On the Statistical Multiplexing Gain of Virtual Base Station Pools

Facing the explosion of mobile data traffic, cloud radio access network (C-RAN) is proposed recently to overcome the efficiency and flexibility problems with the traditional RAN architecture by centralizing baseband processing. However, there lacks a mathematical model to analyze the statistical multiplexing gain from the pooling of virtual base stations (VBSs) so that the expenditure on fronthaul networks can be justified. In this paper, we address this problem by capturing the session-level dynamics of VBS pools with a multi-dimensional Markov model. This model reflects the constraints imposed by both radio resources and computational resources. To evaluate the pooling gain, we derive a product-form solution for the stationary distribution and give a recursive method to calculate the blocking probabilities. For comparison, we also derive the limit of resource utilization ratio as the pool size approaches infinity. Numerical results show that VBS pools can obtain considerable pooling gain readily at medium size, but the convergence to large pool limit is slow because of the quickly diminishing marginal pooling gain. We also find that parameters such as traffic load and desired Quality of Service (QoS) have significant influence on the performance of VBS pools.Comment: Accepted by GlobeCom'1

Feat: Functional Enumeration of Algebraic Types

In mathematics, an enumeration of a set S is a bijective function from (an initial segment of) the natural numbers to S. We define "functional enumerations" as efficiently computable such bijections. This paper describes a theory of functional enumeration and provides an algebra of enumerations closed under sums, products, guarded recursion and bijections. We partition each enumerated set into numbered, finite subsets. We provide a generic enumeration such that the number of each part corresponds to the size of its values (measured in the number of constructors). We implement our ideas in a Haskell library called testing-feat, and make the source code freely available. Feat provides efficient "random access" to enumerated values. The primary application is property-based testing, where it is used to define both random sampling (for example QuickCheck generators) and exhaustive enumeration (in the style of SmallCheck). We claim that functional enumeration is the best option for automatically generating test cases from large groups of mutually recursive syntax tree types. As a case study we use Feat to test the pretty-printer of the Template Haskell library (uncovering several bugs)

On the enumeration of closures and environments with an application to random generation

Environments and closures are two of the main ingredients of evaluation in lambda-calculus. A closure is a pair consisting of a lambda-term and an environment, whereas an environment is a list of lambda-terms assigned to free variables. In this paper we investigate some dynamic aspects of evaluation in lambda-calculus considering the quantitative, combinatorial properties of environments and closures. Focusing on two classes of environments and closures, namely the so-called plain and closed ones, we consider the problem of their asymptotic counting and effective random generation. We provide an asymptotic approximation of the number of both plain environments and closures of size $n$. Using the associated generating functions, we construct effective samplers for both classes of combinatorial structures. Finally, we discuss the related problem of asymptotic counting and random generation of closed environemnts and closures