On the modelling and performance measurement of service networks with heterogeneous customers
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On the modelling and performance measurement of service networks with heterogeneous customers Ryan Palmer1
· Martin Utley2
© The Author(s) 2019
Abstract Service networks are common throughout the modern world, yet understanding how their individual services effect each other and contribute to overall system performance can be difficult. An important metric in these systems is the quality of service. This is an often overlooked measure when modelling and relates to how customers are affected by a service. Presented is a novel perspective for evaluating the performance of multi-class queueing networks through a combination of operational performance and service quality—denoted the “flow of outcomes”. Here, quality is quantified by customers moving between or remaining in classes as a result of receiving service or lacking service. Importantly, each class may have different flow parameters, hence the positive/negative impact of service quality on the system’s operational performance is captured. A fluid–diffusion approximation for networks of stochastic queues is used since it allows for several complex flow dynamics: the sequential use of multiple services; abandonment and possible rejoin; reuse of the same service; multiple customers classes; and, class and time dependent parameters. The scalability of the approach is a significant benefit since, the modelled systems may be relatively large, and the included flow dynamics may render the system analytically intractable or computationally burdensome. Under the right conditions, this method provides a framework for quickly modelling large time-dependent systems. This combination of computational speed and the “flow of outcomes” provides new avenues for the analysis of multi-class service networks where both service quality and operational efficiency interact. Keywords Queueing · Multi-class networks · System performance · Fluid and diffusion approximation · Flow of outcomes
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10479-01903391-z) contains supplementary material, which is available to authorized users.
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Ryan Palmer [email protected]
1
Department of Mathematics, UCL, Gower Street, London WC1E 6BT, UK
2
Clinical Operational Research Unit, UCL, 4 Taviton Street, London WC1H 0BT, UK
123
Annals of Operations Research
1 Introduction Throughout the modern world service systems such as health care services, telecommunications and computer networks are common and of significant importance to world economies. Typically these systems consist several, semi-autonomous services that each have a distinct function yet are linked by an overarching purpose to which they contribute to achieving. For such systems, the quality of the service provided/received by customers is important (Seth et al. 2005; Ghotbabadi et al. 2015). Particularly, the quality of service or the service outcomes are a key metric for gauging how well services are performing, individually and as a whole, and relate closely to the overarchin
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