Service Provisioning for Multi-source IoT Applications in Mobile Edge Computing

We are embracing an era of Internet of Things (IoT). The latency brought by unstable wireless networks caused by limited resources of IoT devices seriously impacts the quality of services of users, particularly the service delay they experienced. Mobile Edge Computing (MEC) technology provides promising solutions to delay-sensitive IoT applications, where cloudlets (edge servers) are co-located with wireless access points in the proximity of IoT devices. The service response latency for IoT applications can be significantly shortened due to that their data processing can be performed in a local MEC network. Meanwhile, most IoT applications usually impose Service Function Chain (SFC) enforcement on their data transmission, where each data packet from its source gateway of an IoT device to the destination (a cloudlet) of the IoT application must pass through each Virtual Network Function (VNF) in the SFC in an MEC network. However, little attention has been paid on such a service provisioning of multi-source IoT applications in an MEC network with SFC enforcement. In this article, we study service provisioning in an MEC network for multi-source IoT applications with SFC requirements and aiming at minimizing the cost of such service provisioning, where each IoT application has multiple data streams from different sources to be uploaded to a location (cloudlet) in the MEC network for aggregation, processing, and storage purposes. To this end, we first formulate two novel optimization problems: the cost minimization problem of service provisioning for a single multi-source IoT application, and the service provisioning problem for a set of multi-source IoT applications, respectively, and show that both problems are NP-hard. Second, we propose a service provisioning framework in the MEC network for multi-source IoT applications that consists of uploading stream data from multiple sources of the IoT application to the MEC network, data stream aggregation and routing through the VNF instance placement and sharing, and workload balancing among cloudlets. Third, we devise an efficient algorithm for the cost minimization problem built upon the proposed service provisioning framework, and further extend the solution for the service provisioning problem of a set of multi-source IoT applications. We finally evaluate the performance of the proposed algorithms through experimental simulations. Simulation results demonstrate that the proposed algorithms are promising.

Finding a Home: Stopping Theory and Its Application to Home Range Establishment in a Novel Environment

Familiarity with the landscape increases foraging efficiency and safety. Thus, when animals are confronted with a novel environment, either by natural dispersal or translocation, establishing a home range becomes a priority. While the search for a home range carries a cost of functioning in an unfamiliar environment, ceasing the search carries a cost of missed opportunities. Thus, when to establish a home range is essentially a weighted sum of a two-criteria cost-minimization problem. The process is predominantly heuristic, where the animal must decide how to study the environment and, consequently, when to stop searching and establish a home range in a manner that will reduce the cost and maximize or at least satisfice its fitness. These issues fall within the framework of optimal stopping theory. In this paper we review stopping theory and three stopping rules relevant to home range establishment: the best-of-n rule, the threshold rule, and the comparative Bayes rule. We then describe how these rules can be distinguished from movement data, hypothesize when each rule should be practiced, and speculate what and how environmental factors and animal attributes affect the stopping time. We provide a set of stopping-theory-related predictions that are testable within the context of translocation projects and discuss some management implications.

A Pollution Sensitive Fuzzy EPQ Model With Endogenous Reliability and Product Deterioration Under Lock Fuzzy Game Theoretic Approach

This article deals with a cost minimization objective function of an economic production quantity (EPQ) inventory model with production breakdown and deterioration. The process reliability and the environmental pollution due to over production have also been considered. The model has been split into two different scenarios according to the breaking time before and after the production period. In scenario 1, no machinery failure occurs during production run time and that of scenario 2 the failure occurs during production run time. We develop a deterministic cost minimization problem first then we fuzzify the model by considering the production rate, the demand rate and all the cost components as lock fuzzy numbers. We convert the fuzzy model into equivalent game problem by considering Gaussian normal strategic probabilities. The model has been solved with the help of different key vectors employed by the decision maker. We have shown that the value of the game might be changed with the change of different key vectors. A comparative study has been made with the numerical results of the general fuzzy and crisp models. Finally, graphical illustrations and sensitivity analysis have been done followed by a conclusion.

Dynamic Decision Making, Distance Functions, and Productive Efficiency

This chapter discusses three concepts of the directional distance function in the presence of internal adjustment costs, designated as adjustment cost directional distance functions. These functions are the building blocks of technical inefficiency measures. Duality between an adjustment cost directional distance function and an indirect optimal value function allows the construction of economic measures of inefficiency. Duality is established between the adjustment cost directional input function and the optimal current value function of the intertemporal cost minimization problem. From this dual relation, a dynamic cost inefficiency measure is derived and decomposed into technical inefficiency and allocative inefficiency. Similarly, dynamic input-output measures of inefficiency are derived from the adjustment cost directional technology distance function and duality between this function and the current profit function.

On the uniqueness of the solution of the cost minimization problem with generalized Sato production function

Whenever a firm is maximizing its profit, it necessarily has to minimize its cost. Thus, the cost minimization problem is one of the central problems in the theory of the firm. When presenting this problem, the majority of microeconomic textbooks use very well-known production functions, such as Leontief, Cobb-Douglas, or other CES production functions. The goal of this paper is to analyze the cost minimization problem with the generalized Sato production function. The generalized Sato production function is one of the non-standard production functions with variable elasticity of substitution. First, we show that the generalized Sato production function is continuous, strictly monotone, strictly quasiconcave and that a positive amount of output requires positive amounts of some of the inputs. Next, by using mathematical programming we show that the cost minimization problem with generalized Sato production function has a unique solution. This result is very important since it implies the existence of the corresponding cost function and conditional input demands.

PEMROGRAMAN LINEAR INTEGER DENGAN ENAM VARIABEL ORIENTASI KARGO UNTUK MASALAH MINIMISASI BIAYA PEMUATAN MULTI-KONTAINER

Penelitian ini bertujuan untuk mengembangkan model matematika untuk masalah minimisasi biaya pemuatan multi-kontainer dengan enam variabel orientasi kargo. Masalah ini dirumuskan sebagai model pemrograman linier biner integer untuk meminimalkan biaya. Faktor-faktor yang dipertimbangkan dalam formulasi termasuk alokasi kargo, lokasi kargo, hubungan kargo, dan orientasi kargo. Sedangkan, biaya yang dipertimbangkan termasuk biaya muatan volume kontainer ke kargo dan biaya transportasi kargo ke kontainer. Validasi model dilakukan melalui percobaan numerik pada ukuran kecil kargo dan kontainer. Hasil penelitian menunjukkan bahwa model dengan konsep orientasi kargo yang dikembangkan dapat menyelesaikan masalah sesuai dengan parameter numerik yang diberikan. Abstract[Integer Linear Programming with Six Cargo Orientation Variables for Multi-Container Loading Cost Minimization Problem] This research aims to develop the mathematic model for multi-container loading cost minimization problems with six cargo orientation variables. The problem is formulated as a binary integer linear programming model to minimize costs. The factors considered in the formulation include cargo allocation, cargo location, cargo relations, and cargo orientation. Whereas, the costs considered include the container volume load cost to cargo and the cargo transport cost to the container. Model validation is performed through numerical experiments on the small size of cargo and containers. The results show that the model with developed cargo orientation concept can solve the problem according to the given numerical parameters.Keywords: integer programming; cargo orientation; container loading; cost minimization

Efficient Black-Box Reductions for Separable Cost Sharing

In cost-sharing games with delays, a set of agents jointly uses a subset of resources. Each resource has a fixed cost that has to be shared by the players, and each agent has a nonshareable player-specific delay for each resource. A separable cost-sharing protocol determines cost shares that are budget-balanced, separable, and guarantee existence of pure Nash equilibria (PNE). We provide black-box reductions reducing the design of such a protocol to the design of an approximation algorithm for the underlying cost-minimization problem. In this way, we obtain separable cost-sharing protocols in matroid games, single-source connection games, and connection games on n-series-parallel graphs. All these reductions are efficiently computable - given an initial allocation profile, we obtain a cheaper profile and separable cost shares turning the profile into a PNE. Hence, in these domains, any approximation algorithm yields a separable cost-sharing protocol with price of stability bounded by the approximation factor.

STEADY-STATE OPTIMIZATION OF AN EXHAUSTIVE LÉVY STORAGE PROCESS WITH INTERMITTENT OUTPUT AND RANDOM OUTPUT RATE

Consider a regenerative storage process with a nondecreasing Lévy input (subordinator) such that every cycle may be split into two periods. In the first (off), the output is shut off and the workload accumulates. This continues until some stopping time. In the second (on), the process evolves like a subordinator minus a positive drift (output rate) until it hits the origin. In addition, we assume that the output rate of every on period is a random variable, which is determined at the beginning of this period. For example, at each period, the output rate may depend on the workload level at the beginning of the corresponding busy period. We derive the Laplace–Stieltjes transform of the steady-state distribution of the workload process and then apply this result to solve a steady-state cost minimization problem with holding, setup and output capacity costs. It is shown that the optimal output rate is a nondecreasing deterministic function of the workload level at the beginning of the corresponding on period.