We consider the statistical study of partially observed queueing systems arising in application areas such as hospital networks, data centers and cloud computing systems. Since these services operate under strict performance requirements, a statistical understanding of their performance is of great practical interest. A key challenge in these settings is that data is typically incomplete, as recording detailed information on every event in a heavily used system mayrequire substantial overheads and is often not feasible. We propose an analytically tractable framework for studying inference problems in these systems. Our approach is based on the robust queueing framework considered in \cite{bandi2015robust}, where the queueing primitives are modeled via polyhedral uncertainty sets. Our goal is to infer the uncertainty sets of queueing primitives given partial information. Specifically, we consider the problem of inferring the service distribution given waiting time data and partial information about the arrival process. We construct the uncertainty set for the service process given the information on the waiting times and the uncertainty set for the arrival process. In chapter 1, we characterize this set for a variety of queueing systems and demonstrate how uncertainty sets can be leveraged to compute various statistics of the service time. We also report results from an implementation of our framework at one of the biggest hospitals in India, where we estimate the service times at various locations throughout the hospital using partial patient flow data. Our methodology achieves significant computational tractability and provides accurate approximations for primitives of the service process relative to simulated values. In chapter 2, the framework is refined. Conditions for consistent estimators based on uncertainty sets are proposed and uncertainty sets are derived for more general arrival processes. Chapter 3 investigates a different setting in which service times can be observed as a decision maker routes jobs through the system such that the overall service requirement is minimized. A discussion of the problem and its variants is given before the link between system throughput is explored and a bound on the regret of the empirical $c\mu$-rule is derived.

Creator

• Proskynitopoulos, Alexej

DOI

• https://doi.org/10.21985/n2-be6y-s930

Subject

• Operations research

Language

• en

Alternate Identifier

• http://dissertations.umi.com/northwestern:15419
• etdadmin_upload_781003

Date created

• 2020-01-01

Resource type

• Dissertation

Rights statement

• In Copyright