Edge computing in the Internet of Things brings applications and content closer to the users by introducing an additional computational layer at the network infrastructure, between cloud and the resource-constrained data producing devices and user equipment. This way, the opportunistic nature of the operational environment is addressed by introducing computational power in location with low latency and high bandwidth. However, location-aware deployment of edge computing infrastructure requires careful placement scheme for edge servers. To provide the best possible Quality of Service for the user applications, their proximity needs to be optimized. Moreover, the deployment faces practical limitations in budget limitations, hardware requirements of servers and in online load balancing between servers. To address these challenges, we formulate the edge server placement as a capacitated location-allocation problem, while minimizing the distance between servers and access points of a real city-wide Wi-Fi network deployment. In our algorithm, we utilize both upper and lower server capacity constraints for load balancing. Furthermore, we enable sharing of workload between servers to facilitate deployments with low capacity servers. The performance of the algorithm is demonstrated in placement scenarios, exemplified by high capacity servers for edge computing and low capacity servers for Fog computing, with different parameters in a real-world data set. The data set consists of both dense deployment of access points in central areas, but also sparse deployment in suburban areas within the same network infrastructure. In comparison, we show that previous approaches do not sufficiently address such deployment. The presented algorithm is able to provide optimal placements that minimize the distances and provide balanced workload with sharing by following the capacity constraints.
To maintain the sufficient QoS within the budget limitations, two main approaches were used for determining the required number of servers. First, a tolerated distance from server was decided and the number of servers was minimized given that the distance constraint is met for each access point @cite_15 @cite_30 @cite_2 . Second, the number of servers was based on budget and servers were placed so that the best proximity is obtained @cite_24 @cite_49 @cite_20 @cite_14 @cite_11 . A third approach was to minimize the distance while penalizing for the number of servers @cite_16 .
@cite_30 @cite_14 @cite_24 @cite_49 @cite_2 @cite_15 @cite_16 @cite_20 @cite_11
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In a Content Distribution Network application, we have a set of servers and a set of clients to be connected to the servers. Often there are a few server types and a hard budget constraint on the number of deployed servers of each type. The simplest goal here is to deploy a set of servers subject to these budget constraints in order to minimize the sum of client connection costs. These connection costs often satisfy metricity, since they are typically proportional to the distance between a client and a server within a single autonomous system. A special case of the problem where there is only one server type is the well-studied k-median problem. In this paper, we consider the problem with two server types and call it the budgeted red-blue median problem. We show, somewhat surprisingly, that running a single-swap local search for each server type simultaneously, yields a constant factor approximation for this case. Its analysis is however quite non-trivial compared to that of the k-median problem (, 2004; Gupta and Tangwongsan, 2008). Later we show that the same algorithm yields a constant approximation for the prize-collecting version of the budgeted red-blue median problem where each client can potentially be served with an alternative cost via a different vendor. In the process, we also improve the approximation factor for the prize-collecting k-median problem from 4 (, 2001) to 3+e, which matches the current best approximation factor for the k-median problem. In a Content Distribution Network (CDN), there are m servers storing the data; each of them has a specific bandwidth. All the requests from a particular client should be assigned to one server because of the routing protocol used. The goal is to minimize the total cost of these assignments—cost of each is proportional to the distance between the client and the server as well as the request size—while the load on each server is kept below its bandwidth limit. When each server also has a setup cost, this is an unsplittable hard-capacitated facility location problem. As much attention as facility location problems have received, there has been no nontrivial approximation algorithm when we have hard capacities (i.e., there can only be one copy of each facility whose capacity cannot be violated) and demands are unsplittable (i.e., all the demand from a client has to be assigned to a single facility). We observe it is NP-hard to approximate the cost to within any bounded factor in this case. Thus, for an arbitrary constant e>0, we relax the capacities to a 1+e factor. For the case where capacities are almost uniform, we give a bicriteria O(log n, 1+e)-approximation algorithm for general metrics and a (1+e, 1+e)-approximation algorithm for tree metrics. A bicriteria (α,β)-approximation algorithm produces a solution of cost at most α times the optimum, while violating the capacities by no more than a β factor. We can get the same guarantees for nonuniform capacities if we allow quasipolynomial running time. In our algorithm, some clients guess the facility they are assigned to, and facilities decide the size of the clients they serve. A straightforward approach results in exponential running time. When costs do not satisfy metricity, we show that a 1.5 violation of capacities is necessary to obtain any approximation. It is worth noting that our results generalize bin packing (zero connection costs and facility costs equal to one), knapsack (single facility with all costs being zero), minimum makespan scheduling for related machines (all connection costs being zero), and some facility location problems. Abstract We consider the problem of placing a specified number ( p ) of facilities on the nodes of a network so as to minimize some measure of the distances between facilities. This type of problem models a number of problems arising in facility location, statistical clustering, pattern recognition, and processor allocation problems in multiprocessor systems. We consider the problem under three different objectives, namely minimizing the diameter, minimizing the average distance, and minimizing the variance. We observe that, in general, the problem is NP -hard under any of the objectives. Further, even obtaining a constant factor approximation for any of the objectives is NP -hard. We present a general framework for obtaining near-optimal solutions to the compact location problems for the above measures, when the distances satisfy the triangle inequality. We show that this framework can be extended to the case when there are also node weights. Further, we investigate the complexity and approximability of more general versions of these problems, where two distance values are specified for each pair of potential sites. In these cases, the goal is to a select a specified number of facilities to minimize a function of one distance metric subject to a budget constraint on the other distance metric. We present algorithms that provide solutions which are within a small constant factor of the objective value while violating the budget constraint by only a small constant factor. Wireless networks are increasingly used to carry applications with QoS constraints. Two problems arise when dealing with traffic with QoS constraints. One is admission control, which consists of determining whether it is possible to fulfill the demands of a set of clients. The other is finding an optimal scheduling policy to meet the demands of all clients. In this paper, we propose a framework for jointly addressing three QoS criteria: delay, delivery ratio, and channel reliability. We analytically prove the necessary and sufficient condition for a set of clients to be feasible with respect to the above three criteria. We then establish an efficient algorithm for admission control to decide whether a set of clients is feasible. We further propose two scheduling policies and prove that they are feasibility optimal in the sense that they can meet the demands of every feasible set of clients. In addition, we show that these policies are easily implementable on the IEEE 802.11 mechanisms. We also present the results of simulation studies that appear to confirm the theoretical studies and suggest that the proposed policies outperform others tested under a variety of settings.