arXiv subjects

Tony T. Lee

Publications and source records attributed to Tony T. Lee.

24 records · Page 2Linked to original sources

arXiv2009

Buffered Aloha with K-Exponential Backoff -- Part II: Delay Analysis

This paper presents the delay analysis for buffered Aloha networks with K-Exponential Backoff. Mean access delay and mean queueing delay are derived and demonstrated via the examples of Geometric Retransmission (K=1) and Exponential Backoff (K=infinity). The comparison shows that higher delay is incurred with Geometric Retransmission when the aggregate input rate is small, and the delay gap is enlarged as the number of nodes n increases. With a high traffic input rate, however, the delay performance with Exponential Backoff severely deteriorates. The mean queueing delay will be unbounded if the aggregate input rate exceeds 0.3. We also extend the analysis to the contention-window-based backoff model which is widely adopted in practical MAC protocols. It will be revealed that both the retransmission-probability-based and the contention-window-based models exhibit the same stable region and achieve similar queueing performance in most cases, which justifies the intuition that was taken but remained unverified in previous studies: the retransmission-probability-based backoff model can serve as a good approximation of the contention-window-based one.

cs.NI↗

arXiv2008

Throughput and Delay Analysis of Wireless Random Access Networks

This paper studies the network throughput and transport delay of a multihop wireless random access network based on a Markov renewal model of packet transportation. We show that the distribution of the source-to-destination (SD) distance plays a critical role in characterizing network performance. We establish necessary and sufficient condition on the SD distance for scalable network throughput, and address the optimal rate allocation issue with fairness and the QoS requirements taken into consideration. In respect to the end-to-end performance, the transport delay is explored in this paper along with network throughput. We characterize the transport delay by relating it to nodal queueing behavior and the SD-distance distribution; the former is a local property while the latter is a global property. In addition, we apply the large deviation theory to derive the tail distribution of transport delay. To put our theory into practical network operation, several traffic scaling laws are provided to demonstrate how network scalability can be achieved by localizing the traffic pattern, and a leaky bucket scheme at the network access is proposed for traffic shaping and flow control.

cs.NI↗

arXiv2008

Stability and Throughput of Buffered Aloha with Backoff

This paper studies the buffered Aloha with K-exponential backoff collision resolution algorithms. The buffered Aloha network is modeled as a multi-queue single-server system. We adopt a widely used approach in packet switching systems to decompose the multi-queue system into independent first-in-first-out (FIFO) queues, which are hinged together by the probability of success of head-of-line (HOL) packets. A unified method is devised to tackle the stability and throughput problems of K-exponential backoff with any cutoff phase K. For networks with a finite number of nodes, we show that the K-exponential backoff is stable if the retransmission factor is properly chosen from the stable region. The maximum stable throughput is derived and demonstrated via examples of geometric retransmission (K=1) and exponential backoff (K=infinity). For networks with an infinite number of nodes, we show that geometric retransmission is unstable, and the stable network throughput of exponential backoff can only be achieved at the cost of potential unbounded delay in each input queue. Furthermore, we address the stability issue of the systems at the undesired stable point. All analytical results presented in this paper are verified and confirmed by simulations.

cs.NI↗

arXiv2006

The Mathematical Parallels Between Packet Switching and Information Transmission

All communication networks comprise of transmission systems and switching systems, even though they are usually treated as two separate issues. Communication channels are generally disturbed by noise from various sources. In circuit switched networks, reliable communication requires the error-tolerant transmission of bits over noisy channels. In packet switched networks, however, not only can bits be corrupted with noise, but resources along connection paths are also subject to contention. Thus, quality of service (QoS) is determined by buffer delays and packet losses. The theme of this paper is to show that transmission noise and packet contention actually have similar characteristics and can be tamed by comparable means to achieve reliable communication, and a number of analogies between switching and transmission are identified. The sampling theorem of bandlimited signals provides the cornerstone of digital communication and signal processing. Recently, the Birkhoff-von Neumann decomposition of traffic matrices has been widely applied to packet switches. With respect to the complexity reduction of packet switching, we show that the decomposition of a doubly stochastic traffic matrix plays a similar role to that of the sampling theorem in digital transmission. We conclude that packet switching systems are governed by mathematical laws that are similar to those of digital transmission systems as envisioned by Shannon in his seminal 1948 paper, A Mathematical Theory of Communication.

cs.IT↗

arXiv2006

A Relational Approach to Functional Decomposition of Logic Circuits

Functional decomposition of logic circuits has profound influence on all quality aspects of the cost-effective implementation of modern digital systems. In this paper, a relational approach to the decomposition of logic circuits is proposed. This approach is parallel to the normalization of relational databases, they are governed by the same concepts of functional dependency (FD) and multi-valued dependency (MVD). It is manifest that the functional decomposition of switching function actually exploits the same idea and serves a similar purpose as database normalization. Partitions play an important role in the decomposition. The interdependency of two partitions can be represented by a bipartite graph. We demonstrate that both FD and MVD can be represented by bipartite graphs with specific topological properties, which are delineated by partitions of minterms. It follows that our algorithms are procedures of constructing those specific bipartite graphs of interest to meet the information-lossless criteria of functional decomposition.

cs.DM↗

arXiv2006

Crosstalk-free Conjugate Networks for Optical Multicast Switching

High-speed photonic switching networks can switch optical signals at the rate of several terabits per second. However, they suffer from an intrinsic crosstalk problem when two optical signals cross at the same switch element. To avoid crosstalk, active connections must be node-disjoint in the switching network. In this paper, we propose a sequence of decomposition and merge operations, called conjugate transformation, performed on each switch element to tackle this problem. The network resulting from this transformation is called conjugate network. By using the numbering-schemes of networks, we prove that if the route assignments in the original network are link-disjoint, their corresponding ones in the conjugate network would be node-disjoint. Thus, traditional nonblocking switching networks can be transformed into crosstalk-free optical switches in a routine manner. Furthermore, we show that crosstalk-free multicast switches can also be obtained from existing nonblocking multicast switches via the same conjugate transformation.

cs.NI↗