The research on call centres has attracted many researchers from different disciplines recently. In this thesis, we focus on call centre modelling, analysis and design. In terms of modelling, traditionally call centres have been modelled as single-node queueing systems. Based on the Semiopen Queueing Network (SOQN) model proposed by Srinivasan et al. [42], we propose and study SOQN models with balking and abandonment (both exponential and general patience time distributions). In addition, we study the corresponding single-node queueing systems and obtain new results. For each model, we study the queue length distribution, waiting time distribution and the related performance measures. To facilitate the computation, we express the performance measures in terms of special functions. In terms of call centre design, we develop a design algorithm to determine the minimal number of CSRs (S) and trunk lines (N) to satisfy a given set of service level constraints.<p> The explicit expressions for performance measures obtained allow for theoretical analysis of the performance measures. For example we prove monotonicity and convexity properties of performance measures for the M/M/S/N and M/M/S/N + M models. We also study the comparison of different patience time distributions for the M/M/S/N+G model.<p> We provide numerical examples for each model and discuss numerical results such as monotonicity properties of performance measures. In particular, we illustrate the efficacy of our design algorithm for various models including patient, balking and abandonment models. The impact of model parameters on the design of call centres is also discussed based on the numerical examples. The results are computed using Matlab, where special functions are available.

The research on call centres has attracted many researchers from different disciplines recently. In this thesis, we focus on call centre modelling, analysis and design. In terms of modelling, traditionally call centres have been modelled as single-node queueing systems. Based on the Semiopen Queueing Network (SOQN) model proposed by Srinivasan et al. [42], we propose and study SOQN models with balking and abandonment (both exponential and general patience time distributions). In addition, we study the corresponding single-node queueing systems and obtain new results. For each model, we study the queue length distribution, waiting time distribution and the related performance measures. To facilitate the computation, we express the performance measures in terms of special functions. In terms of call centre design, we develop a design algorithm to determine the minimal number of CSRs (S) and trunk lines (N) to satisfy a given set of service level constraints.<p> The explicit expressions for performance measures obtained allow for theoretical analysis of the performance measures. For example we prove monotonicity and convexity properties of performance measures for the M/M/S/N and M/M/S/N + M models. We also study the comparison of different patience time distributions for the M/M/S/N+G model.<p> We provide numerical examples for each model and discuss numerical results such as monotonicity properties of performance measures. In particular, we illustrate the efficacy of our design algorithm for various models including patient, balking and abandonment models. The impact of model parameters on the design of call centres is also discussed based on the numerical examples. The results are computed using Matlab, where special functions are available.

Waiting for service is inevitable. Service cannot be easily supplied to match fluctuating peaks of demand, and its pre-production is limited. Unfortunately, however, most people do not tolerate waiting well. To effectively deal with the inevitable waiting, service organizations endeavor to manage customer perceptions of the wait using various strategies to make waiting seem short and less wasteful and uncomfortable. Therefore, finding ways to manage customer perceptions of waiting is an essential part of the service experience. To encourage customers to join in and help them remain being patient, service operations provide estimated waiting time. Information on the estimated wait time affects customer expectations and responses, which may further lead to undesirable customer behaviors such as balking (i.e., refusal to wait in line) and reneging (i.e., give up to get the service and leave away from the line). That is, customers’ understanding of quantitative meanings often deviates from the objective value even when the estimated waiting time is well delivered. Therefore, how service providers structure and deliver quantitative information causes customers to differ in their estimation of the time to be waitlisted as well as the expectation of service promptness, and eventually determine their behaviors. Existing research, however, has overlooked how customer experience of waiting is altered by the wait time is communicated as part of strategies for managing waiting for services. While waiting, people will have quantitative information for the duration in both numbers and units. Thus, granularity and its effect on customers’ affective and cognitive responses as well as their waiting behaviors (i.e., joining in, keep staying on, or leaving away from the line) require further investigation in that numbers and units are inseparable and change simultaneously. The purpose of this study was to explore how information, through various psychological mechanisms both cognitive and affective responses, affects waiting behavior. This dissertation consisted of three studies. Study 1 was conducted to investigate how information on delays have a granularity effect on customer perceptions of time estimation for being waitlisted in numerical cognition, particularly depending on its format. Study 2 further explored the effect of information on waiting with communicator’s cooperativeness on balking behavior, and that are incorporated into expectation of the service promptness and anxiety as a part of cognitive and affective responses. Finally, Study 3 examined the effect of information on time delays on reneging behavior with customer mind-sets with matching of cognitive salience of unit (verse number), especially when delays are imposed by the wait staff, and that are incorporated into understanding psychological mechanisms (information processing fluency and anxiety). Study 1 found that providing waiting information in a coarse-grained unit with an interval is not ideal for customers assured to join a queue because they less expected the time on being waitlisted far less shortly. In general, less balking occurs if information is delivered as a single value (than an interval), even the information is delivered in a coarse-grained unit. Therefore, for an in-depth understanding of the granularity effect of information on waiting to be seated, Study 2 was narrowed to use only a single value. Study 2 showed that when information is delivered in a coarse-grained unit with a point estimate by a professionally trained employee, balking is far less common than if the same information is delivered by an unprofessional employee because the professional employee elicits a higher level of expectation of service promptness. With emphasizing the role of the employees, how employees deliver the information in point estimate professionally encourages customers to less balking or more joining a queue even if the information is delivered in a coarse-grained unit (i.e., hours). Finally, Study 3 revealed that more reneging occurred when additional wait time was communicated in a coarse-grained interval than when the wait time was delivered in a fine-grained interval. Furthermore, when the additional wait time was communicated using a coarse-grained (rather than a fine-grained) interval to customers with an abstract mind-set, they felt more anxious and subsequently were more likely to renege. During sequential delays, therefore, information on waiting could be framed at a concrete level (how-laden) to reduce anxiety and further to keep customers stay in line. The insight gained from the three studies is discussed, and theoretical and practical implications presented in conclusion. / Tourism and Sport

An investigation into the impact of generalised maximum entropy solutions on the study of queues with or without arrival balking and their applications to congestion management in communication networks Keywords: Queues, Balking, Maximum Entropy (ME) Principle, Global Balance (GB), Queue Length Distribution (QLD), Generalised Geometric (GGeo), Generalised Exponential (GE), Generalised Discrete Half Normal (GdHN), Congestion Management, Packet Dropping Policy (PDP) Generalisations to links between discrete least biased (i.e. maximum entropy (ME)) distribution inferences and Markov chains are conjectured towards the performance modelling, analysis and prediction of general, single server queues with or without arrival balking. New ME solutions, namely the generalised discrete Half Normal (GdHN) and truncated GdHN (GdHNT) distributions are characterised, subject to appropriate mean value constraints, for inferences of stationary discrete state probability distributions. Moreover, a closed form global balance (GB) solution is derived for the queue length distribution (QLD) of the M/GE/1/K queue subject to extended Morse balking, characterised by a Poisson prospective arrival process, i.i.d. generalised exponential (GE) service times and finite capacity, K. In this context, based on comprehensive numerical experimentation, the latter GB solution is conjectured to be a special case of the GdHNT ME distribution. ii Owing to the appropriate operational properties of the M/GE/1/K queue subject to extended Morse balking, this queueing system is applied as an ME performance model of Internet Protocol (IP)-based communication network nodes featuring static or dynamic packet dropping congestion management schemes. A performance evaluation study in terms of the model’s delay is carried out. Subsequently, the QLD’s of the GE/GE/1/K censored queue subject to extended Morse balking under three different composite batch balking and batch blocking policies are solved via the technique of GB. Following comprehensive numerical experimentation, the latter QLD’s are also conjectured to be special cases of the GdHNT. Limitations of this work and open problems which have arisen are included after the conclusions.

An investigation into the impact of generalised maximum entropy solutions on the study of queues with or without arrival balking and their applications to congestion management in communication networks Keywords: Queues, Balking, Maximum Entropy (ME) Principle, Global Balance (GB), Queue Length Distribution (QLD), Generalised Geometric (GGeo), Generalised Exponential (GE), Generalised Discrete Half Normal (GdHN), Congestion Management, Packet Dropping Policy (PDP) Generalisations to links between discrete least biased (i.e. maximum entropy (ME)) distribution inferences and Markov chains are conjectured towards the performance modelling, analysis and prediction of general, single server queues with or without arrival balking. New ME solutions, namely the generalised discrete Half Normal (GdHN) and truncated GdHN (GdHNT) distributions are characterised, subject to appropriate mean value constraints, for inferences of stationary discrete state probability distributions. Moreover, a closed form global balance (GB) solution is derived for the queue length distribution (QLD) of the M/GE/1/K queue subject to extended Morse balking, characterised by a Poisson prospective arrival process, i.i.d. generalised exponential (GE) service times and finite capacity, K. In this context, based on comprehensive numerical experimentation, the latter GB solution is conjectured to be a special case of the GdHNT ME distribution. ii Owing to the appropriate operational properties of the M/GE/1/K queue subject to extended Morse balking, this queueing system is applied as an ME performance model of Internet Protocol (IP)-based communication network nodes featuring static or dynamic packet dropping congestion management schemes. A performance evaluation study in terms of the model’s delay is carried out. Subsequently, the QLD’s of the GE/GE/1/K censored queue subject to extended Morse balking under three different composite batch balking and batch blocking policies are solved via the technique of GB. Following comprehensive numerical experimentation, the latter QLD’s are also conjectured to be special cases of the GdHNT. Limitations of this work and open problems which have arisen are included after the conclusions