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This course will focus on stochastic models of service systems. One goal is to help students learn about that application context. A second goal is to focus on a class of mathematical models and analysis techniques that have proven useful in that application context. As is almost always the case in operations research, these models and analysis techniques have many other applications, so that the course can be useful even if you are primarily interested in other applications.

This course provides an introduction to the theory behind Service Engineering, as applied mainly in healthcare (hospitals) and tele-services (e.g., call centers). Many topics are relevant and interesting for both applications, e.g., staffing of nurses in hospital and call center agents in call centers. Of special interests are topics that involve multi-disciplinary aspects such as queueing theory, statistics, game theory and psychology. There will be a focus on service system data. Students will be encouraged to become familiar with the data resources, such as available at the SEE-Laboratory at the Technion.

From the mathematical perspective, the course focuses on multi-server queues, and networks of such multi-server queues. Important customer behavior includes balking (deciding upon arrival not to wait), reneging or abandoning (leaving after waiting a while), retrying (coming back later after balking or reneging) and returning (coming back for additional service). There may be multiple types of customers and customer service representatives (agents) with different sets of skills. Automatic call distributors provide the capability of skill-based routing, but there remains an opportunity to improve the routing.

Consistent with the instructors' recent research, the course we will pay special attention to many-server queues. One main topic is staffing to cope with time-varying arrival rates. A second main topic is many-server heavy-traffic limits, in which both the arrival rate and the number of servers approach infinity. Three different limiting regimes emerge, depending on the way these variables approach infinity: (i) the quality-driven (QD) regime, (ii) the efficiency-driven (ED) regime and (iii) the quality-and-efficiency-driven (QED) regime. These limits yield useful approximations.