The matched queueing network PH/M/c→oPH/PH/1

We consider a matched queueing network PH/M/coPH/PH/1, where the output of the first subsystem PH/M/c is regarded as one of the inputs of the second subsystem and matched with another input of PH-renewal process, and they are served by a single server with PH-service-distribution. The stationary state probabilities, the distribution of the virtual waiting times in the two subsystems, and the distribution of the total virtual waiting time are derived.The work was supported by the Max-Planck-Gesellschaft, Germany, and the Chinese Academy ofSciences.     

Development of a multiplexed microbioreactor system for high-throughput bioprocessing

A multiplexed microbioreactor system for parallel operation of multiple microbial fermentation is described. The system includes miniature motors for magnetic stirring of the microbioreactors and optics to monitor the fermentation parameters optical density (OD), dissolved oxygen (DO), and pH, in-situ and in real time. The microbioreactors are fabricated out of poly(methylmethacrylate)(PMMA) and poly(dimethylsiloxane)(PDMS), and have a working volume of 150 microl. Oxygenation of the cells occurs through a thin PDMS membrane at the top of the reactor chamber. Stirring is achieved with a magnetic spin bar in the reactor chamber. Parallel microbial fermentations with Escherichia coli are carried out in four stirred microbioreactors and demonstrate the reproducible performance of the multiplexed system. The profiles for OD, DO, and pH compare favourably to fermentations performed in bioreactor systems with multiple bench-scale reactors. Finally, the multiplexed system is used to compare two different reactor designs, demonstrating that the reproducibility of the system permits the quantification of microbioreactor performance.