Theses Doctoral

Three Sojourns in Queueing Theory

Bergquist, Jacob Mason

In this thesis, we present three works on queues. In chapter 1, we analyze two non-work-conserving variations of the M/G/1 preemptive LIFO queue, focusing on deriving expressions for the limiting distribution of workload and related quantities. In the first model, preempted customers return to the front of the queue with a new service time, while in the second, they return with their original service time. We use queueing theory methods such as the Rate Conservation Law, PASTA, regenerative process theory and Little's Law. Our results include stability and heavy-traffic limits, as well as tail asymptotics for stationary workload.

In chapter 2, we analyze a queueing model with price-sensitive customers, where the service provider aims to maximize revenue and minimize the average queue length. Customers arrive according to a Poisson process, join the queue if their willingness-to-pay exceeds the offered price, and are served in a first-in first-out manner with exponential service times. Our model is applicable to cloud computing, make-to-order manufacturing, and food delivery. We provide performance guarantees for a class of static pricing policies that can achieve a constant fraction of the optimal revenue with a small increase in expected queue length. We present results for the single-server, multi-server, and multi-class cases and provide numerical findings to demonstrate the empirical performance of our policies.

In chapter 3, we analyze the Adaptive Non-deterministic Transmission Policy (ANTP), a technique addressing the Massive Access Problem (MAP) in telecommunications, which involves delaying packets at the points of origin to reduce congestion. We frame these delays as time spent at a "cafe" before proceeding to the service facility. We present sample-path results, giving conditions under which ANTP does not change the total sojourn time of packets, and results under a general stochastic framework, focusing on stability and constructing proper stationary versions of the model. We prove Harris recurrence of an underlying Markov process and find positive recurrent regeneration points under i.i.d. assumptions.


  • thumnail for Bergquist_columbia_0054D_17888.pdf Bergquist_columbia_0054D_17888.pdf application/pdf 541 KB Download File

More About This Work

Academic Units
Industrial Engineering and Operations Research
Thesis Advisors
Sigman, Karl
Elmachtoub, Adam N.
Ph.D., Columbia University
Published Here
June 28, 2023