On the modelling and performance measurement of service networks with heterogeneous customers

Ryan Palmer, Martin Utley
2019 Annals of Operations Research  
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
more » ... ce 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. 2 Description of the stochastic system Consider a network consisting of J multi-server services. For any service, during a time interval [0, T ], customers may: arrive as a new customer; abandon the queue and potentially rejoin it, seek to use an alternative service or leave the system as a loss (L); or, receive service and potentially reuse the same service, use another service within the network, or exit having completed service (E)-see Fig. 1 . Each service therefore consists of five process orbits: the service and queue (Q), the rejoin process (R), the reuse process (U ), the alternative service process (A), and the other service process (O). Note that the term alternative service always refers to a use of another service after abandonment, and that other service refers to a use of another service having just completed service. Suppose that at any time, a customer belongs to a class k ∈ {1, 2, . . . , K } = Cla. Each class represents a level of progressive measure of quality/customer need that customers move between as they proceed through the system. For a service i ∈ {1, 2, . . . , J } = Ser and class k ∈ Cla, at time t ∈ [0, T ], denote: Z k,Q,i (t) := number of customers in the queue or service, Z k,R,i (t) := number of customers in the rejoin orbit, Z k,U ,i (t) := number of customers in the reuse orbit, Z k,A,i (t) := number of customers in the alternative service orbit, Z k,O,i (t) := number of customers in the other service orbit, Z k,L,i (t) := number of customers lost due to abandonment, Z k,E,i (t) := number of customers leave after service.
doi:10.1007/s10479-019-03391-z fatcat:4ns7y5vjtnhu3aaep7dovqxa5a