Diffusion approximation for a processor sharing queue in heavy traffic

Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps track of the residual service times of all jobs in the system at any given time. From this measure valued process, one can recover the traditional performance processes, including queue length and workload. We show that under mild assumptions, including standard heavy traffic assumptions, the (suitably rescaled) measure valued processes corresponding to a sequence of processor sharing queues converge in distribution to a measure valued diffusion process. The limiting process is characterized as the image under an appropriate lifting map, of a one-dimensional reflected Brownian motion. As an immediate consequence, one obtains a diffusion approximation for the queue length process of a processor sharing queue

The Co-Principalship: It\u27s Not Lonely at the Top

The coprincipalship has been suggested as an organizational structure that addresses the increasing workload and time demands of the principal as well as the shortage of qualified applicants for the position. This article presents the findings of a qualitative study of coprincipals in public and private schools in California, Illinois, Massachusetts, Maine, Oregon, and Wisconsin. The participants describe the rationale for the model, its strengths and weaknesses, and how it functions. The coprincipals expressed particular satisfaction at sharing workloads and decision making because they were not isolated as solo leaders. Though the coprincipalship model offers possibilities for making the role of principal attractive, additional information is needed to develop a sustainable model

Federal Taxation: Formal Stockholder Vote Held Controlling in Determining When a Plan of Liquidation Is Adopted Under Section 337 of the Internal Revenue Code of 1954

The correctness  of real-time systems does not only depend on the validity of the output, but also the temporal validity. Tasks are typically designed with strict deadlines and they need to respond in time, which are the timing constraints of real-time systems. Schedulability analysis is one of the approaches to study the workload of the task system. DRTRS (Digraph Real-Time task model with resource  sharing) is introduced to describe the system task model, abstracting away most functional behaviour and focus on the timing properties. We have also developed an efficient schedulability analysis under different resource  access protocols

Flexible learning support in an inflexible society

In this paper the author describes an approach to improving staff-student communications in order to better support full-time students in Higher Education. The paper proposes that a suitable method to support modern learners might be to adopt a blended approach to post lecture support using technology to promote staff student interaction on an individual basis. To this end a qualitative trial was conducted to test the concept. The trial had three main practical objectives, 1) to investigate document sharing tools for use in Higher Education, 2) to use such tools to enable an individual and accountable dialogue with students and 3) to examine whether improving dialog was seen as a positive improvement to quality in teaching. The results of the work indicate that the relationship with students is improved when communication is individually focused and that students can better manage their academic workload, but at the same time raises issues around staff workload and practices

Dynamic resource allocation scheme for distributed heterogeneous computer systems

This invention relates to a resource allocation in computer systems, and more particularly, to a method and associated apparatus for shortening response time and improving efficiency of a heterogeneous distributed networked computer system by reallocating the jobs queued up for busy nodes to idle, or less-busy nodes. In accordance with the algorithm (SIDA for short), the load-sharing is initiated by the server device in a manner such that extra overhead in not imposed on the system during heavily-loaded conditions. The algorithm employed in the present invention uses a dual-mode, server-initiated approach. Jobs are transferred from heavily burdened nodes (i.e., over a high threshold limit) to low burdened nodes at the initiation of the receiving node when: (1) a job finishes at a node which is burdened below a pre-established threshold level, or (2) a node is idle for a period of time as established by a wakeup timer at the node. The invention uses a combination of the local queue length and the local service rate ratio at each node as the workload indicator