This grant provides funding for the development of mathematical models and analysis methods for large-scale service systems, such as customer contact centers and hospitals, which have many "servers" working in parallel (e.g., agents or nurses). These models will be applied to develop algorithms to determine optimal staffing levels and to perform real-time delay estimation to use in staffing and making delay announcements. These algorithms will be evaluated by making comparisons to computer simulations. The models will be many-server queueing systems, which capture essential features of realistic service systems such as randomness in the arrival and service times, but not the full operational complexity because they have only a single large pool of homogeneous servers and a single class of homogeneous customers. Special emphasis will be given to realistic features that can have a big impact on performance but make these models difficult to analyze, including time-varying arrival rates, customer abandonment and non-exponential probability distributions. To address these complications, asymptotic methods will be exploited, leading to fluid and diffusion approximations.
If successful, the results of this research will ultimately lead to improvements in the design and management of service systems, leading to more efficient operations. The long-term goal is to establish a sound scientific basis for resource allocation (e.g., staffing) in service systems, which balances the cost of the congestion experienced by customers and the cost of providing the resources. The goal is to develop new design principles, control policies and mathematical methods for improving system performance. If successful, the research will demonstrate the advantage of the asymptotic approach as a way to effectively reduce the complexity of large-scale stochastic systems. The aim is to show that it is possible to transform the challenge of large scale into an advantage. The proposed work will thus contribute to the computational tools and methodologies of operations research and applied probability as well as service enterprise systems.
