| Summary: | The service sector lies at the heart of industrialized societies. Since the early decades of the twentieth century queueing theory has provided service managers with a mathematical framework to evaluate the operational service quality and service efficiency of their services, and to strive for a balance between the two aspects. Unlike most textbook queueing models, however, real service operations have time-varying arrival rates, usually with significant variations over a day. This non-stationarity of the arrival process, which often coincides with time-varying staffing levels; makes queueing models difficult to analyze. Two of the important problems arising when considering time-dependent queues concern service quality evaluation of queues with given parameters in terms of measures like customers' waiting times, and finding the minimal time-dependent staffing levels required for achieving a given service quality target. The former is addressed in the first part of the thesis, and the latter is addressed in the second part. In the first part of the thesis, we evaluate the potential and limitations of numerical methods and investigate approximation approaches proposed in the literature for service quality evaluation of time-dependent single and multiple facility queues. We also propose, implement, and test a novel approximation approach for service quality evaluation of a particular type of time-dependent queues, namely single-class, multi-class, and networks of loss queues. Combining an exact equation derived using infinite-server models with an approximate equation motivated by stationary loss models, the proposed approach produces close to exact results in very short times. The second part of the thesis is dedicated to the staffing problem of non-stationary service networks. In particular, we focus on complex services provided by English emergency departments where a Government set waiting time target must be achieved. Drawing upon infinite-server models' results and a square root staffing law as well as the strength and flexibility of simulation models, we propose a new heuristic approach for staffing emergency departments, based on the concept of time-stable performance. The approach accounts for complexities like multiple classes of customers and resource sharing, and is shown to achieve the desired target while saving some staff-hours in typical situations where staffing levels do not allow properly for the time lags in the workloads.
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