Delay Performance of MISO Wireless Communications

Ultra-reliable, low latency communications (URLLC) are currently attracting significant attention due to the emergence of mission-critical applications and device-centric communication. URLLC will entail a fundamental paradigm shift from throughput-oriented system design towards holistic designs for guaranteed and reliable end-to-end latency. A deep understanding of the delay performance of wireless networks is essential for efficient URLLC systems. In this paper, we investigate the network layer performance of multiple-input, single-output (MISO) systems under statistical delay constraints. We provide closed-form expressions for MISO diversity-oriented service process and derive probabilistic delay bounds using tools from stochastic network calculus. In particular, we analyze transmit beamforming with perfect and imperfect channel knowledge and compare it with orthogonal space-time codes and antenna selection. The effect of transmit power, number of antennas, and finite blocklength channel coding on the delay distribution is also investigated. Our higher layer performance results reveal key insights of MISO channels and provide useful guidelines for the design of ultra-reliable communication systems that can guarantee the stringent URLLC latency requirements.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Stochastic Analysis of a Churn-Tolerant Structured Peer-to-Peer Scheme

We present and analyze a simple and general scheme to build a churn (fault)-tolerant structured Peer-to-Peer (P2P) network. Our scheme shows how to "convert" a static network into a dynamic distributed hash table(DHT)-based P2P network such that all the good properties of the static network are guaranteed with high probability (w.h.p). Applying our scheme to a cube-connected cycles network, for example, yields a $O(\log N)$ degree connected network, in which every search succeeds in $O(\log N)$ hops w.h.p., using $O(\log N)$ messages, where $N$ is the expected stable network size. Our scheme has an constant storage overhead (the number of nodes responsible for servicing a data item) and an $O(\log N)$ overhead (messages and time) per insertion and essentially no overhead for deletions. All these bounds are essentially optimal. While DHT schemes with similar guarantees are already known in the literature, this work is new in the following aspects: (1) It presents a rigorous mathematical analysis of the scheme under a general stochastic model of churn and shows the above guarantees; (2) The theoretical analysis is complemented by a simulation-based analysis that validates the asymptotic bounds even in moderately sized networks and also studies performance under changing stable network size; (3) The presented scheme seems especially suitable for maintaining dynamic structures under churn efficiently. In particular, we show that a spanning tree of low diameter can be efficiently maintained in constant time and logarithmic number of messages per insertion or deletion w.h.p. Keywords: P2P Network, DHT Scheme, Churn, Dynamic Spanning Tree, Stochastic Analysis

Efficient Gauss Elimination for Near-Quadratic Matrices with One Short Random Block per Row, with Applications

In this paper we identify a new class of sparse near-quadratic random Boolean matrices that have full row rank over F_2 = {0,1} with high probability and can be transformed into echelon form in almost linear time by a simple version of Gauss elimination. The random matrix with dimensions n(1-epsilon) x n is generated as follows: In each row, identify a block of length L = O((log n)/epsilon) at a random position. The entries outside the block are 0, the entries inside the block are given by fair coin tosses. Sorting the rows according to the positions of the blocks transforms the matrix into a kind of band matrix, on which, as it turns out, Gauss elimination works very efficiently with high probability. For the proof, the effects of Gauss elimination are interpreted as a ("coin-flipping") variant of Robin Hood hashing, whose behaviour can be captured in terms of a simple Markov model from queuing theory. Bounds for expected construction time and high success probability follow from results in this area. They readily extend to larger finite fields in place of F_2. By employing hashing, this matrix family leads to a new implementation of a retrieval data structure, which represents an arbitrary function f: S -> {0,1} for some set S of m = (1-epsilon)n keys. It requires m/(1-epsilon) bits of space, construction takes O(m/epsilon^2) expected time on a word RAM, while queries take O(1/epsilon) time and access only one contiguous segment of O((log m)/epsilon) bits in the representation (O(1/epsilon) consecutive words on a word RAM). The method is readily implemented and highly practical, and it is competitive with state-of-the-art methods. In a more theoretical variant, which works only for unrealistically large S, we can even achieve construction time O(m/epsilon) and query time O(1), accessing O(1) contiguous memory words for a query. By well-established methods the retrieval data structure leads to efficient constructions of (static) perfect hash functions and (static) Bloom filters with almost optimal space and very local storage access patterns for queries

On the waiting time of arriving aircrafts and the capacity of airports with one or two runways

In this paper we examine a model for the landing procedure of aircrafts at an airport. The characteristic feature here is that due to air turbulence the safety distance between two landing aircrafts depends on the types of these two machines. Hence, an eficient routing of the aircraft to two runways may reduce their waiting time. First, we use M/SM/1 queues (with dependent service times) to model a single runway. We give the stability condition and a formula for the average waiting time of the aircrafts. Moreover, we derive easy to compute bounds on the waiting times by comparison to simpler queuing systems. In particular we study the effect of neglecting the dependency of the service times when using M/G/1-models. We then consider the case of two runways with a number of heuristic routing strategies such as coin flipping, type splitting, Round Robin and variants of the join-the-least-load rule. These strategies are analyzed and compared numerically with respect to the average delay they cause. It turns out that a certain modication of join-the-least-load gives the best results