@article {26184, title = {Double-Sided Queues with Batch Markovian Arrival Processes and Abandonment}, year = {Submitted}, abstract = {We study a double-sided queueing model with batch Markovian arrival processes and abandonment, which arises in various stochastic systems such as perishable inventory systems and financial markets. In the first part of the paper, we propose an approach to obtain the joint stationary distributions of the age processes via the stationary analysis of a multi-layer Markov modulated fluid flow (MMFF) process. In the second part of the paper, using the joint stationary distribution of the age processes, we derive a number of queueing quantities related to matching rates, fill rates, sojourn times and queue length for both sides of the system. Numerical examples are presented to demonstrate the effectiveness of the approach and to show an application in inventory control of vaccine in healthcare.}, author = {Haoran Wu and Qi-Ming He and Fatih Safa Erenay} } @article {26185, title = {Time Trajectories of Critical Events in Amyotrophic Lateral Sclerosis Progression}, year = {Submitted}, author = {{\"O}zden O. Dalg{\i}{\c c} and Haoran Wu and F. Safa Erenay and Mustafa Y. Sir and Osman Y. {\"O}zalt{\i}n and Brian A. Crum and Kalyan S. Pasupathy} } @article {26182, title = {Double-sided Queues with Marked Markovian Arrival Processes and Abandonment}, journal = {Stochastic Models}, year = {2020}, abstract = {In this paper, we study a double-sided queueing model with marked Markovian arrival processes and finite discrete abandonment times. We apply the theory of multi-layer Markov modulated fluid flow (MMFF) processes to analyze the queueing model. First, we define three age processes for the queueing system and convert them into a multi-layer\ MMFF\ process. Then we analyze the multi-layer\ MMFF\ process to find queueing performance measures related to the age processes, matching rates/probabilities, waiting times, and queue lengths for both sides of the queueing system. We obtain a number of aggregate quantities as well as quantities for individual types of inputs, which can be useful for the analysis and design of, for examples, passenger-taxi service systems and organ transplantation systems.}, url = {https://www.tandfonline.com/doi/full/10.1080/15326349.2020.1794898}, author = {Haoran Wu and Qi-Ming He} } @article {26183, title = {Multi-Layer MMFF Processes and the MAP/PH/K +GI Queue: Theory and Algorithms}, journal = {Queueing Models and Service Management}, volume = {3}, year = {2020}, pages = {37-87}, abstract = {This paper is concerned with the basic theory and algorithms of multi-layer Markov modulated fluid flow (MMFF) processes and an MAP/PH/K queue with customer abandonment. For multi-layer MMFF processes, we review and refine the existing theory to make it easy to understand, and to make related algorithms meticulously organized. For the queueing system, we combine the MMFF approach and the count-server-for-phase (CSFP) method to make it possible to analyze it, and to develop an algorithm for computing queueing quantities related to customer abandonment, waiting times, and queue lengths. Some of the quantities are difficult to compute through other means. For both the multi-layer MMFF processes and the queueing system, we try to make the analysis easy to follow and the algorithm easy to implement.}, url = {http://qmsm.pu.edu.tw/papers/paper/QMSM_2020_5_002_Final.pdf}, author = {Qi-Ming He and Haoran Wu} }