Structural Properties of Single Server Queueing Systems: Efficient Methods via Lumping and Dynamic Programming

Leiden Repository

Structural Properties of Single Server Queueing Systems: Efficient Methods via Lumping and Dynamic Programming

Type: Doctoral Thesis
Title: Structural Properties of Single Server Queueing Systems: Efficient Methods via Lumping and Dynamic Programming
Author: Ertiningsih, D.
Issue Date: 2020-02-05
Keywords: QSF process
successively lumpable
deriving bounds
optimal policies
value iteration
Abstract: 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.
Promotor: Supervisor: Spieksma F.M., Hollander W.T.F. den
Faculty: Faculty of Science
University: Leiden University
Handle: http://hdl.handle.net/1887/84693
 

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application/pdf Cover 153.2Kb View/Open
application/pdf Title pages_Contents_Preface 268.3Kb View/Open
application/pdf Chapter 1 392.5Kb View/Open
application/pdf Chapter 2 507.5Kb View/Open Full text at publisher site
application/pdf Chapter 3 381.9Kb Under embargo until 2021-09-05
application/pdf Chapter 4 565.7Kb Under embargo until 2021-09-05
application/pdf Chapter 5 1.762Mb View/Open Full text at publisher site
application/pdf References 209.5Kb View/Open
application/pdf Summary in Dutch 170.0Kb View/Open
application/pdf Summary in English 193.3Kb View/Open
application/pdf Acknowledgements_Curriculum Vitae 97.65Kb View/Open
application/pdf Propositions 220.3Kb View/Open

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