Diffusion Models for Double-ended Queues with Renewal Arrival Processes

We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers simultaneously in the system. We assume that sellers and buyers arrive at the system according to independent renewal processes, and they would leave the system after independent exponential patience times. We establish fluid and diffusion approximations for the queue length process under a suitable asymptotic regime. The fluid limit is the solution of an ordinary differential equation, and the diffusion limit is a time-inhomogeneous asymmetric Ornstein-Uhlenbeck process (O-U process). A heavy traffic analysis is also developed, and the diffusion limit in the stronger heavy traffic regime is a time-homogeneous asymmetric O-U process. The limiting distributions of both diffusion limits are obtained. We also show the interchange of the heavy traffic and steady state limits

The snowball effect of customer slowdown in critical many-server systems

Customer slowdown describes the phenomenon that a customer's service requirement increases with experienced delay. In healthcare settings, there is substantial empirical evidence for slowdown, particularly when a patient's delay exceeds a certain threshold. For such threshold slowdown situations, we design and analyze a many-server system that leads to a two-dimensional Markov process. Analysis of this system leads to insights into the potentially detrimental effects of slowdown, especially in heavy-traffic conditions. We quantify the consequences of underprovisioning due to neglecting slowdown, demonstrate the presence of a subtle bistable system behavior, and discuss in detail the snowball effect: A delayed customer has an increased service requirement, causing longer delays for other customers, who in turn due to slowdown might require longer service times.Comment: 23 pages, 8 figures -- version 3 fixes a typo in an equation. in Stochastic Models, 201

Self-Selecting Priority Queues with Burr Distributed Waiting Costs

Service providers, in the presence of congestion and heterogeneity of customer waiting costs, often introduce a fee-based premier option using which the customers self-segment themselves. Examples of this practice are found in health care, amusement parks, government (consular services), and transportation. Using a single-server queuing system with customer waiting costs modeled as a Burr Distribution, we perform a detailed analysis to (i) determine the conditions (fees, cost structure, etc.) under which this strategy is profitable for the service provider, (ii) quantify the benefits accrued by the premier customers; and (iii) evaluate the resulting impact on the other customers. We show that such self-selecting priority systems can be pareto-improving in the sense that they are beneficial to everyone. These benefits are larger when the variance in the customer waiting costs is high and the system utilization is high. We use income data from the poorest and richest areas (identified by zipcode) in the United States along with the countrywide income distribution to illustrate our results. Numerical results indicate that planning for a 20–40% enrollment in the high-priority option is robust in ensuring that all the stakeholders benefit from the proposed strategy

Limiting distributions of functionals of Markov chains

Let {Xn, n ≥ 0\s} and {Yn, n ≥ 0} be two stochastic processes such that Yn depends on Xn in a stationary manner, i.e. P(Yn ∊ A|Xn) does not depend on n. Sufficient conditions are derived for Yn to have a limiting distribution. If Xn is a Markov chain with stationary transition probabilities and Yn = f(Xn,..., Xn+k) then Yn depends on Xn is a stationary way. Two situations are considered: (i) {Xn, n ≥ 0} has a limiting distribution (ii) {Xn, n ≥ 0} does not have a limiting distribution and exits every finite set with probability 1. Several examples are considered including that of a non-homogeneous Poisson process with periodic rate function where we obtain the limiting distribution of the interevent times

H3K36 Methylation Regulates Nutrient Stress Response in Saccharomyces cerevisiae by Enforcing Transcriptional Fidelity

Set2-mediated histone methylation at H3K36 regulates diverse activities, including DNA repair, mRNA splicing, and suppression of inappropriate (cryptic) transcription. Although failure of Set2 to suppress cryptic transcription has been linked to decreased lifespan, the extent to which cryptic transcription influences other cellular functions is poorly understood. Here, we uncover a role for H3K36 methylation in the regulation of the nutrient stress response pathway. We found that the transcriptional response to nutrient stress was dysregulated in SET2-deleted (set2Δ) cells and was correlated with genome-wide bi-directional cryptic transcription that originated from within gene bodies. Antisense transcripts arising from these cryptic events extended into the promoters of the genes from which they arose and were associated with decreased sense transcription under nutrient stress conditions. These results suggest that Set2-enforced transcriptional fidelity is critical to the proper regulation of inducible and highly regulated transcription programs

On the inadequacy of environment impact assessments for projects in Bhagwan Mahavir Wildlife Sanctuary and National Park of Goa, India : a peer review

The Environment Impact Assessment (EIA) is a regulatory framework adopted since 1994 in India to evaluate the impact and mitigation measures of projects, however, even after 25 years of adoption, EIAs continue to be of inferior quality with respect to biodiversity documentation and assessment of impacts and their mitigation measures. This questions the credibility of the exercise, as deficient EIAs are habitually used as a basis for project clearances in ecologically sensitive and irreplaceable regions. The authors reiterate this point by analysing impact assessment documents for three projects: the doubling of the National Highway-4A, doubling of the railway-line from Castlerock to Kulem, and laying of a 400-kV transmission line through the Bhagwan Mahavir Wildlife Sanctuary and National Park in the state of Goa. Two of these projects were recently granted ‘Wildlife Clearance’ during a virtual meeting of the Standing Committee of the National Board of Wildlife (NBWL) without a thorough assessment of the project impacts. Assessment reports for the road and railway expansion were found to be deficient on multiple fronts regarding biodiversity assessment and projected impacts, whereas no impact assessment report was available in the public domain for the 400-kV transmission line project. This paper highlights the biodiversity significance of this protected area complex in the Western Ghats, and highlights the lacunae in biodiversity documentation and inadequacy of mitigation measures in assessment documents for all three diversion projects. The EIA process needs to improve substantially if India is to protect its natural resources and adhere to environmental protection policies and regulations nationally and globally

The Galois System: Optimistic Parallelization of Irregular Programs

The last several years have seen multicore architectures become ascendant in the computing world. As a result, it is no longer sufficient to rely on increasing single-threaded performance to improve application performance; instead, programmers must turn to parallelization to realize the performance gains of multicore architectures. While much research over the past three decades have focused on parallelizing regular programs which operate over arrays and matrices, much less effort has been focused on irregular programs which operate over pointer-based data structures such as trees and graphs. In fact, it is not even clear that a significant amount of parallelism even exists in these applications. We identify a common type of parallelism that arises in irregular programs that operate over worklists of various kinds, which we call amorphous data-parallelism. Due to the data-dependent nature of these applications, static compiler analysis does not suffice to uncover any parallelism. Instead, successful parallelization requires speculative, or optimistic, parallelization. However, existing speculation techniques, such as thread-level speculation, are too low-level to recognize and extract useful parallelism from these applications. We present the Galois system for optimistic parallelization which uses high-level abstractions to express amorphous data-parallelism in irregular programs, and uses semantic properties of data structures to automatically parallelize such programs. These abstractions allow programs with amorphous data-parallelism to be written in a sequential manner, relying on run-time support to extract parallelism. We then develop abstractions which allow programmers to succinctly capture locality properties of irregular data structures. We show how these abstractions can be used to improve locality, improve speculation performance and reduce speculation overhead. We also present a novel parallel scheduling framework which allows programmers to leverage algorithm semantics to intelligently schedule concurrent computation, improving performance. We demonstrate the utility of the Galois approach, as well as the extensions that we propose, across a wide range of irregular applications demonstrating amorphous data-parallelism. We find that the Galois approach can be used to extract significant parallelism with low programmer overhead.DOE HPCS Fellowshi