Waiting and sojourn times in a multi-server queue with mixed priorities

We consider a multi-server queue with K priority classes. In this system, customers of the P highest priorities (P<K) can preempt customers with lower priorities, ejecting them from service and sending them back into the queue. Service times are assumed exponential with the same mean for all classes. The Laplace–Stieltjes transforms of waiting times are calculated explicitly and the Laplace–Stieltjes transforms of sojourn times are provided in an implicit form via a system of functional equations. In both cases, moments of any order can be easily calculated. Specifically, we provide formulae for the steady state means and the second moments of waiting times for all priority classes. We also study some approximations of sojourn-time distributions via their moments. In a practical part of our paper, we discuss the use of mixed priorities for different types of Service Level Agreements, including an example based on a real scheduling problem of IT support teams.      

Chemical Modification of a Bacterial Siderophore by a Competitor in Dual-Species Biofilms

Chemical communication between competing bacteria in multi-species environments often enables both species to adapt and survive, and perhaps even thrive. P. aeruginosa and S. aureus are two bacterial pathogens found in natural biofilms, especially in the lungs of cystic fibrosis (CF) patients, where recent studies showed that there is often cooperation between the two species, leading to increased disease severity and antibiotic resistance. However, the mechanisms behind this cooperation are poorly understood. In this study, we analyzed co-cultured biofilms in various settings, and we applied untargeted mass spectrometry-based metabolomics analyses, combined with synthetic validation of candidate compounds. We unexpectedly discovered that S. aureus can convert pyochelin into pyochelin methyl ester, an analogue of pyochelin with reduced affinity for iron (III). This conversion allows S. aureus to coexist more readily with P. aeruginosa and unveils a mechanism underlying the formation of robust dual-species biofilms.