Backlog and Delay Reasoning in HARQ Systems

Recently, hybrid-automatic-repeat-request (HARQ) systems have been favored in particular state-of-the-art communications systems since they provide the practicality of error detections and corrections aligned with repeat-requests when needed at receivers. The queueing characteristics of these systems have taken considerable focus since the current technology demands data transmissions with a minimum delay provisioning. In this paper, we investigate the effects of physical layer characteristics on data link layer performance in a general class of HARQ systems. Constructing a state transition model that combines queue activity at a transmitter and decoding efficiency at a receiver, we identify the probability of clearing the queue at the transmitter and the packet-loss probability at the receiver. We determine the effective capacity that yields the maximum feasible data arrival rate at the queue under quality-of-service constraints. In addition, we put forward non-asymptotic backlog and delay bounds. Finally, regarding three different HARQ protocols, namely Type-I HARQ, HARQ-chase combining (HARQ-CC) and HARQ-incremental redundancy (HARQ-IR), we show the superiority of HARQ-IR in delay robustness over the others. However, we further observe that the performance gap between HARQ-CC and HARQ-IR is quite negligible in certain cases. The novelty of our paper is a general cross-layer analysis of these systems, considering encoding/decoding in the physical layer and delay aspects in the data-link layer

Local Uniqueness of the Circular Integral Invariant

This article is concerned with the representation of curves by means of integral invariants. In contrast to the classical differential invariants they have the advantage of being less sensitive with respect to noise. The integral invariant most common in use is the circular integral invariant. A major drawback of this curve descriptor, however, is the absence of any uniqueness result for this representation. This article serves as a contribution towards closing this gap by showing that the circular integral invariant is injective in a neighbourhood of the circle. In addition, we provide a stability estimate valid on this neighbourhood. The proof is an application of Riesz-Schauder theory and the implicit function theorem in a Banach space setting

Understanding Fairness and its Impact on Quality of Service in IEEE 802.11

The Distributed Coordination Function (DCF) aims at fair and efficient medium access in IEEE 802.11. In face of its success, it is remarkable that there is little consensus on the actual degree of fairness achieved, particularly bearing its impact on quality of service in mind. In this paper we provide an accurate model for the fairness of the DCF. Given M greedy stations we assume fairness if a tagged station contributes a share of 1/M to the overall number of packets transmitted. We derive the probability distribution of fairness deviations and support our analytical results by an extensive set of measurements. We find a closed-form expression for the improvement of long-term over short-term fairness. Regarding the random countdown values we quantify the significance of their distribution whereas we discover that fairness is largely insensitive to the distribution parameters. Based on our findings we view the DCF as emulating an ideal fair queuing system to quantify the deviations from a fair rate allocation. We deduce a stochastic service curve model for the DCF to predict packet delays in IEEE 802.11. We show how a station can estimate its fair bandwidth share from passive measurements of its traffic arrivals and departures

Routing in turn-prohibition based feed-forward networks

Abstract. The application of queuing theory to communications systems often requires that the respective networks are of a feed-forward nature, that is they have to be free of cyclic dependencies. An effective way to ensure this property is to identify a certain set of critical turns and to prohibit their use. A turn is a concatenation of two adjacent, consecutive links. Unfortunately, current routing algorithms are usually not equipped to handle forbidden turns and the required extensions are nontrivial. We discuss the relevant issues for the example of the widely deployed Dijkstra algorithm. Then, we address the general case and introduce the Turnnet concept, which supports arbitrary combinations of routing algorithms with turn-prohibiting feed-forward mechanisms