scholarly journals Performance Evaluation and Dimensioning of Systems through Kernel Estimation

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
G. M. Gontijo ◽  
G. S. Atuncar ◽  
F. R. B. Cruz ◽  
L. Kerbache
Keyword(s):  
Performance Measures ◽  
Call Center ◽  
Kernel Smoothing ◽  
Blocking Probability ◽  
Queueing Systems ◽  
Real Life ◽  
Kernel Estimation ◽  
Queue Size ◽  
Number Of Customers ◽  
Arrival Pattern

We extend the analysis of queueing systems for real-life situations, where the arrival pattern of customers is unknown. In real systems, we must understand how the choice of a method of estimation influences the configuration of the system. Using kernel smoothing, we evaluate algorithms to estimate performance measures of a system, including the invariant probability distribution of the number of customers in the system, the blocking probability, the average queue size, and the average client queue time. We successfully apply the method to the arrivals to a call center to plan and improve the performance of these important queueing systems.

scholarly journals Neutrosophic Event-Based Queueing Model

2020 ◽  
pp. 48-55
Author(s):  
Mohamed Bisher Zeina ◽  
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Communication Systems ◽  
Queueing Systems ◽  
Real Life ◽  
Main Tool ◽  
Expected Number ◽  
Mean Waiting Time ◽  
Event Based ◽  
Number Of Customers

In this paper we have defined the concept of neutrosophic queueing systems and defined its neutrosophic performance measures. An important application of neutrosophic logic in queueing systems we face in real life were discussed, that is the neutrosophic events accuring times, because of its wide applications in networking and simulating communication systems specialy when probability distribution is not known, and because it’s more realistic to consider and to not ignore the imprecise events times. Event-based table of a neutrosophic queueing system was presented and its neutrosophic performance measures were derived, i.e. neutrosophic mean waiting time in queue, neutrosophic mean waiting time in system, neutrosophic expected number of customers in queue and neutrosophic expected number of customers in system. Neutrosophic Little’s Formulas (NLF) were also defined which is a main tool in queueing systems problems to make it easier finding performance measures from each other.

scholarly journals Upper Bounds on Performance Measures of Heterogeneous Queues

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
F. S. Q. Alves ◽  
H. C. Yehia ◽  
L. A. C. Pedrosa ◽  
F. R. B. Cruz ◽  
Laoucine Kerbache
Keyword(s):  
State Space ◽  
Performance Measures ◽  
Queueing Systems ◽  
Real Life ◽  
Upper Bounds ◽  
The State ◽  
Actual Behavior ◽  
Single Class ◽  
Simple Method

In many real-life queueing systems, the servers are often heterogeneous, namely they work at different rates. This paper provides a simple method to compute tight upper bounds on two important performance measures of single-class heterogeneous multi-server Markovian queueing systems, namely the average number in queue and the average waiting time in queue. This method is based on an expansion of the state space that is followed by an approximate reduction of the state space, only considering the most probable states. In most cases tested, we were able to approximate the actual behavior of the system with smaller errors than those obtained from traditional homogeneous multiserver Markovian queues, as shown by GPSS simulations. In addition, we have correlated the quality of the approximation with the degree of heterogeneity of the system, which was evaluated using its Gini index. Finally, we have shown that the bounds are robust and still useful, even considering quite different allocation strategies. A large number of simulation results show the accuracy of the proposed method that is better than that of classical homogeneous multiserver Markovian formulae in many situations.

Optimal design of a multi-server queueing system with delay information

2016 ◽  
Vol 116 (1) ◽  
pp. 147-169 ◽  
Author(s):  
Miao Yu ◽  
Jun Gong ◽  
Jiafu TANG
Keyword(s):  
Optimal Design ◽  
Performance Measures ◽  
Call Center ◽  
Queueing System ◽  
Call Centers ◽  
Queueing Systems ◽  
Staffing Level ◽  
Content Type ◽  
Multi Server ◽  
Delay Information

Purpose – The purpose of this paper is to provide a framework for the optimal design of queueing systems of call centers with delay information. The main decisions in the design of such systems are the number of servers, the appropriate control to announce delay anticipated. Design/methodology/approach – This paper models a multi-server queueing system as an M/M/S+M queue with customer reactions. Based on customer psychology in waiting experiences, a number of different service-level definitions are structured and the explicit computation of their performance measures is performed. This paper characterizes the level of satisfaction with delay information to modulate customer reactions. Optimality is defined as the number of agents that maximize revenues net of staffing costs. Findings – Numerical studies show that the solutions to optimal design of staffing levels and delay information exhibit interesting differences, especially U-shaped curve for optimal staffing level. Experiments show how call center managers can determine economically optimal anticipated delay and number of servers so that they could control the trade-off between revenue loss and customer satisfaction. Originality/value – Many results that pertain to announcing delay information, customer reactions, and links to satisfaction with delay information have not been established in previous studies, however, this paper analytically characterizes these performance measures for staffing call centers.

scholarly journals A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ekaterina Evdokimova ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Poisson Processes ◽  
Series Expansions ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
State Space Explosion ◽  
Finite Queues ◽  
Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

Tollbooth tandem queues with infinite homogeneous servers

2015 ◽  
Vol 52 (4) ◽  
pp. 941-961 ◽  
Author(s):  
Xiuli Chao ◽  
Qi-Ming He ◽  
Sheldon Ross
Keyword(s):  
Performance Measures ◽  
System Performance ◽  
Stochastic Ordering ◽  
Tandem Queues ◽  
Poisson Arrival ◽  
Arrival Processes ◽  
Poisson Arrivals ◽  
Number Of Customers ◽  
Steady State Solutions ◽  
Transient And Steady State

In this paper we analyze a tollbooth tandem queueing problem with an infinite number of servers. A customer starts service immediately upon arrival but cannot leave the system before all customers who arrived before him/her have left, i.e. customers depart the system in the same order as they arrive. Distributions of the total number of customers in the system, the number of departure-delayed customers in the system, and the number of customers in service at time t are obtained in closed form. Distributions of the sojourn times and departure delays of customers are also obtained explicitly. Both transient and steady state solutions are derived first for Poisson arrivals, and then extended to cases with batch Poisson and nonstationary Poisson arrival processes. Finally, we report several stochastic ordering results on how system performance measures are affected by arrival and service processes.

A single server Markovian queuing system with limited buffer and reverse balking

2021 ◽  
Vol 12 (7) ◽  
pp. 1774-1784
Author(s):  
Girin Saikia ◽  
Amit Choudhury
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Mutual Fund ◽  
System Size ◽  
Queuing System ◽  
Single Server ◽  
Insurance Company ◽  
Number Of Customers ◽  
Steady State Probabilities

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived.

scholarly journals Kernel density estimation and its application

2018 ◽  
Vol 23 ◽  
pp. 00037 ◽  
Author(s):  
Stanisław Węglarczyk
Keyword(s):  
Probability Density Function ◽  
Probability Distribution ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Real Life ◽  
Kernel Estimation ◽  
Kernel Density ◽  
Two Dimensional ◽  
2D Histogram ◽  
Function Shape

Kernel density estimation is a technique for estimation of probability density function that is a must-have enabling the user to better analyse the studied probability distribution than when using a traditional histogram. Unlike the histogram, the kernel technique produces smooth estimate of the pdf, uses all sample points' locations and more convincingly suggest multimodality. In its two-dimensional applications, kernel estimation is even better as the 2D histogram requires additionally to define the orientation of 2D bins. Two concepts play fundamental role in kernel estimation: kernel function shape and coefficient of smoothness, of which the latter is crucial to the method. Several real-life examples, both for univariate and bivariate applications, are shown.

Relations Among Moments of Waiting Time and Queue Size Distribution in Bulk Queueing Systems

1987 ◽  
Vol 36 (1-2) ◽  
pp. 63-68
Author(s):  
A. Ghosal ◽  
S. Madan ◽  
M.L. Chaudhry
Keyword(s):  
Size Distribution ◽  
Waiting Time ◽  
Queueing Systems ◽  
Queueing Models ◽  
Queue Size ◽  
Different Types

This paper brings out relations among the moments of various orders of the waiting time and the queue size in different types of bulk queueing models.

A Tutorial on the Use of ROC Analysis for Computer-Aided Diagnostic Systems

2005 ◽  
Vol 27 (3) ◽  
pp. 181-198 ◽  
Author(s):  
Ulrich Scheipers ◽  
Christian Perrey ◽  
Stefan Siebers ◽  
Christian Hansen ◽  
Helmut Ermert
Keyword(s):  
Performance Measures ◽  
Roc Curve ◽  
Roc Analysis ◽  
Real Life ◽  
Performance Measure ◽  
Diagnostic Systems ◽  
Life Data ◽  
Separation Threshold ◽  
Real Life Data ◽  
Computer Aided

The application of the receiver operating characteristic (ROC) curve for computer-aided diagnostic systems is reviewed. A statistical framework is presented and different methods of evaluating the classification performance of computer-aided diagnostic systems, and, in particular, systems for ultrasonic tissue characterization, are derived. Most classifiers that are used today are dependent on a separation threshold, which can be chosen freely in many cases. The separation threshold separates the range of output values of the classification system into different target groups, thus conducting the actual classification process. In the first part of this paper, threshold specific performance measures, e.g., sensitivity and specificity; are presented. In the second part, a threshold-independent performance measure, the area under the ROC curve, is reviewed. Only the use of separation threshold-independent performance measures provides classification results that are overall representative for computer-aided diagnostic systems. The following text was motivated by the lack of a complete and definite discussion of the underlying subject in available textbooks, references and publications. Most manuscripts published so far address the theme of performance evaluation using ROC analysis in a manner too general to be practical for everyday use in the development of computer-aided diagnostic systems. Nowadays, the user of computer-aided diagnostic systems typically handles huge amounts of numerical data, not always distributed normally. Many assumptions made in more or less theoretical works on ROC analysis are no longer valid for real-life data. The paper aims at closing the gap between theoretical works and real-life data. The review provides the interested scientist with information needed to conduct ROC analysis and to integrate algorithms performing ROC analysis into classification systems while understanding the basic principles of classification.

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