Structural Properties of Single Server Queueing Systems: Efficient Methods via Lumping and Dynamic Programming
This thesis consists of two main parts. The first part (Chapters 2 and 3) deals with a class of Markov process called Quasi-Skipfree (QSF) processes.
- Ertiningsih, D.
- 05 February 2020
- Thesis in Leiden Repository
This thesis consists of two main parts. The first part (Chapters 2 and 3) deals with a class of Markov process called Quasi-Skipfree (QSF) processes. In particular, for QSF processes with the special structure called successive lumpability, we derive properties of the stationary distribution as well as explicit formulae. As an application, we have discussed the Cox(k)/M^Y/1 queueing system as a QSF process with a two-dimensional state space. The second part (Chapters 4 and 5) deals with Markov decision processes. In these chapters we study structural properties of the value function and optimal policies for various single server queueing systems. In Chapter 4 we consider an uncontrolled system with impatient customers that may retry. The interarrival and retrial times are allowed to have a general distribution. As an example, we have studied the GI/G/1+M+G retrial queue. We have shown convexity and supermodularity properties of the relative value function, when the cost function is monotone non-decreasing. In Chapter 5 we study monotonic convergence properties of n-horizon threshold and switching curve optimal policies via dynamic programming for Markovian controlled queueing systems. Our analysis focuses on how to choose the initial function v_0 in the value iteration algorithm.