Application of multiserver queueing to call centres
- Authors: Majakwara, Jacob
- Date: 2010
- Subjects: Call centers , ERLANG (Computer program language) , Queuing theory
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5578 , http://hdl.handle.net/10962/d1015461
- Description: The simplest and most widely used queueing model in call centres is the M/M/k system, sometimes referred to as Erlang-C. For many applications the model is an over-simplification. Erlang-C model ignores among other things busy signals, customer impatience and services that span multiple visits. Although the Erlang-C formula is easily implemented, it is not easy to obtain insight from its answers (for example, to find an approximate answer to questions such as "how many additional agents do I need if the arrival rate doubles?"). An approximation of the Erlang-C formula that gives structural insight into this type of question would be of use to better understand economies of scale in call centre operations. Erlang-C based predictions can also turn out highly inaccurate because of violations of underlying assumptions and these violations are not straightforward to model. For example, non-exponential service times lead one to the M/G/k queue which, in stark contrast to the M/M/k system, is difficult to analyse. This thesis deals mainly with the general M/GI/k model with abandonment. The arrival process conforms to a Poisson process, service durations are independent and identically distributed with a general distribution, there are k servers, and independent and identically distributed customer abandoning times with a general distribution. This thesis will endeavour to analyse call centres using M/GI/k model with abandonment and the data to be used will be simulated using EZSIM-software. The paper by Brown et al. [3] entitled "Statistical Analysis of a Telephone Call Centre: A Queueing-Science Perspective," will be the basis upon which this thesis is built.
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- Authors: Majakwara, Jacob
- Date: 2010
- Subjects: Call centers , ERLANG (Computer program language) , Queuing theory
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5578 , http://hdl.handle.net/10962/d1015461
- Description: The simplest and most widely used queueing model in call centres is the M/M/k system, sometimes referred to as Erlang-C. For many applications the model is an over-simplification. Erlang-C model ignores among other things busy signals, customer impatience and services that span multiple visits. Although the Erlang-C formula is easily implemented, it is not easy to obtain insight from its answers (for example, to find an approximate answer to questions such as "how many additional agents do I need if the arrival rate doubles?"). An approximation of the Erlang-C formula that gives structural insight into this type of question would be of use to better understand economies of scale in call centre operations. Erlang-C based predictions can also turn out highly inaccurate because of violations of underlying assumptions and these violations are not straightforward to model. For example, non-exponential service times lead one to the M/G/k queue which, in stark contrast to the M/M/k system, is difficult to analyse. This thesis deals mainly with the general M/GI/k model with abandonment. The arrival process conforms to a Poisson process, service durations are independent and identically distributed with a general distribution, there are k servers, and independent and identically distributed customer abandoning times with a general distribution. This thesis will endeavour to analyse call centres using M/GI/k model with abandonment and the data to be used will be simulated using EZSIM-software. The paper by Brown et al. [3] entitled "Statistical Analysis of a Telephone Call Centre: A Queueing-Science Perspective," will be the basis upon which this thesis is built.
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Lag length selection for vector error correction models
- Authors: Sharp, Gary David
- Date: 2010
- Subjects: Akaike Information Criterion Mathematical models -- Evaluation Autoregression (Statistics) Error analysis (Mathematics)
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:5568 , http://hdl.handle.net/10962/d1002808
- Description: This thesis investigates the problem of model identification in a Vector Autoregressive framework. The study reviews the existing research, conducts an extensive simulation based analysis of thirteen information theoretic criterion (IC), one of which is a novel derivation. The simulation exercise considers the evaluation of seven alternative error restricted vector autoregressive models with four different lag lengths. Alternative sample sizes and parameterisations are also evaluated and compared to results in the existing literature. The results of the comparative analysis provide strong support for the efficiency based criterion of Akaike and in particular the selection capability of the novel criterion, referred to as a modified corrected Akaike information criterion, demonstrates useful finite sample properties.
- Full Text:
- Authors: Sharp, Gary David
- Date: 2010
- Subjects: Akaike Information Criterion Mathematical models -- Evaluation Autoregression (Statistics) Error analysis (Mathematics)
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:5568 , http://hdl.handle.net/10962/d1002808
- Description: This thesis investigates the problem of model identification in a Vector Autoregressive framework. The study reviews the existing research, conducts an extensive simulation based analysis of thirteen information theoretic criterion (IC), one of which is a novel derivation. The simulation exercise considers the evaluation of seven alternative error restricted vector autoregressive models with four different lag lengths. Alternative sample sizes and parameterisations are also evaluated and compared to results in the existing literature. The results of the comparative analysis provide strong support for the efficiency based criterion of Akaike and in particular the selection capability of the novel criterion, referred to as a modified corrected Akaike information criterion, demonstrates useful finite sample properties.
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