Stochastic Analysis of Maintenance and Routing Policies in Queueing Systems
Creators: name: Doroudi, Sherwin
Publisher: name: Carnegie Mellon University
Year: 2016
Subjects: subject: 150399 Business and Management not elsewhere classified
subject: FOS: Economics and business
subject: FOS: Economics and business

description: This dissertation focuses on reexamining traditional management problems that emerge in service systems where customers or jobs queue for service. In particular, we investigate how a manger should make maintenance and routing decisions in settings where there is a departure from traditional modeling assumptions. In many cases, the performance evaluation of a management problems has, at its heart, a complex, infinite Markov chain which must be solved before any optimization can begin. Unfortunately, most Markov chains are not analytically tractable. In the first essay, we address the solution of infinite state Markov chains. We focus on class M Markov chains, a broad class of chains which is representative of a wide array of problems arising in the management of computer, service, and manufacturing systems where queueing parameters change over time according to a restricted stochastic pattern. We develop a new method, called Clearing Analysis on Phases, for the limiting probability distribution of such chains in exact closed form. In the second essay, we apply the CAP method to answer the question of how a manager should maintain a system in a setting where an online customer-facing service is vulnerable to persistent malware infections. These infections can cause performance degradation and facilitate data theft, both of which have monetary repercussions. Infections can go undetected and can only be removed by a timeconsuming cleanup procedure, which takes the service offline and causes all existing jobs to be discarded without service. In particular, we provide recommendations for when (and in response to what events) a manager should initiate cleanup procedures by solving an infinite state maintenance problem. We quantify the efficiency of various cleanup (maintenance) policies by proposing a revenue model which incorporates both delay-based pricing and data theft costs. In the third essay, we examine queueing systems in call centers and answer the question of a how a manager should route customers to strategic staff who choose their own service rates in response to workload incentives. We address this problem using game theoretic techniques. In particular, we introduce a utility model where the servers choose their service rate in order to maximize a tradeoff between an “effort cost” and a “value of idleness.” We find that relaxing the classical assumption that all servers work at a fixed rate renders traditional routing policies inadequate. Our approach allows us to recommend novel routing policies that are both fair for the staff and efficient for the customers. In the fourth essay we look at web server farms and answer the question of how jobs should be immediately routed to computer servers in a setting where some jobs are more valuable or more important than others. Such settings arise when some jobs are generated by users who are paying for a premium service. We address how a manager should incorporate information about a job’s value when making routing decisions in order to minimize expected value-weighted response times. The heterogeneity in job values greatly the dimensionality of this problem. Via a combination of exact analysis, asymptotic analysis, and simulation, we are able to deduce many unexpected results regarding routing.