Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion

Mixed-Integer Second-Order Cone Programs (MISOCPs) form a nice class of mixed-inter convex programs, which can be solved very efficiently due to the recent advances in optimization solvers. Our paper bridges the gap between modeling a class of optimization problems and using MISOCP solvers. It is shown how various performance metrics of M/G/1 queues can be molded by different MISOCPs. To motivate our method practically, it is first applied to a challenging stochastic location problem with congestion, which is broadly used to design socially optimal service networks. Four different MISOCPs are developed and compared on sets of benchmark test problems. The new formulations efficiently solve large-size test problems, which cannot be solved by the best existing method. Then, the general applicability of our method is shown for similar optimization problems that use queue-theoretic performance measures to address customer satisfaction and service quality

High-Frequency (30 MHz–6 GHz) Breast Tissue Characterization Stabilized by Suction Force for Intraoperative Tumor Margin Assessment

A gigahertz (GHz) range antenna formed by a coaxial probe has been applied for sensing cancerous breast lesions in the scanning platform with the assistance of a suction tube. The sensor structure was a planar central layer and a metallic sheath of size of 3 cm2 connected to a network analyzer (keySight FieldFox N9918A) with operational bandwidth up to 26.5 GHz. Cancer tumor cells have significantly higher water content (as a dipolar molecule) than normal breast cells, changing their polarization responses and dielectric losses to incoming GHz-based stimulation. Principal component analysis named S11, related to the dispersion ratio of the input signal, is used as a parameter to identify malignant tumor cells in a mouse model (in vivo) and tumor specimens of breast cancer patients (in vitro) (both central and marginal parts). The results showed that S11 values in the frequency range from 5 to 6 GHz were significantly higher in cancer-involved breast lesions. Histopathological analysis was the gold standard for achieving the S11 calibration to distinguish normal from cancerous lesions. Our calibration on tumor specimens presented 82% positive predictive value (PPV), 100% negative predictive value (NPV), and 86% accuracy. Our goal is to apply this system as an in vivo non-invasive tumor margin scanner after further investigations in the future