Recent advances in Internet technologies have led to the proliferation of new distributed applications in the transportation, healthcare, mining, security, and entertainment sectors. The emerging applications have characteristics such as being bandwidth-hungry, latency-critical, and applications with a user population contained within a limited geographical area, and require high availability, low jitter, and security.

One way of addressing the challenges arising because of these emerging applications, is to move the computing capabilities closer to the end-users, at the logical edge of a network, in order to improve the performance, operating cost, and reliability of applications and services. These distributed new resources and software stacks, situated on the path between today's centralized data centers and devices in close proximity to the last mile network, are known as Mobile Edge Clouds (MECs). The distributed MECs provides new opportunities for the management of compute resources and the allocation of applications to those resources in order to minimize the overall cost of application deployment while satisfying end-user demands in terms of application performance.

However, these opportunities also present three significant challenges. The first challenge is where and how much computing resources to deploy along the path between today's centralized data centers and devices for cost-optimal operations. The second challenge is where and how much resources should be allocated to which applications to meet the applications' performance requirements while minimizing operational costs. The third challenge is how to provide a framework for application deployment on resource-constrained IoT devices in heterogeneous environments.

This thesis addresses the above challenges by proposing several models, algorithms, and simulation and software frameworks. In the first part, we investigate methods for early detection of short-lived and significant increase in demand for computing resources (also called spikes) which may cause significant degradation in the performance of a distributed application. We make use of adaptive signal processing techniques for early detection of spikes. We then consider trade-offs between parameters such as the time taken to detect a spike and the number of false spikes that are detected. In the second part, we study the resource planning problem where we study the cost benefits of adding new compute resources based on performance requirements for emerging applications. In the third part, we study the problem of allocating resources to applications by formulating as an optimization problem, where the objective is to minimize overall operational cost while meeting the performance targets of applications. We also propose a hierarchical scheduling framework and policies for allocating resources to applications based on performance metrics of both applications and compute resources. In the last part, we propose a framework, Calvin Constrained, for resource-constrained devices, which is an extension of the Calvin framework and supports a limited but essential subset of the features of the reference framework taking into account the limited memory and processing power of the resource-constrained IoT devices.