scholarly journals A Novel Scheduling Index Rule Proposal for QoE Maximization in Wireless Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ianire Taboada ◽  
Fidel Liberal
Keyword(s):  
Resource Allocation ◽  
Wireless Channels ◽  
Optimal Solution ◽  
Decision Processes ◽  
Closed Form Expression ◽  
Time Varying ◽  
Form Expression ◽  
Markovian Decision Processes ◽  
Perception Of Quality ◽  
Allocation Strategies

This paper deals with the resource allocation problem aimed at maximizing users’ perception of quality in wireless channels with time-varying capacity. First of all, we model the subjective quality-aware scheduling problem in the framework of Markovian decision processes. Then, given that the obtaining of the optimal solution of this model is unachievable, we propose a simple scheduling index rule with closed-form expression by using a methodology based on Whittle approach. Finally, we analyze the performance of the achieved scheduling proposal in several relevant scenarios, concluding that it outperforms the most popular existing resource allocation strategies.

Optimizing Series Repairable Systems with Imperfect Repair

2011 ◽  
Vol 2 (2) ◽  
pp. 92-102 ◽  
Author(s):  
Mohammed Hajeeh
Keyword(s):  
Mathematical Model ◽  
Optimal Solution ◽  
Closed Form Expression ◽  
Repairable Systems ◽  
Nonlinear Mathematical Model ◽  
Form Expression ◽  
Repair Rate ◽  
Imperfect Repair ◽  
Repair Models ◽  
Minimum Costs

Repairable systems are either repaired perfectly to a state of as good as new or imperfectly. In this work, a system which undergoes imperfect repair is investigated. A nonlinear mathematical model is formulated for a system with the objective of finding the optimum failure and repair rate with the minimum costs subject to attaining a pre-specified performance level. Two imperfect repair models are examined. In the first model, the system is replaced by a new one after several failures. In the second model, the system is either replaced with a specific probability (1-p) or is imperfectly repaired after each failure with probability p. The optimal solution is presented in a closed form expression.

scholarly journals Synthesizing of Planar and Conformal Double-Sided Parallel-Cross Dipoles FSS Based on Closed-Form Expression

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Yassine Zouaoui ◽  
Larbi Talbi ◽  
Khelifa Hettak ◽  
Naresh K. Darimireddy
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

scholarly journals Temporal concatenation for Markov decision processes

2021 ◽  
pp. 1-28
Author(s):  
Ruiyang Song ◽  
Kuang Xu
Keyword(s):  
Markov Decision Processes ◽  
Large Scale ◽  
Optimal Solution ◽  
Upper Bounds ◽  
Black Box ◽  
Decision Processes ◽  
Optimal Solutions ◽  
Wide Range ◽  
Markov Decision ◽  
Speed Up

We propose and analyze a temporal concatenation heuristic for solving large-scale finite-horizon Markov decision processes (MDP), which divides the MDP into smaller sub-problems along the time horizon and generates an overall solution by simply concatenating the optimal solutions from these sub-problems. As a “black box” architecture, temporal concatenation works with a wide range of existing MDP algorithms. Our main results characterize the regret of temporal concatenation compared to the optimal solution. We provide upper bounds for general MDP instances, as well as a family of MDP instances in which the upper bounds are shown to be tight. Together, our results demonstrate temporal concatenation's potential of substantial speed-up at the expense of some performance degradation.

scholarly journals Balancing scarce hospital resources during the COVID-19 pandemic using discrete-event simulation

2021 ◽  
Author(s):  
G.J. Melman ◽  
A.K. Parlikad ◽  
E.A.B. Cameron
Keyword(s):  
Resource Allocation ◽  
Discrete Event Simulation ◽  
Elective Surgery ◽  
Discrete Event ◽  
Specific Patient ◽  
Event Simulation ◽  
The Impact ◽  
Allocation Decisions ◽  
Allocation Strategies ◽  
Resource Allocation Decisions

AbstractCOVID-19 has disrupted healthcare operations and resulted in large-scale cancellations of elective surgery. Hospitals throughout the world made life-altering resource allocation decisions and prioritised the care of COVID-19 patients. Without effective models to evaluate resource allocation strategies encompassing COVID-19 and non-COVID-19 care, hospitals face the risk of making sub-optimal local resource allocation decisions. A discrete-event-simulation model is proposed in this paper to describe COVID-19, elective surgery, and emergency surgery patient flows. COVID-19-specific patient flows and a surgical patient flow network were constructed based on data of 475 COVID-19 patients and 28,831 non-COVID-19 patients in Addenbrooke’s hospital in the UK. The model enabled the evaluation of three resource allocation strategies, for two COVID-19 wave scenarios: proactive cancellation of elective surgery, reactive cancellation of elective surgery, and ring-fencing operating theatre capacity. The results suggest that a ring-fencing strategy outperforms the other strategies, regardless of the COVID-19 scenario, in terms of total direct deaths and the number of surgeries performed. However, this does come at the cost of 50% more critical care rejections. In terms of aggregate hospital performance, a reactive cancellation strategy prioritising COVID-19 is no longer favourable if more than 7.3% of elective surgeries can be considered life-saving. Additionally, the model demonstrates the impact of timely hospital preparation and staff availability, on the ability to treat patients during a pandemic. The model can aid hospitals worldwide during pandemics and disasters, to evaluate their resource allocation strategies and identify the effect of redefining the prioritisation of patients.

scholarly journals Colored HOMFLY-PT for hybrid weaving knot $$ {\hat{\mathrm{W}}}_3 $$(m, n)

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Vivek Kumar Singh ◽  
Rama Mishra ◽  
P. Ramadevi
Keyword(s):  
Closed Form ◽  
Topological Strings ◽  
Chebyshev Polynomials ◽  
Fibonacci Numbers ◽  
Infinite Family ◽  
Closed Form Expression ◽  
Two Dimensional ◽  
Laurent Polynomials ◽  
Form Expression ◽  
Torus Knots

Abstract Weaving knots W(p, n) of type (p, n) denote an infinite family of hyperbolic knots which have not been addressed by the knot theorists as yet. Unlike the well known (p, n) torus knots, we do not have a closed-form expression for HOMFLY-PT and the colored HOMFLY-PT for W(p, n). In this paper, we confine to a hybrid generalization of W(3, n) which we denote as $$ {\hat{W}}_3 $$ W ̂ 3 (m, n) and obtain closed form expression for HOMFLY-PT using the Reshitikhin and Turaev method involving $$ \mathrm{\mathcal{R}} $$ ℛ -matrices. Further, we also compute [r]-colored HOMFLY-PT for W(3, n). Surprisingly, we observe that trace of the product of two dimensional $$ \hat{\mathrm{\mathcal{R}}} $$ ℛ ̂ -matrices can be written in terms of infinite family of Laurent polynomials $$ {\mathcal{V}}_{n,t}\left[q\right] $$ V n , t q whose absolute coefficients has interesting relation to the Fibonacci numbers $$ {\mathrm{\mathcal{F}}}_n $$ ℱ n . We also computed reformulated invariants and the BPS integers in the context of topological strings. From our analysis, we propose that certain refined BPS integers for weaving knot W(3, n) can be explicitly derived from the coefficients of Chebyshev polynomials of first kind.

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