Marginal productivity index policies for problems of admission control and routing to parallel queues with delay

In this paper we consider the problem of admission control of Bernoulli arrivals to a buffer with geometric server, in which the controller’s actions take effect one period after the actual change in the queue length. An optimal policy in terms of marginal productivity indices (MPI) is derived for this problem under the following three performance objectives: (i) minimization of the expected total discounted sum of holding costs and rejection costs, (ii) minimization of the expected time-average sum of holding costs and rejection costs, and (iii) maximization of the expected time-average number of job completions. Our employment of existing theoretical and algorithmic results on restless bandit indexation together with some new results yields a fast algorithm that computes the MPI for a queue with a buffer size of I performing only O(I) arithmetic operations. Such MPI values can be used both to immediately obtain the optimal thresholds for the admission control problem, and to design an index policy for the routing problem (with possible admission control) in the multi-queue system. Thus, this paper further addresses the problem of designing and computing a tractable heuristic policy for dynamic job admission control and/or routing in a discrete time Markovian model of parallel loss queues with one-period delayed state observation and/or action implementation, which comes close to optimizing an infinite-horizon problem under the above three objectives. Our approach seems to be tractable also for the analogous problems with larger delays and, more generally, for arbitrary restless bandits with delays

Marginal productivity index policies for problems of admission control and routing to parallel queues with delay

In this paper we consider the problem of admission control of Bernoulli arrivals to a buffer with geometric server, in which the controller’s actions take effect one period after the actual change in the queue length. An optimal policy in terms of marginal productivity indices (MPI) is derived for this problem under the following three performance objectives: (i) minimization of the expected total discounted sum of holding costs and rejection costs, (ii) minimization of the expected time-average sum of holding costs and rejection costs, and (iii) maximization of the expected time-average number of job completions. Our employment of existing theoretical and algorithmic results on restless bandit indexation together with some new results yields a fast algorithm that computes the MPI for a queue with a buffer size of I performing only O(I) arithmetic operations. Such MPI values can be used both to immediately obtain the optimal thresholds for the admission control problem, and to design an index policy for the routing problem (with possible admission control) in the multi-queue system. Thus, this paper further addresses the problem of designing and computing a tractable heuristic policy for dynamic job admission control and/or routing in a discrete time Markovian model of parallel loss queues with one-period delayed state observation and/or action implementation, which comes close to optimizing an infinite-horizon problem under the above three objectives. Our approach seems to be tractable also for the analogous problems with larger delays and, more generally, for arbitrary restless bandits with delays.Admission control, Routing, Parallel queues, Delayed information, Delayed action implementation, Index policy, Restless bandits, Marginal productivity index

Inflow control device in openhole horizontal well

An Inflow-control device (ICD) is a permanent completion hardware that is installed as part of well completions which often known as an equalizer or choking device. It offers numbers of unique benefits especially in the horizontal application, but it is not adjustable or non-retrievable hardware. Frictional pressure drops caused by fluid flow in horizontal section resulted in higher drawdown pressure at the heels section which causing an unbalance fluid distribution profile. Hence the main challenge of horizontal wells is an early water and/or gas breakthrough near the heel section which leads to a loss in production and reserves extraction, and ultimately, a decrease in profitability. Therefore, the purpose of this study is to develop the best ICD modelling design for a specific case study (Well ETA-06) and to investigate the effect of few important parameters towards the performance and functionality of the ICD along horizontal wellbore. ICD modelling was developed using NEToolTM software for appropriate number of open-flow ports and the optimum length and/or numbers of ICDs required for evenly distributing the flow profile along the screen length in order to achieve the proactive functionality of the ICDs. A sensitivity study has been run towards the best resulted ICD parameters, namely (1) ICD size, (2) flow port size, (3) swell packer usability, (4) flow rate, (5) ICD roughness, and (6) discharge coefficient in simulating influx along the horizontal wellbore by coupling fluid flow through porous media and hydraulic flow into nozzle type of ICD completion architecture. In the homogeneous reservoir, the heel section tends to produce more oil compared to the toe section thereby will allow water or gas production in a brief period. On the other hand, the ICD has reduced or choked the fluid inflow at the higher permeability section and produces more at the low permeability area. In general, ICDs are unchangeable; once installed downhole in the well, the location of the device and the relationship between the rate and pressure drop are fixed. Consequently, the best design of a well completion and ICDs is extremely crucial in order to ensure the functionality and effectiveness of the ICDs in obtaining the optimum production at lesser water or gas production

O(1/ε)O(1/\varepsilon) is the answer in online weighted throughput maximization

We study a fundamental online scheduling problem where jobs with processing times, weights, and deadlines arrive online over time at their release dates. The task is to preemptively schedule these jobs on a single or multiple (possibly unrelated) machines with the objective to maximize the weighted throughput, the total weight of jobs that complete before their deadline. To overcome known lower bounds for the competitive analysis, we assume that each job arrives with some slack $\varepsilon > 0$; that is, the time window for processing job $j$ on any machine $i$ on which it can be executed has length at least $(1+\varepsilon)$ times $j$'s processing time on machine $i$. Our contribution is a best possible online algorithm for weighted throughput maximization on unrelated machines: Our algorithm is $O\big(\frac1\varepsilon\big)$-competitive, which matches the lower bound for unweighted throughput maximization on a single machine. Even for a single machine, it was not known whether the problem with weighted jobs is "harder" than the problem with unweighted jobs. Thus, we answer this question and close weighted throughput maximization on a single machine with a best possible competitive ratio $\Theta\big(\frac1\varepsilon\big)$. While we focus on non-migratory schedules, our algorithm achieves the same (up to constants) performance guarantee when compared to an optimal migratory schedule

Elastic DVS Management in Processors with Discrete Voltage/Frequency Modes

Applying classical dynamic voltage scaling (DVS) techniques to real-time systems running on processors with discrete voltage/frequency modes causes a waste of computational resources. In fact, whenever the ideal speed level computed by the DVS algorithm is not available in the system, to guarantee the feasibility of the task set, the processor speed must be set to the nearest level greater than the optimal one, thus underutilizing the system. Whenever the task set allows a certain degree of flexibility in specifying timing constraints, rate adaptation techniques can be adopted to balance performance (which is a function of task rates) versus energy consumption (which is a function of the processor speed). In this paper, we propose a new method that combines discrete DVS management with elastic scheduling to fully exploit the available computational resources. Depending on the application requirements, the algorithm can be set to improve performance or reduce energy consumption, so enhancing the flexibility of the system. A reclaiming mechanism is also used to take advantage of early completions. To make the proposed approach usable in real-world applications, the task model is enhanced to consider some of the real CPU characteristics, such as discrete voltage/frequency levels, switching overhead, task execution times nonlinear with the frequency, and tasks with different power consumption. Implementation issues and experimental results for the proposed algorithm are also discussed

Correlation Between Student Success and On-Campus Jobs

This study examined the level of degree on-campus jobs at Eastern Kentucky University assist with the overall student success rate regarding retention, grade point average and degrees awarded to ensure state and other funding sources are maximized. Specifically, this study focuses on major student employers on campus including the Admissions Office, Library Services, Student Life, Campus Recreation, University Housing, and a culmination of Other Departments. The data used was collected from Eastern Kentucky University’s institutional research office from the Fall 2016 to Fall 2018 academic year. The analysis of the results drew positive conclusions regarding on-campus employment resulting in a higher grade point average, increased degree completion and the correlation of on-campus housing for students with an on-campus job. Recommendations for policy implications and future research are provided

Reservoir Characterization and Waterflood Performance Evaluation of Granite Wash Formation, Anadarko Basin

The Granite wash formation in the Anadarko basin is classified as a tight-gas play and is located along the Texas – Oklahoma border. It has a complex mineralogy and consists of stacked-pay series of tight sands. Our zone of interest is the liquid-rich Missourian Wash B interval in Wheeler County in which two horizontal wells have been drilled. The purpose of this research is to characterize the reservoir through geologic modeling and determine the feasibility of a waterflood using simulation studies. A set of field data was provided by the operator and other necessary parameters were obtained through publicly available field studies and literature. The final objective is implementing advanced reservoir simulation to integrate well log data, PVT data, diagnostic fracture injection test and microseismic analysis into a plan of development. The Missourian Wash B formation has a maximum net pay thickness of 50ft. The target sand is laterally continuous which makes it an ideal horizontal drilling prospect. The wells are stimulated by multi-stage hydraulic fracturing. The initial production gas-oil ratio is 1800 scf/stb and PVT reports indicate presence of an oil reservoir above bubble point pressure. PVT correlations show that the 42º API oil and potential injection water at the reservoir temperature have almost the same viscosity. All these factors point towards the formation being a good waterflood candidate. Well log analysis was performed to obtain porosity and saturation estimates. The microseismic mapping report provides a good overview of the well completion efficiency. Laboratory PVT data was tuned to predict reservoir fluid behavior by parameter regression and component lumping. An isotropic black-oil simulator by Computer Modeling Group Ltd was selected for our work. The reservoir model was validated by sensitivity studies and history matching of production rates was performed. Simulation result of waterflood implementation by utilizing offset horizontal wells as injectors is analyzed, and three different plans of development are discussed. It is seen that the overall response to waterflooding is poor due to low formation permeability leading to low water injectivity. But a greater reservoir area can be drained if production is initiated from additional horizontal wells. A well-spacing of four horizontal wells in 600 acres section is recommended. The stimulated reservoir volumes of adjacent wells should be close to each other for effective reservoir drainage

Task allocation in a multi-server system

We consider a slotted queueing system with $C$ servers (processors) that can handle tasks (jobs). Tasks arrive in batches of random size at the start of every slot. Any task can be executed by any server in one slot with success probability $alpha$. If a task execution fails, then the task must be handled in some later time slot until it has been completed successfully. Tasks may be processed by several servers simultaneously. In that case, the task is completed successfully if the task execution is successful on at least one of the servers. We determine the distribution of the number of tasks in the system for a broad class of task allocation strategies. Subsequently, we examine the impact of various allocation strategies on the mean number of tasks in the system and the mean response time of tasks. It is proven that both these performance measures are minimized by the strategy which always distributes the tasks over the servers as evenly as possible. Some numerical experiments are performed to illustrate the performance characteristics of the various strategies for a wide range of scenarios