Bounded Pareto Distribution Research Articles

Game Theory-Based Minimization of the Ostracism Risk in Construction Companies

Strategic and managemerial decision-making in an organization can have a crucial effect for the whole entity; however, it rarely involves the organization’s employees evenly at the different organizational levels. The result is—what is addressed in this paper as—the ostracism risk, namely the risk accruing from the lack of satisfaction of underprivileged employees’ groups during the decision-making process. The ostracism risk could jeopardize the organization’s integrity and therefore requires effective treatment. This paper aims at verifying a conceptual approach, which is proposed as a methodology for assessing the probability of organizational cooperation when deciding under risk, thus minimizing ostracism risk. The proposed approach is based on organizational and human resources management (HRM) theories and is contextualized for construction through the understanding of systems theory. The proposed methodology presents a potential modelling via game theory of a medium-sized construction company that is organized according to Mintzberg’s organizational model. The utilization of the bounded Pareto distribution is presented as an approach of the model’s probabilistic processing, and the potential for estimating the probabilities to adopt a favorable cooperational decision is verified. The paper concludes with the reference to the next steps required for the methodology’s validation and further improvement.

Analysis of the Task Assignment based on Guessing Size policy

We study the Task Assignment based on Guessing Size (TAGS) policy in a parallel and homogeneous server system. The policy parameters are the number of servers h and a set of cutoffs s1<s2,ldots,sh−1. In this policy, all the incoming jobs are routed to the first server and jobs are run up to s1 time units. If they complete they leave the system, but jobs that do not complete after s1 time units are killed and moved to the end of the queue of the second server, where service starts from scratch. Likewise, jobs that are executed in server i and complete service before si units of time, leave the system, whereas jobs that do not complete are killed and routed to the next server. We first study the stability of such system and provide a precise utilization threshold for the existence of stable parameters for a given job size distribution. We compute the threshold for several families of distributions and provide bounds for others. We show that TAGS is most stable for bounded Pareto distributions with parameter α=1. Besides, we provide tight bounds on the performance of the TAGS policy where the cutoffs are chosen to minimize average waiting time in the asymptotic regime where the largest job size tends to infinity for the Bounded Pareto distribution and the system load smaller than one. In this case, we show that the performance ratio between TAGS and a version called SITA which does require knowledge of job size is at most 2. We then consider more broadly the same asymptotic regime and consider a bound on the average waiting time for any distribution. This is compatible with having a conservative policy which will work well for any job size distribution. We show rather tight upper and lower bounds which again match those of SITA up to a factor of 2. These bounds are considerably lower than the corresponding bounds of competing policies such as Random or Least Work Remaining. We also show that for all these policies the bounded Pareto distribution with α=1 is close to being the worst possible among all distributions with the same job size range. We show using the stability results that in the same regime, if we increase the load the gap between SITA and TAGS grows dramatically and eventually, the TAGS system cannot be stabilized. The conclusion from all our analysis is that TAGS is best used as a conservative policy with minimal requirements on small systems with relatively low utilization and where the range of job sizes is large.

Restoring the product variety and pro-competitive gains from trade with heterogeneous firms and bounded productivity

The monopolistic competition model in international trade offers three sources of gains from trade beyond that of traditional comparative advantage: an endogenous expansion in product variety; a pro-competitive reduction in the markups charged by firms; and the self-selection of more efficient firms into exporting. Recent literature on trade with heterogeneous firms has emphasized the third of these effects, while the first two effects are ruled out when using a Pareto distribution for productivity with a support that is unbounded above, and no fixed costs. The goal of this paper is to restore a theoretical role for product variety and pro-competitive gains from trade by using a bounded Pareto distribution for productivity, and to demonstrate their empirical importance. For the U.S. economy over 1992–2005, we find that product variety and the reduction in markups jointly contribute about 75% to the increase in welfare resulting from trade expansion, whereas an upper bound to the selection effect is that it contributes the remaining 25% to the increase in U.S. welfare.

Behavioral Heterogeneity: Pareto Distributions of Homothetic Preference Scales and Aggregate Expenditures Income Elasticities

We evaluate the income elasticity of the aggregate budget share spent on a sub-group of commodities, in a competitive framework, by a continuum of agents having the same income, but heterogeneous behavior described by an homothetic preferences scaling having a bounded Pareto distribution in the population. If individual budget share increases globally significantly in the limit from low to large incomes, aggregate budget share is locally increasing with medium range incomes when the logarithm of the heterogeneity factor has an increasing (exponential) density with a large support. Aggregate income elasticity converges to that exponential density parameter when its support becomes infinitely large. Symmetric results hold in the decreasing case. Applications are made to market expenditures, wealth effects on portfolio choice with many risky assets, concave expenditures, that are compatible with standard (expected) utility maximization or other behavioral decision making processes.

Efficiency in the Worst Production Situation Using Data Envelopment Analysis

Data envelopment analysis (DEA) measures relative efficiency among the decision making units (DMU) without considering noise in data. The least efficient DMU indicates that it is in the worst situation. In this paper, we measure efficiency of individual DMU whenever it losses the maximum output, and the efficiency of other DMUs is measured in the observed situation. This efficiency is the minimum efficiency of a DMU. The concept of stochastic data envelopment analysis (SDEA) is a DEA method which considers the noise in data which is proposed in this study. Using bounded Pareto distribution, we estimate the DEA efficiency from efficiency interval. Small value of shape parameter can estimate the efficiency more accurately using the Pareto distribution. Rank correlations were estimated between observed efficiencies and minimum efficiency as well as between observed and estimated efficiency. The correlations are indicating the effectiveness of this SDEA model.

Comparative evaluation of contiguous allocation strategies on 3D mesh multicomputers

The performance of contiguous allocation strategies can be significantly affected by the type of the distribution adopted for job execution times. In this paper, the performance of the existing contiguous allocation strategies for 3D mesh multicomputers is re-visited in the context of heavy-tailed distributions (e.g., a Bounded Pareto distribution). The strategies are evaluated and compared using simulation experiments for both First-Come-First-Served (FCFS) and Shortest-Service-Demand (SSD) scheduling strategies under a variety of system loads and system sizes. The results show that the performance of the allocation strategies degrades considerably when job execution times follow a heavy-tailed distribution. Moreover, SSD copes much better than FCFS scheduling strategy in the presence of heavy-tailed job execution times. The results also reveal that allocation strategies that employ a list of allocated sub-meshes for both allocation and de-allocation exhibit low allocation overhead, and maintain good system performance in terms of average turnaround time and mean system utilization.

Robust Processing Rate Allocation for Proportional Slowdown Differentiation on Internet Servers

A desirable behavior of an Internet server is that a request's queuing delay depends on its service time in a linear fashion. Measuring the quality of service in terms of slowdown, the ratio of a request's queuing delay to its service time, provides a simple way to attain the objective. Moreover, it treats client requests equally regardless of their service time, whereas response time favors requests that need more processing resources. In this paper, we propose a proportional slowdown differentiation (PSD) service model on Internet servers. It aims to maintain prespecified slowdown ratios between different classes of client requests. To provide PSD services, we first derive a closed-form expression of the expected slowdown in an M/G/1 FCFS queuing system with a typical heavy-tailed service time distribution, the bounded Pareto distribution. Based on the closed-form expression, we design a queuing-theoretic strategy of processing-rate allocation. The rate allocation is realized by deploying a virtual server for each class. Simulation results show that the strategy can provide controllable PSD services on Internet servers. It, however, comes along with large variance and weak predictability due to the dynamics of Internet traffic. To address these issues, we design an integral feedback controller and integrate it into the queuing-theoretic strategy. Simulation results demonstrate that the integrated strategy is robust and can deliver predictable PSD services at a superior fine-grained level. We modified the Apache Web server with an implementation of the integrated processing-rate allocation strategy. Experimental results further demonstrate its effectiveness and feasibility in practice.