Matched Queues with Flexible Customers and Impatient Customers

This paper studies a double-ended queue with four Poisson inputs and flexible customers, and its stability is guaranteed by customers’ impatient behavior. We show that such a queue can be expressed as a quasi birth-and-death (QBD) process with infinitely many phases. For this purpose, we provide a detailed analysis for the QBD process, including the system stability, the stationary probability vector, the sojourn time, and so forth. Finally, numerical examples are employed to verify the correctness of our theoretical results, and demonstrate how the performance measures of this queue are influenced by key system parameters. We believe that the methodology and results described in this paper can be applied to analyze many practical issues, such as those encountered in sharing economy, organ transplantation, employee recruitment, onlinedating, and so on.

Toward QbD Process Understanding on DNA Vaccine Purification Using Design of Experiment

DNA vaccines, the third generation of vaccines, are a promising therapeutic option for many diseases as they offer the customization of their ability on protection and treatment with high stability. The production of DNA vaccines is considered rapid and less complicated compared to others such as mRNA vaccines, viral vaccines, or subunit protein vaccines. However, the main issue for DNA vaccines is how to produce the active DNA, a supercoiled isoform, to comply with the regulations. Our work therefore focuses on gaining a process understanding of the purification step which processes parameters that have impacts on the critical quality attribute (CQA), supercoiled DNA and performance attribute (PA), and step yield. Herein, pVax1/lacZ was used as a model. The process parameters of interest were sample application flow rates and salt concentration at washing step and at elution step in the hydrophobic interaction chromatography (HIC). Using a Design of Experiment (DoE) with central composite face centered (CCF) approach, 14 experiments plus four additional runs at the center points were created. The response data was used to establish regression predictive models and simulation was conducted in 10,000 runs to provide tolerance intervals of these CQA and PA. The approach of this process understanding can be applied for Quality by Design (QbD) on other DNA vaccines and on a larger production scale as well.