Queueing theory and modeling provide us with “closed-form” analytical solutions to problems involving, reasonably enough, queues. Indeed, this type of performance-focused modeling is central to properly planning and sizing infrastructure and facilities of many types, from a new hospital building with interconnected services to servers, bridges, and routers on a distributed communications network, checkout registers at a retailer, toll booths (and lanes) on an interstate, conveyor belts at an airport, or teller and drive-through windows at a bank. Complex models can be joined to form queueing networks.
In staff scheduling, a nurse manager may be trying to staff her floor in the best way for the coming week. What can happen if this is done informally, by a “seat of the pants” approach?
Optimization is yet another important field in mathematics and engineering, with many useful real-life applications in planning and other areas. In essence, it is a mathematical approach to solving problems that have as a general goal finding the best outcome possible.