scholarly journals Stochastic Analysis of the $k$-Server Problem on the Circle

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Aris Anagnostopoulos ◽  
Clément Dombry ◽  
Nadine Guillotin-Plantard ◽  
Ioannis Kontoyiannis ◽  
Eli Upfal
Keyword(s):  
Steady State ◽  
Stochastic Analysis ◽  
Arbitrary Distribution ◽  
Convergence Properties ◽  
Expected Cost ◽  
Greedy Strategy ◽  
Stochastic Version ◽  
International Audience ◽  
Server Problem ◽  
The Cost

International audience We consider a stochastic version of the $k$-server problem in which $k$ servers move on a circle to satisfy stochastically generated requests. The requests are independent and identically distributed according to an arbitrary distribution on a circle, which is either discrete or continuous. The cost of serving a request is the distance that a server needs to move to reach the request. The goal is to minimize the steady-state expected cost induced by the requests. We study the performance of a greedy strategy, focusing, in particular, on its convergence properties and the interplay between the discrete and continuous versions of the process.

scholarly journals The slow server problem: a queue with stalling

1985 ◽  
Vol 22 (4) ◽  
pp. 879-892 ◽  
Author(s):  
Michael Rubinovitch
Keyword(s):  
Steady State ◽  
Stochastic Analysis ◽  
Server Problem ◽  
Poisson Arrivals ◽  
Steady State Probabilities

A queue with Poisson arrivals and two different exponential servers is considered. It is assumed that customers are allowed to stall, i.e., to wait for a busy fast server at times when the slow server is free. A stochastic analysis of the queue is given, steady-state probabilities are computed, and policies for overall optimization are characterized and computed. The issue of individual customer's optimization versus overall optimization is also discussed.

scholarly journals The slow server problem: a queue with stalling

1985 ◽  
Vol 22 (04) ◽  
pp. 879-892 ◽  
Author(s):  
Michael Rubinovitch
Keyword(s):  
Steady State ◽  
Stochastic Analysis ◽  
Server Problem ◽  
Poisson Arrivals ◽  
Steady State Probabilities

A queue with Poisson arrivals and two different exponential servers is considered. It is assumed that customers are allowed to stall, i.e., to wait for a busy fast server at times when the slow server is free. A stochastic analysis of the queue is given, steady-state probabilities are computed, and policies for overall optimization are characterized and computed. The issue of individual customer's optimization versus overall optimization is also discussed.

scholarly journals A Cost Analysis of School-Based Lifestyle Interventions

2018 ◽  
Vol 19 (6) ◽  
pp. 716-727 ◽  
Author(s):  
Marije Oosterhoff ◽  
Hans Bosma ◽  
Onno C.P. van Schayck ◽  
Manuela A. Joore
Keyword(s):  
Physical Activity ◽  
Steady State ◽  
Primary School ◽  
Relative Effectiveness ◽  
First Year ◽  
Lifestyle Interventions ◽  
Stakeholder Perspectives ◽  
School Based ◽  
The Cost ◽  
Cost Offsets

Abstract A uniform approach for costing school-based lifestyle interventions is currently lacking. The objective of this study was to develop a template for costing primary school-based lifestyle interventions and apply this to the costing of the “Healthy Primary School of the Future” (HPSF) and the “Physical Activity School” (PAS), which aim to improve physical activity and dietary behaviors. Cost-effectiveness studies were reviewed to identify the cost items. Societal costs were reflected by summing up the education, household and leisure, labor and social security, and health perspectives. Cost inputs for HPSF and PAS were obtained for the first year after implementation. In a scenario analysis, the costs were explored for a hypothetical steady state. From a societal perspective, the per child costs were €2.7/$3.3 (HPSF) and €− 0.3/$− 0.4 (PAS) per day during the first year after implementation, and €1.0/$1.2 and €− 1.3/$− 1.6 in a steady state, respectively (2016 prices). The highest costs were incurred by the education perspective (first year: €8.7/$10.6 (HPSF) and €4.0/$4.9 (PAS); steady state: €6.1/$7.4 (HPSF) and €2.1/$2.6 (PAS)), whereas most of the cost offsets were received by the household and leisure perspective (first year: €− 6.0/$− 7.3 (HPSF) and €− 4.4/$− 5.4 (PAS); steady state: €− 5.0/$− 6.1 (HPSF) and €− 3.4/$− 4.1 (PAS)). The template proved helpful for costing HPSF and PAS from various stakeholder perspectives. The costs for the education sector were fully (PAS) and almost fully (HPSF) compensated by the savings within the household sector. Whether the additional costs of HPSF over PAS represent value for money will depend on their relative effectiveness.

scholarly journals Research on Cooperative Innovation Behavior of Industrial Cluster Based on Subject Adaptability

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
Xiaohui Jia ◽  
Minghui Jiang ◽  
Lei Shi
Keyword(s):  
Steady State ◽  
Evolutionary Game ◽  
Industrial Cluster ◽  
Industrial Clusters ◽  
Government Support ◽  
Correlated Equilibrium ◽  
Game Model ◽  
Cooperative Innovation ◽  
The Cost ◽  
The Impact

From the perspective of the interactive cooperation among subjects, this paper portrays the process of cooperative innovation in industrial cluster, in order to capture the correlated equilibrium relationship among them. Through the utilization of two key tools, evolutionary stable strategy and replicator dynamics equations, this paper considers the cost and gains of cooperative innovation and the amount of government support as well as other factors to build and analyze a classic evolutionary game model. On this basis, the subject’s own adaptability is introduced, which is regarded as the system noise in the stochastic evolutionary game model so as to analyze the impact of adaptability on the game strategy selection. The results show that, in the first place, without considering subjects’ adaptability, their cooperation in industrial clusters depends on the cost and gains of innovative cooperation, the amount of government support, and some conditions that can promote cooperation, namely, game steady state. In the second place after the introduction of subjects’ adaptability, it will affect both game theory selection process and time, which means that the process becomes more complex, presents the nonlinear characteristics, and helps them to make faster decisions in their favor, but the final steady state remains unchanged.

Minimizing the cost of wildland fire suppression: a model with uncertainty in predicted flame length and fire-line width produced

1994 ◽  
Vol 24 (6) ◽  
pp. 1253-1259 ◽  
Author(s):  
Romain Mees ◽  
David Strauss ◽  
Richard Chase
Keyword(s):  
Line Width ◽  
Wildland Fire ◽  
Fire Suppression ◽  
Flame Length ◽  
Burned Area ◽  
Expected Cost ◽  
Control Time ◽  
The Cost ◽  
Attack Strategy

We describe a model that estimates the optimal total expected cost of a wildland fire, given uncertainty in both flame length and fire-line width produced. In the model, a sequence of possible fire-line perimeters is specified, each with a forecasted control time. For a given control time and fire line, the probability of containment of the fire is determined as a function of the fire-fighting resources available. Our procedure assigns the resources to the fire line so as to minimize the total expected cost. A key feature of the model is that the probabilities reflect the degree of uncertainty in (i) the width of fire line that can be built with a given resource allocation, and (ii) the flame length of the fire. The total expected cost associated with a given choice of fire line is the sum of: the loss or gain of value of the area already burned; the cost of the resources used in the attack; and the expected loss or gain of value beyond the fire line. The latter is the product of the probability that the chosen attack strategy fails to contain the fire and the value of the additional burned area that would result from such a failure. The model allows comparison of the costs of the different choices of fire line, and thus identification of the optimal strategy. A small case study is used to illustrate the procedure.

scholarly journals On a Class of Optimal Stopping Problems with Mixed Constraints

2010 ◽  
Vol Vol. 12 no. 2 ◽  
Author(s):  
F. Thomas Bruss
Keyword(s):  
Selection Strategy ◽  
Optimal Selection ◽  
Recursive Structure ◽  
Limiting Behavior ◽  
Mixed Constraints ◽  
Selection Strategies ◽  
International Audience ◽  
Optimal Stopping Problems ◽  
The Cost ◽  
Independent Identically Distributed

International audience Let X(1),X(2),...,X(n) be independent, identically distributed uniform random variables on [0, 1]. We can observe the outcomes sequentially and must select online at least r of them, and, moreover, in expectation at least mu >= r. Here mu need not be integer. We see X(k) as the cost of selecting item k and want to minimize the expected total cost under the described combined (r, mu)-constraint. We will see that an optimal selection strategy exists on the set S(n) of all selection strategies for which the decision at instant k may depend on the value X(k), on the number N(k) of selections up to time k and of the number n - k of forthcoming observations. Let sigma(r,mu)(n) be the corresponding S(n)-optimal selection strategy and v(r,mu)(n) its value. The main goal of this paper is to determine these and to understand the limiting behavior of v(r,mu)(n). After discussion of the specific character of this combination of two types of constraints we conclude that the S(n)-problem has a recursive structure and solve it in terms of a double recursion. Our interest will then focus on the limiting behavior of nv(r,mu)(n) as n -> infinity. This sequence converges and its limit allows for the interpretation of a normalized limiting cost L (r, mu) of the (r, mu)-constraint. Our main result is that L(r, mu) = g(r) ((mu - r)(2)/(2)) where g(r) is the r(th) iterate of the function g(x) = 1 + x + root 1 + 2x. Our motivation to study mixed-constraints problems is indicated by several examples of possible applications. We also shortly discuss the intricacy of the expectational part of the constraint if we try to extend the class of strategies S n to the set of full-history-dependent and/or randomized strategies.

Nonlinear Ship Loads: Stochastic Models for Extreme Response

1998 ◽  
Vol 42 (01) ◽  
pp. 46-55
Author(s):  
Rune Torhaug ◽  
Steven R. Winterstein ◽  
Arne Braathen
Keyword(s):  
Time Domain ◽  
Stochastic Models ◽  
Stochastic Analysis ◽  
Short Wave ◽  
Response Analysis ◽  
Correct Result ◽  
Sea State ◽  
Extreme Response ◽  
Computational Resources ◽  
The Cost

In this study we focus on stochastic analysis methods for selective simulations, and we consider the extreme midspan moment of a fast-moving ship subjected to random Gaussian waves. We concentrate on analysis within a stationary sea state and our purpose is to accurately estimate hourly maximum ship response (compared with the correct result per hour) within a sea state with as little computational resources as possible. We consider how the use of a limited number of short simulations with "critical wave episodes" (short wave segments which are likely candidates to produce extreme response in the simulated hour-long history) reduces the cost of nonlinear time-domain ship response analysis.

Analysis of Some Stochastic Inventory System in Supply Chain

2016 ◽  
pp. 124-147
Author(s):  
Bakthavachalam Rengarajan
Keyword(s):  
Steady State ◽  
Lead Time ◽  
Distribution Center ◽  
Setup Cost ◽  
Steady State Probability ◽  
Stochastic Inventory ◽  
Replenishment Policy ◽  
System States ◽  
Policy Supply ◽  
The Cost

In this chapter we consider a three echelon inventory control system which is modeled as a warehouse, single distribute and one retailer system handling a single product. A finished product is supplied from warehouse to distribution center which adopts one-for-one replenishment policy. The replenishment of items in terms of packets from warehouse to distribution center with exponential lead time having parameter µ1. Then the product is supplied from distribution center to retailer who adopts (s, S) policy. Supply to the retailer in packets of Q (= S - s) items is administrated with exponential lead time having parameter µ0. The demand at retailer node follows a Poisson with mean lambda. The steady state probability distribution of system states and the measures of system performance in the steady state are obtained explicitly. The Cost function is computed by using numerical searching algorithms, the optimal reorder points are obtained for various input parameters. Sensitivity analysis are discussed for various cost parameter such as holding cost, setup cost etc.

COST ANALYSIS OF THE R-UNRELIABLE-UNLOADER QUEUEING SYSTEM

2008 ◽  
Vol 25 (01) ◽  
pp. 57-73
Author(s):  
KUO-HSIUNG WANG ◽  
CHUN-CHIN OH ◽  
JAU-CHUAN KE
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Queueing System ◽  
Cost Model ◽  
Analytic Solutions ◽  
Queueing Model ◽  
Exponential Distributions ◽  
System Parameters ◽  
Optimal Values ◽  
The Cost

This paper analyzes the unloader queueing model in which N identical trailers are unloaded by R unreliable unloaders. Steady-state analytic solutions are obtained with the assumptions that trip times, unloading times, finishing times, breakdown times, and repair times have exponential distributions. A cost model is developed to determine the optimal values of the number of unloaders and the finishing rate simultaneously, in order to minimize the expected cost per unit time. Numerical results are provided in which several steady-state characteristics of the system are calculated based on assumed numerical values given to the system parameters and the cost elements. Sensitivity analysis is also studied.

scholarly journals Sparse Adaptive Channel Estimation Based onlp-Norm-Penalized Affine Projection Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yingsong Li ◽  
Wenxing Li ◽  
Wenhua Yu ◽  
Jian Wan ◽  
Zhiwei Li
Keyword(s):  
Steady State ◽  
Channel Estimation ◽  
Convergence Speed ◽  
Projection Algorithm ◽  
Broadband Wireless ◽  
Sparse Channel Estimation ◽  
Affine Projection ◽  
Affine Projection Algorithm ◽  
The Cost ◽  
Steady State Performance

We propose anlp-norm-penalized affine projection algorithm (LP-APA) for broadband multipath adaptive channel estimations. The proposed LP-APA is realized by incorporating anlp-norm into the cost function of the conventional affine projection algorithm (APA) to exploit the sparsity property of the broadband wireless multipath channel, by which the convergence speed and steady-state performance of the APA are significantly improved. The implementation of the LP-APA is equivalent to adding a zero attractor to its iterations. The simulation results, which are obtained from a sparse channel estimation, demonstrate that the proposed LP-APA can efficiently improve channel estimation performance in terms of both the convergence speed and steady-state performance when the channel is exactly sparse.

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