Elsevier

Computer Networks

Volume 122, 20 July 2017, Pages 105-119
Computer Networks

Improving the queue size and delay performance with the I-CSMA link scheduling algorithm

https://doi.org/10.1016/j.comnet.2017.04.011Get rights and content

Abstract

In a prior work, we proposed a new CSMA-like randomized link scheduling algorithm for wireless networks, called I-CSMA, based on a modified version of the Ising model in physics. I-CSMA is a generalization of earlier Glauber-dynamics-based algorithms, and it was shown to be throughput-optimal. In this paper, we evaluate the queue size/delay performance of I-CSMA. The simulation results show that, while maintaining throughput-optimality, I-CSMA gives better queue-size/delay performance than the popular Q-CSMA algorithm. The improvement is significant and consistent, particularly in the regime of low to moderately high traffic intensity. We analyze the control overhead of I-CSMA, discuss parameter tuning for the algorithm, and show the effects of parameter tuning with simulation results. We also propose a simpler, heuristic I-CSMA algorithm and show that it has similar performance as I-CSMA. To make I-CSMA immediately useful, we provide a device-based implementation of the I-CSMA algorithm as a reference implementation.

Introduction

Efficient utilization of the network resources is vitally important in wireless networks, as the capacity of such networks is often severely limited. Link transmission scheduling is one of the key mechanisms for improvement in both network resource utilization and user perceived performance. An ideal link scheduling algorithm should achieve high throughput, low delay, and it should do so at low complexity. A family of scheduling algorithms has attracted much attention recently: randomized algorithms in which the link activation probabilities are dependent on the queue sizes [1], [2], [3], [4], [5], [6]. A representative one is the Q-CSMA algorithm [4]. These algorithms can be implemented similarly to the Carrier Sense Multiple Access (CSMA) scheme used in practical systems such as WIFI 802.11x. The implementation is decentralized and requires only local information and control. Interestingly, despite having simple operations, some of these algorithms are proven to be throughput-optimal. These algorithms share a common feature: Behind the scene, they each have a Glauber dynamics, which is a special type of Markov chain.

Previously, we introduced a new CSMA-like randomized link scheduling algorithm, called I-CSMA, based on a physics model called the Ising model [7]. I-CSMA is a generalization of earlier Glauber-dynamics-based, throughput-optimal algorithms, and it has removed a major restriction in earlier related algorithms. I-CSMA in fact has many different versions. We have shown that all versions of I-CSMA are throughput-optimal, in the sense that they each can stabilize the network queues for all arrival rate vectors in the interior of the capacity region. Thus, I-CSMA offers more flexibility and expands the choices of throughput-optimal algorithms. A network can exploit that new freedom to achieve secondary objectives after achieving throughput-optimality. Important secondary objectives considered by the community include the delay experienced by packets and practicality of the algorithm [5], [8], [9], [10], [11].

Having known that I-CSMA is throughput-optimal, this paper focuses on the queue-size/delay performance. The main contribution of the paper is to show that a version of I-CSMA results in a significantly smaller expected total queue size (thus, by Little’s Law, less expected delay) than the closest related algorithm, Q-CSMA. Such improvement has been reliably demonstrated by our extensive simulation experiments on different networks under different traffic models. The improvement is generally over the entire range of traffic intensity; it is especially consistent in the regime of low to moderately high traffic intensity. I-CSMA works especially well, with respect to the queue-size/delay performance, under weight functions that increase very slowly with the queue size, e.g., log log  function of the queue size.

Our second contribution is to make I-CSMA more practical and more useful. This consists of two parts. First, to make I-CSMA simpler to operate and easier to implement, we provide a heuristic version of I-CSMA. Our simulation experiments have shown that the heuristic algorithm performs nearly as well as I-CSMA.1 Second, for ease of presentation, the main I-CSMA algorithm is presented as a link-based algorithm, where the subject that executes the algorithm is a link. However, in reality, a control algorithm is implemented at the wireless devices. To make I-CSMA immediately useful, we provide a device-based description of the algorithm as a reference implementation.

Our third contribution is that we analyze the control overhead of I-CSMA, discuss parameter tuning for the algorithm, and illustrate the effects of parameter tuning with simulation results.

The rest of the paper is organized as follows. In Section 2, we discuss additional related work. In Section 3, we present a modified Ising model and the main I-CSMA algorithm. In Section 4, we provide an analysis of I-CSMA, contrast it with Q-CSMA and discuss additional issues such as control overhead and parameter tuning. In Section 5, we introduce a heuristic I-CSMA algorithm, which is a simplification of the I-CSMA algorithm. In Section 6, we present simulation results for both I-CSMA and the heuristic algorithm, and compare the performance of I-CSMA with Q-CSMA. Conclusions are given in Section 7. In Appendix A, we describe a device-based I-CSMA algorithm.

Section snippets

Other related work

With respect to improving the queue-size/delay performance, we briefly review several existing studies. A related queue-based randomized algorithm is proposed in [5]. The authors show that, on a part of the capacity region, the queue dynamics is a fast-mixing Markov chain and the total queue size is bounded by a polynomial in the network size, provided the degrees of the interference graphs are bounded by a constant. It is unclear whether the algorithm is throughput-optimal. The authors of [12]

System model and notations

We consider a single-channel wireless network characterized by an undirected interference graph, G=(V,E), where the vertex set V represents the wireless links and the edge set E indicates the interference relations between the links. Link u and v are connected by an edge (u, v) ∈ E if and only if their transmissions interfere each other. Interfering links cannot successfully transmit simultaneously. Without loss of generality, we assume the graph G has at least two nodes and is connected.

We

Relationship with Q-CSMA

Q-CSMA works as follows. Suppose link v is selected for consideration of activation. When link v’s neighbors are all OFF, the activation probability for link v is equal to eWv/(1+eWv), where the weight Wv is a slowly increasing function of link v’s queue size Qv, e.g. Wv=log(αQv+1) or Wv=loglog(αQv+e). When any of link v’s neighbors are ON, link v will not be turned ON.

The Markov chain in I-CSMA is in the space of all configurations Ω. In contrast, the Markov chain in Q-CSMA is in the space of

Heuristic I-CSMA scheduling algorithm

As discussed in Remark 4, the I-CSMA algorithm in Section 3.4 selects an independent set ξ(t) for parallel update during control phase I on each time slot. Parallel update speeds up the Markov chain transitions and potentially reduces the mixing time and queue sizes. Requiring the updating set ξ(t) to be an independent set is for the theoretical reason that one can still easily compute the stationary distribution of the Glauber dynamics. However, much of the complexity of control phase I is due

Simulation results

In this section, we show simulation-based performance evaluation of the I-CSMA algorithm. We compare I-CSMA with Q-CSMA, which is both popular and quite related to I-CSMA. Having proved throughput-optimality, our focus here is the average total queue length, which, by Little’s law, is related to the average delay experienced by packets (Fig. 1).

We used three interference graphs to evaluate the algorithms in different situations. One is a 4 × 4 grid with 16 vertices; another is a clique with 10

Conclusions

In this paper, we evaluate the queue-size/delay performance of a randomized link scheduling algorithm, I-CSMA. The simulation results show that, while maintaining throughput-optimality, I-CSMA gives better queue-size/delay performance than the popular Q-CSMA. The improvement is significant and consistent, particularly in the regime of low to moderately high traffic intensity. We also analyze the algorithm’s control overhead, discuss parameter tuning for the algorithm, and show the effects of

Yi Wang graduated with Ph.D. degree at the Computer and Information Science and Engineering department of the University of Florida in 2016. He received the B.S. and M.S. degree in Electrical Engineering from Huazhong University of Science and Technology in 2009 and University of Southern California in 2011, respectively. His research interests are in the area of algorithm design, optimization, wireless networks and cloud computing.

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    Yi Wang graduated with Ph.D. degree at the Computer and Information Science and Engineering department of the University of Florida in 2016. He received the B.S. and M.S. degree in Electrical Engineering from Huazhong University of Science and Technology in 2009 and University of Southern California in 2011, respectively. His research interests are in the area of algorithm design, optimization, wireless networks and cloud computing.

    Ye Xia is an associate professor at the Computer and Information Science and Engineering department at the University of Florida, starting in August 2003. He has a PhD degree from the University of California, Berkeley, in 2003, an MS degree in 1995 from Columbia University, and a BA degree in 1993 from Harvard University, all in Electrical Engineering. Between June 1994 and August 1996, he was a member of the technical staff at Bell Laboratories, Lucent Technologies in New Jersey. His main research area is computer networking, including performance evaluation of network protocols and algorithms, resource allocation, wireless network scheduling, network optimization, and load balancing on peer-to-peer networks. He also works on cache organization and performance evaluation for chip multiprocessors. He is interested in applying probabilistic models to the study of computer systems.

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