In this paper, we develop a new approach to studying the asymptotic behavior of fluid model solutions for critically loaded processor sharing queues. For this, we introduce a notion of relative entropy associated with measure-valued fluid model solutions. In contrast to the approach used in [12], which does not readily generalize to networks of processor sharing queues, we expect the approach developed in this paper to be more robust. Indeed, we anticipate that similar notions involving relative entropy may be helpful for understanding the asymptotic behavior of critical fluid model solutions for stochastic networks operating under various resource sharing protocols naturally described by measure-valued processes.
Introduction.In the context of multiclass queueing networks operating under head-of-the-line (HL) service disciplines, Bramson [1] and Williams [15] have developed a modular approach for establishing heavy traffic diffusion approximations to such networks. In particular, they have given sufficient conditions under which asymptotic behavior of critical fluid model solutions can be used to prove state space collapse and thereby a heavy traffic limit theorem justifying a diffusion approximation. Although the HL assumption covers a wide variety of service disciplines, including firstin-first-out (FIFO) and static priorities, it requires that service for a given job class is concentrated on the job at the head-of-the-line. Consequently, it does not cover some disciplines that arise naturally in applications, such as the processor sharing discipline. While it is desirable to have a modular approach to proving diffusion approximations for stochastic networks with
COVID-19 has accelerated a reliance on virtual technology for the delivery of postgraduate surgical education. We sought to develop a regional teaching programme with robust quality assurance. Webinars were delivered on a weekly basis by subspecialty experts using Zoom™ augmented with interactive polling software. Trainee feedback comprised Likert item rating on content and delivery, free text comments and self-assessed confidence levels using visual analogue scale (VAS) scores. A focus group was also convened and transcripts assessed with grounded theory analysis. Likert items revealed 442 (93.2%) positive responses regarding content and 642 (96.7%) positive responses regarding trainer delivery. There were statistically significant improvements in VAS scores across all programme content. Key themes from the focus group analysis were the pragmatics of delivering online education, issues surrounding trainer interactivity in the virtual world, the identification of the FRCS as a driving factor and a desire for case-based content and pre-learning of information (the “flipped classroom”). We are continuing to be reactive to trainee feedback in developing our online learning programme which will also include a regional Moodle-based virtual learning environment (VLE), the subject of future educational research in our region.
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