A Diffusion Approximation to the Multi-Server Queue

Exact solutions to queueing problems with customer interarrival times and customer service times drawn from arbitrary (generalized) distributions have not been found. We are, therefore, much interested in good quality approximate solutions to such problems. This paper presents a methodology for obtaining (approximately) the distribution of the number of customers in a multiserver queue for which both the customer interarnval and customer service times are drawn from arbitrary distributions. The approximation is based on the theory of diffusion, depends only on the means and variances of the interarnval and service time distributions, and as the numeric examples attest is of very good quality when the queueing system is heavily loaded. The approximate solution is obtained via a very simple computational procedure, so that good quality approximate solutions to such problems can be easily produced.

Accurate Prediction of Antimicrobial Susceptibility for Point‐of‐Care Testing of Urine in Less than 90 Minutes via iPRISM Cassettes

Abstract The extensive and improper use of antibiotics has led to a dramatic increase in the frequency of antibiotic resistance among human pathogens, complicating infectious disease treatments. In this work, a method for rapid antimicrobial susceptibility testing (AST) is presented using microstructured silicon diffraction gratings integrated into prototype devices, which enhance bacteria‐surface interactions and promote bacterial colonization. The silicon microstructures act also as optical sensors for monitoring bacterial growth upon exposure to antibiotics in a real‐time and label‐free manner via intensity‐based phase‐shift reflectometric interference spectroscopic measurements (iPRISM). Rapid AST using clinical isolates of Escherichia coli (E. coli) from urine is established and the assay is applied directly on unprocessed urine samples from urinary tract infection patients. When coupled with a machine learning algorithm trained on clinical samples, the iPRISM AST is able to predict the resistance or susceptibility of a new clinical sample with an Area Under the Receiver Operating Characteristic curve (AUC) of ∼ 0.85 in 1 h, and AUC > 0.9 in 90 min, when compared to state‐of‐the‐art automated AST methods used in the clinic while being an order of magnitude faster