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2002a), “Statistical Analysis of a Telephone Call Center: A Queueing Science Perspective,” technical report, University of Pennsylvania, downloadable at http://iew3.technion.ac.il/serveng/References/references.html
"... A call center is a service network in which agents provide telephonebased services. Customers who seek these services are delayed in telequeues. This article summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking cal ..."
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Cited by 242 (35 self)
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A call center is a service network in which agents provide telephonebased services. Customers who seek these services are delayed in telequeues. This article summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer patience, and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these techniques is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. Finally, the article surveys how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations.
Effective bandwidths: call admission, traffic policing, and filtering for ATM networks
, 1994
"... In this paper we review and extend the effective bandwidth results of Kelly [28], and Kesidis, Walrand and Chang [29, 6]. These results provide a framework for call admission schemes which are sensitive to constraints on the mean delay or the tail distribution of the workload in buffered queues. We ..."
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Cited by 75 (8 self)
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In this paper we review and extend the effective bandwidth results of Kelly [28], and Kesidis, Walrand and Chang [29, 6]. These results provide a framework for call admission schemes which are sensitive to constraints on the mean delay or the tail distribution of the workload in buffered queues. We present results which are valid for a wide variety of traffic streams and discuss their applicability for traffic management in ATM networks. We discuss the impact of traffic policing schemes, such as thresholding and ltering, on the effective bandwidth of sources. Finally we discuss effective bandwidth results for Brownian traffic models for which explicit results reveal the interaction arising in finite buffers.
Effective bandwidths with priorities
 IEEE/ACM Transactions on Networking
, 1998
"... Abstract — The notion of effective bandwidths has provided a useful practical framework for connection admission control and capacity planning in highspeed communication networks. The associated admissible set with a single linear boundary makes it possible to apply stochasticlossnetwork (general ..."
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Cited by 51 (1 self)
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Abstract — The notion of effective bandwidths has provided a useful practical framework for connection admission control and capacity planning in highspeed communication networks. The associated admissible set with a single linear boundary makes it possible to apply stochasticlossnetwork (generalizedErlang) models for capacity planning. In this paper we consider the case of network nodes that use a priorityservice discipline to support multiple classes of service, and we wish to determine an appropriate notion of effective bandwidths. Just as was done previously for the firstin firstout discipline, we use largebuffer asymptotics (large deviations principles) for workload tail probabilities as a theoretical basis. We let each priority class have its own buffer and its own constraint on the probability of buffer overflow. Unfortunately, however, this leads to a constraint for each priority class. Moreover, the largebuffer asymptotic theory with priority classes does not produce an admissible set with linear boundaries, but we show that it nearly does and that a natural bound on the admissible set does have this property. We propose it as an approximation for priority classes. Then there is one linear constraint for each priority class. This linearadmissibleset structure implies a new notion of effective bandwidths, where a given connection is associated with multiple effective bandwidths: one for the priority level of the given connection and one for each lower priority level. This structure can be used regardless of whether the individual effective bandwidths are determined by largebuffer asymptotics or by some other method. 1
Stochastic Modeling Of Traffic Processes
 Frontiers in Queueing: Models, Methods and Problems
, 1996
"... Modern telecommunications networks are being designed to accomodate a heterogenous mix of traffic classes ranging from traditional telephone calls to video and data services. Thus, traffic models are of crucial importance to the engineering and performance analysis of telecommunications system, nota ..."
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Cited by 34 (0 self)
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Modern telecommunications networks are being designed to accomodate a heterogenous mix of traffic classes ranging from traditional telephone calls to video and data services. Thus, traffic models are of crucial importance to the engineering and performance analysis of telecommunications system, notably congestion and overload controls and capacity estimation. This chapter surveys teletraffic models, addressing both theoretical and computational aspects. It first surveys the main classes of teletraffic models commonly used in teletraffic modeling, and then proceeds to survey traffic methods for computing statistics relevant to the engineering a teletraffic network. 1 INTRODUCTION Traffic is the driving force of telecommunications systems, representing customers making phone calls, transferring data files and other electronic information, or more recently, transmitting compressed video frames to a display device. The most common modeling context is queueing; traffic is offered to a qu...
An Overview Of Tes Processes And Modeling Methodology
 SpringerVerlag Lecture Notes in Computer Science
, 1993
"... TES (TransformExpandSample) is a versatile methodology for modeling stationary time series with general marginal distributions and a broad range of dependence structures. From the viewpoint of Monte Carlo simulation, TES constitutes a new and flexible input analysis approach whose principal mer ..."
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Cited by 33 (10 self)
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TES (TransformExpandSample) is a versatile methodology for modeling stationary time series with general marginal distributions and a broad range of dependence structures. From the viewpoint of Monte Carlo simulation, TES constitutes a new and flexible input analysis approach whose principal merit is its potential ability to simultaneously capture firstorder and secondorder statistics of empirical time series. That is, TES is designed to fit an arbitrary empirical marginal distribution (histogram), and to simultaneously approximate the leading empirical autocorrelations. This paper is a tutorial introduction to the theory of TES processes and to the modeling methodology based on it. It employs a didactic approach which relies heavily on visual intuition as a means of conveying key ideas and an aid in building deep understanding of TES. This approach is in line with practical TES modeling which itself is based on visual interaction under software support. The interaction t...
The Impact of Autocorrelation on Queuing Systems
 Management Science
, 1993
"... The performance of singleserver queues with independent interarrival intervals and service demands is well understood, and often analytically tractable. In particular, the M/M/1 queue has been thoroughly studied, due to its analytical tractability. Little is known, though, when autocorrelation is i ..."
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Cited by 26 (11 self)
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The performance of singleserver queues with independent interarrival intervals and service demands is well understood, and often analytically tractable. In particular, the M/M/1 queue has been thoroughly studied, due to its analytical tractability. Little is known, though, when autocorrelation is introduced into interarrival times or service demands, resulting in loss of analytical tractability. Even the simple case of an M/M/1 queue with autocorrelations does not appear to be well understood. Such autocorrelations do, in fact, abound in reallife systems, and worse, simplifying independence assumptions can lead to very poor estimates of performance measures. This paper reports the results of a simulation study of the impact of autocorrelation on performance in a FIFO queue. The study used two computer methods for generating autocorrelated random sequences, with different autocorrelation characteristics. The simulation results show that the injection of autocorrelation into interarriv...
Tes Modeling of Video Traffic
 IEICE Transactions on Communications
, 1993
"... Video service is slated to be a major application of emerging highspeed communications networks of the future. In particular, fullmotion video is designed to take advantage of the high bandwidths that will become affordably available with the advent of BISDN. A salient feature of compressed vi ..."
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Cited by 23 (9 self)
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Video service is slated to be a major application of emerging highspeed communications networks of the future. In particular, fullmotion video is designed to take advantage of the high bandwidths that will become affordably available with the advent of BISDN. A salient feature of compressed video sources is that they give rise to autocorrelated traffic streams, which are difficult to model with traditional modeling techniques. In this paper, we describe a new methodology, called TES (TransformExpand Sample), for modeling general autocorrelated time series, and we apply it to traffic modeling of compressed video. The main characteristic of this methodology is that it can model an arbitrary marginal distributionand approximate the autocorrelation structure of an empirical sample such as traffic measurements. Furthermore, the empirical marginal (histogram) and leading autocorrelations are captured simultaneously. Practical TES modeling is computationally intensive and is ef...
Autocorrelation and Power Density Spectrum of ATM Multiplexer Output Processes
, 1992
"... We consider a finitecapacity ATM multiplexer in discretetime domain. The input traffic is the superposition of the traffic from different classes. Each class is formed by a number of periodic input sources (e.g. voice or shaped VBR sources) which are of the same periodicity. We investigate the aut ..."
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Cited by 20 (6 self)
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We consider a finitecapacity ATM multiplexer in discretetime domain. The input traffic is the superposition of the traffic from different classes. Each class is formed by a number of periodic input sources (e.g. voice or shaped VBR sources) which are of the same periodicity. We investigate the autocorrelation function and the power density spectrum to show traffic dependencies in the multiplexer output process. We derive an exact solution for the autocorrelation function and the power density spectrum of the multiplexer output process when only one traffic class is considered. We show that the algorithm for the finitecapacitymultiplexer can also be applied for the case of an infinitecapacity multiplexer when the number of buffer places is set to a sufficiently large but finite value. By numerical examples it is shown that considering ON/OFF input sources instead of periodic input sources lead only to slightchanges in the autocorrelation function and that the main characteristics of it are preserved. We propose an approximate analysis for more than one input traffic class which uses the exact results for one traffic class. The numerical results are compared to simulation results and are in good agreement. It turns out that the power density spectrum of the multiplexer output process can be used to determine how many sources of which periodicity deliver cells to the multiplexer input. Since the measurement of the power density spectrum can be performed by standard signal processing equipment the power density spectrum can be used for several control functions (e.g. routing, admission control) inside an ATM network.
Towards better multiclass parametricdecomposition approximations for open queueing networks
 Annals of Operations Research
, 1994
"... Methods are developed for approximately characterizing the departure process of each customer class from a multiclass singleserver queue with unlimited waiting space and the firstin firstout service discipline. The model is Σ(GI i / GI i)/1 with a nonPoisson renewal arrival process and a nonex ..."
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Cited by 19 (0 self)
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Methods are developed for approximately characterizing the departure process of each customer class from a multiclass singleserver queue with unlimited waiting space and the firstin firstout service discipline. The model is Σ(GI i / GI i)/1 with a nonPoisson renewal arrival process and a nonexponential servicetime distribution for each class. The methods provide a basis for improving parametricdecomposition approximations for analyzing nonMarkov open queueing networks with multiple classes. For example, parametricdecomposition approximations are the Queueing Network Analyzer (QNA). The specific approximations here extend ones developed by G. Bitran and D. Tirupati (1988). For example, the effect of classdependent service times is considered here. With all procedures proposed here, the approximate variability parameter of the departure process of each class is a linear function of the variability parameters of the arrival processes of all the classes served at that queue, thus ensuring that the final arrival variability parameters in a general open network can be calculated by solving a system of linear equations.
Performance Modeling and Management of HighSpeed Networks
, 1993
"... High transmission speeds, increased burstiness of traffic, and statistical multiplexing of traffic render traditional approaches to network management and control ineffective. This thesis develops insight into the operation and performance of highspeed networks by developing tractable models and ..."
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Cited by 17 (0 self)
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High transmission speeds, increased burstiness of traffic, and statistical multiplexing of traffic render traditional approaches to network management and control ineffective. This thesis develops insight into the operation and performance of highspeed networks by developing tractable models and approximations. The insight gained is utilized to propose ways of enhancing the efficiency of network resources and facilitating ease of network management and control. Dynamic routing algorithms for routing Virtual Circuits (VCs) in Asynchronous Transfer Mode (ATM) must take into account their heterogeneous bandwidth characteristics and quality of service requirements. We classify ATM networks according to the network characteristics which have the greatest bearing on the performance of dynamic routing algorithms and discuss appropriate routing algorithms for each cla...