probability vector, the sojourn time, and so forth. Finally, numerical examples are employed to verify the correctness of our theoretical results, and demonstrate how the performance measures of this queue are influenced by key system parameters. We believe that the methodology and results described in this paper can be applied to analyze many practical issues, such as those encountered in sharing economy, organ transplantation, employee recruitment, onlinedating, and so on.

scholarly journals Optimising peak energy reduction in networks of buildings

2021 ◽  
Author(s):  
Anush Poghosyan ◽  
Nick McCullen ◽  
Sukumar Natarajan
Keyword(s):  
Control Systems ◽  
System Stability ◽  
Mitigation Measures ◽  
Optimal Size ◽  
Coordination Networks ◽  
System Parameters ◽  
Electricity System ◽  
Peak Energy ◽  
Building Load ◽  
Theoretical Results

Abstract Buildings are amongst the world's largest energy consumers and simultaneous peaks in demand from networks of buildings can decrease electricity system stability. Current mitigation measures either entail wasteful supply-side over-specification or complex centralised demand-side control. Here, we investigate a new schema for decentralised, self-organising building-to-building load coordination that requires very little information and no direct intervention. We find that the theoretically optimal size for load-coordination networks can be surprisingly small, analogous to other complex systems such as coordination between flocks of birds. The schema outperforms existing techniques, giving substantial peak-reductions as well as being remarkably robust to changes in other system parameters such as the network topology. This not only demonstrates that significant reductions in network peaks are achievable using remarkably simple control systems but also reveals theoretical results and new insights which which will be of great interest to the complexity and network science communities.

On a Markovian queue with weakly correlated interarrival times

1981 ◽  
Vol 18 (01) ◽  
pp. 190-203 ◽  
Author(s):  
Guy Latouche
Keyword(s):  
Time Distribution ◽  
Queueing System ◽  
Interarrival Time ◽  
Probability Vector ◽  
Common Value ◽  
Markovian Queue ◽  
The Stability ◽  
Number Of Customers ◽  
Stationary Probabilities ◽  
Stationary Probability Vector

A queueing system with exponential service and correlated arrivals is analysed. Each interarrival time is exponentially distributed. The parameter of the interarrival time distribution depends on the parameter for the preceding arrival, according to a Markov chain. The parameters of the interarrival time distributions are chosen to be equal to a common value plus a factor ofε, where ε is a small number. Successive arrivals are then weakly correlated. The stability condition is found and it is shown that the system has a stationary probability vector of matrix-geometric form. Furthermore, it is shown that the stationary probabilities for the number of customers in the system, are analytic functions ofε, for sufficiently smallε, and depend more on the variability in the interarrival time distribution, than on the correlations.

THE ALLOCATION OF CUSTOMERS IN A DISCRETE-TIME MULTI-SERVER QUEUEING SYSTEM

2010 ◽  
Vol 27 (06) ◽  
pp. 649-667 ◽  
Author(s):  
WEI SUN ◽  
NAISHUO TIAN ◽  
SHIYONG LI
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Queueing System ◽  
Arrival Rate ◽  
Allocation Problem ◽  
Optimal Outcome ◽  
The Subject ◽  
Multi Server ◽  
Theoretical Results

This paper, analyzes the allocation problem of customers in a discrete-time multi-server queueing system and considers two criteria for routing customers' selections: equilibrium and social optimization. As far as we know, there is no literature concerning the discrete-time multi-server models on the subject of equilibrium behaviors of customers and servers. Comparing the results of customers' distribution at the servers under the two criteria, we show that the servers used in equilibrium are no more than those used in the socially optimal outcome, that is, the individual's decision deviates from the socially preferred one. Furthermore, we also clearly show the mutative trend of several important performance measures for various values of arrival rate numerically to verify the theoretical results.

FREEMAN'S K MODELS AS RESERVOIR COMPUTING ARCHITECTURES

2009 ◽  
Vol 05 (01) ◽  
pp. 265-286
Author(s):  
MUSTAFA C. OZTURK ◽  
JOSE C. PRINCIPE
Keyword(s):  
Computational Models ◽  
Temporal Dynamics ◽  
Temporal Structure ◽  
Reservoir Computing ◽  
Short Term ◽  
System Parameters ◽  
History Of ◽  
Spatio Temporal ◽  
Universal Approximators ◽  
Theoretical Results

Walter Freeman in his classic 1975 book "Mass Activation of the Nervous System" presented a hierarchy of dynamical computational models based on studies and measurements done in real brains, which has been known as the Freeman's K model (FKM). Much more recently, liquid state machine (LSM) and echo state network (ESN) have been proposed as universal approximators in the class of functionals with exponential decaying memory. In this paper, we briefly review these models and show that the restricted K set architecture of KI and KII networks share the same properties of LSM/ESNs and is therefore one more member of the reservoir computing family. In the reservoir computing perspective, the states of the FKM are a representation space that stores in its spatio-temporal dynamics a short-term history of the input patterns. Then at any time, with a simple instantaneous read-out made up of a KI, information related to the input history can be accessed and read out. This work provides two important contributions. First, it emphasizes the need for optimal readouts, and shows how to adaptively design them. Second, it shows that the Freeman model is able to process continuous signals with temporal structure. We will provide theoretical results for the conditions on the system parameters of FKM satisfying the echo state property. Experimental results are presented to illustrate the validity of the proposed approach.

Design-Oriented Analysis of Slow-Scale Bifurcations in Single Phase DC–AC Inverters via Autonomous Transformation Approach

2017 ◽  
Vol 27 (06) ◽  
pp. 1750086 ◽  
Author(s):  
Hao Zhang ◽  
Honghui Ding ◽  
Chuanzhi Yi
Keyword(s):  
Theoretical Analysis ◽  
Circuit Design ◽  
Single Phase ◽  
Underlying Mechanism ◽  
System Stability ◽  
Equivalent Model ◽  
Eigenvalue Sensitivity ◽  
Physical Experiments ◽  
Averaged Model ◽  
Theoretical Results

This paper deals with the design-oriented analysis of slow-scale bifurcations in single phase DC–AC inverters. Since DC–AC inverter belongs to a class of nonautonomous piecewise systems with periodic equilibrium orbits, the original averaged model has to be translated into an equivalent autonomous one via a virtual rotating coordinate transformation in order to simplify the theoretical analysis. Based on the virtual equivalent model, eigenvalue sensitivity is used to estimate the effect of the important parameters on the system stability. Furthermore, theoretical analysis is performed to identify slow-scale bifurcation behaviors by judging in what way the eigenvalue loci of the Jacobian matrix move under the variation of some important parameters. In particular, the underlying mechanism of the slow-scale unstable phenomenon is uncovered and discussed thoroughly. In addition, some behavior boundaries are given in the parameter space, which are suitable for optimizing the circuit design. Finally, physical experiments are performed to verify the above theoretical results.

scholarly journals Heavy-tailed asymptotics of stationary probability vectors of Markov chains of gi/g/1 type

2005 ◽  
Vol 37 (02) ◽  
pp. 482-509 ◽  
Author(s):  
Quan-Lin Li ◽  
Yiqiang Q. Zhao
Keyword(s):  
Transition Matrix ◽  
Stationary Probability ◽  
Probability Vector ◽  
Necessary And Sufficient Condition ◽  
Hopf Equation ◽  
Novel Approach ◽  
Matrix Sequence ◽  
Heavy Tailed ◽  
Necessary And Sufficient ◽  
Stationary Probability Vector

In this paper, we provide a novel approach to studying the heavy-tailed asymptotics of the stationary probability vector of a Markov chain of GI/G/1 type, whose transition matrix is constructed from two matrix sequences referred to as a boundary matrix sequence and a repeating matrix sequence, respectively. We first provide a necessary and sufficient condition under which the stationary probability vector is heavy tailed. Then we derive the long-tailed asymptotics of the R-measure in terms of the RG-factorization of the repeating matrix sequence, and a Wiener-Hopf equation for the boundary matrix sequence. Based on this, we are able to provide a detailed analysis of the subexponential asymptotics of the stationary probability vector.

The disasters queue with working breakdowns and impatient customers

2020 ◽  
Vol 54 (3) ◽  
pp. 815-825
Author(s):  
Mian Zhang ◽  
Shan Gao
Keyword(s):  
Size Distribution ◽  
Performance Measures ◽  
Sojourn Time ◽  
Queue Length ◽  
Slow Rate ◽  
System Size ◽  
Impatient Customers ◽  
Numerical Examples ◽  
The Mean ◽  
Mean Queue Length

We consider the M/M/1 queue with disasters and impatient customers. Disasters only occur when the main server being busy, it not only removes out all present customers from the system, but also breaks the main server down. When the main server is down, it is sent for repair. The substitute server serves the customers at a slow rate(working breakdown service) until the main server is repaired. The customers become impatient due to the working breakdown. The system size distribution is derived. We also obtain the mean queue length of the model and mean sojourn time of a tagged customer. Finally, some performance measures and numerical examples are presented.

Hydrostatic Transmission for Wind Turbines: An Old Concept, New Dynamics

2013 ◽  
Author(s):  
Johannes Schmitz ◽  
Milos Vukovic ◽  
Hubertus Murrenhoff
Keyword(s):  
Wind Turbines ◽  
Mobile Applications ◽  
Test Bench ◽  
System Behavior ◽  
Hydrostatic Transmission ◽  
System Parameters ◽  
Standard Application ◽  
Mobile Machinery ◽  
Drive Systems ◽  
Theoretical Results

Hydrostatic drives are commonly used in mobile machinery. A new application for this technology is the renewable energy sector, especially wind power. Despite using the same basic components the dynamics of these new drive systems are somewhat different compared to those used in mobile applications. In order to design an appropriate control system for a wind turbine it is necessary to understand these differences and how they affect the system. In this paper, the system behavior of a hydrostatic transmission for wind turbines is compared to commonly used hydrostatic drives in mobile machinery. The analysis begins by explaining that the characteristics of the loading acting on a turbine are fundamentally different to the load torque present in a standard application. Using mathematical models of both systems these differences are highlighted and discussed with special reference to how changes in system parameters can affect stability and lead to non-minimum phase behavior. These theoretical results are validated using measurements of a 1 MW hydrostatic transmission installed on a test bench.

Equilibrium and Socially Optimal Balking Strategies in Markovian Queues with Vacations and Sequential Abandonment

2016 ◽  
Vol 33 (05) ◽  
pp. 1650036 ◽  
Author(s):  
Gopinath Panda ◽  
Veena Goswami ◽  
Abhijit Datta Banik
Keyword(s):  
Performance Measures ◽  
Numerical Experiments ◽  
Optimal Strategies ◽  
Cost Structure ◽  
Single Server ◽  
System Parameters ◽  
Optimal Behavior ◽  
Markovian Queue ◽  
Queues With Vacations ◽  
The Individual

In this paper, we consider customers’ equilibrium and socially optimal behavior in a single-server Markovian queue with multiple vacations and sequential abandonments. Upon arrival customers decide for themselves whether to join or balk, based on the level of information available to them. During the server’s vacation, present customers become impatient and decide sequentially whether they will abandon the system or not upon the availability of a secondary transport facility. Assuming the linear reward-cost structure, we analyze the equilibrium balking strategies of customers under four cases: fully and almost observable as well as fully and almost unobservable. In all the above cases, the individual and social optimal strategies are derived. Finally, the dependence of performance measures on system parameters are demonstrated via numerical experiments.

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