拓扑透明调度：CAC与SCAC性能对比研究

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本文是一篇研究论文，主要探讨了基于拓扑透明调度的冲突避免代码（Conflict-Avoiding Codes, CACs）和强冲突避免代码（Strongly Conflict-Avoiding Codes, SCACs）在移动自组网络和无线传感器网络中的性能比较。拓扑透明调度是一种确定性的介质访问控制协议，其核心在于仅依赖两个参数：网络中的节点数量和最大邻域大小。这种调度方式的一大优点是每个节点能够保证在有限的延迟内成功传输多个数据包，不受其邻居节点变化的影响，对于难以实现帧同步的移动节点尤为适用。文章的焦点在于分析两种调度策略在时隙同步网络和异步网络下的表现差异。在时隙同步网络中，CACs通过精确的时间安排来减少冲突，而SCACs则进一步提高了冲突避免的能力。然而，在异步网络中，由于节点间的时钟不一致，这些策略的效果可能会有所变化。作者对这两种调度方法在最大延迟、平均延迟以及平均能耗等方面进行了深入的仿真研究。通过对不同参数的设置和实际环境模拟，论文试图揭示出哪种调度方案在特定条件下更能优化网络性能，这对于理解和设计适用于各种网络拓扑和通信环境的高效协议具有重要意义。这篇论文为理解和选择适合的拓扑透明调度算法提供了有价值的理论依据和实践经验，对于无线网络设计者和研究人员来说，是一篇不可或缺的研究成果。

A Performance Comparison Between CACs and

SCACs Based Topology-Transparent Scheduling

Yijin Zhang, Jun Wei, Ming Zhang, Aijie Zou and Feng Shu

School of Electronic and Optical Engineering

Nanjing University of Science and Technology

Nanjing, China

Abstract—Topology-transparent sched uling is a deterministic

medium access control protocol for mobile ad hoc networks and

wireless sensor networks. This approach only depends on two pa-

rameters: the number of nodes in the network and the maximum

size of neighborhood. An attractive property is that each node

can guarantee a bounded delay in wh ich several packets can be

successfully transmitted, no matter which nodes are its neighbors.

In this paper, we study conﬂict-avoiding codes (CACs) and

strongly conﬂict-avoiding codes (SCACs) based scheduling for

slot-synchronized and asynchronous network, respectively, since

it i s difﬁcult for mobile nodes to achieve frame-synchronization.

The effect of synchronization on maximal delay is examined.

In addition, we investigate average delay and average energy

consumption by simulation.

Index Terms—Top ology-transparent scheduling, conﬂict-

avoiding codes, strongly conﬂict-avoiding codes, synchronization.

I. INTRODUCTION

In mobile ad hoc networks (MANETs) or wireless sensor

networks (WSNs), it is challenging for medium access control

(MAC) protocols to provide bounde d delay and short- te rm

fairness, due to the nod e mobility and multi-hop communi-

cation. As such, topology-transpare nt strategies [1]–[6] have

been drawing attentions to overcome these problems. This

approa ch only depends on two param eters: the number of

nodes in the network, and the maximum size of neighborhood.

A topology -transparent schedule (TTS) is said to be g-robust

if it ensures a favorable property that each node can send g

collision-fre e packets to its each neig hbor within a predeﬁned

schedule length . This is a strict guarantee with pro bability one,

in con trast to random and contention-based schemes.

A TTS is acco mplished by assigning each node a determin-

istic binary sequence. Ea ch node transmits a packet within

one time slot duration if the sequence value is one, an d

keeps listening for one time slot if it is zero. Th e transceiver

is half-duplex, i.e., a tran sm itting node cannot receive any

message. A collision occurs if a packet starts or en ds within the

transmission duration of another packet. Only those packets

without suffering any co llision c an be rece ived correctly.

Considering different synchron iz ation level, the re are d-

ifferent combinatorial objects underling the corresponding

TTS constructions. By assuming that the nodes a re frame

synchro nized, most known TTSs [1], [2], [5], [6] are de-

signed based on cover-free families and orthogonal arrays.

In [3], [4], optica l orthogonal codes (OOCs) are employed

to design TTSs in the slot-synchronized and asynchronous

network. However, the Hamming auto-c orrelation constraint in

OOCs is inessential in TTSs to avoid con ﬂicts. This motivates

researchers to ﬁnd that conﬂict-a voiding codes (CACs) [8],

[9] and strongly con ﬂict-avoiding codes (SCACs) [10] are

more su itable to construct 1-robust TTSs for these two weak-

er synchronization models, as their combinatorial structures

only depe nd on Hamming cross-co rrelation. Moreover, they

both have the minimum Hamming weight, which yields re-

transmitting times and energy cost as small a s possible.

Three criteria are commonly conside red to eva luate the

perfor mance of TTSs: (i) the maximal delay, w hich is upper

bounded by the schedule length; (ii) the average delay, which

depends on the sequence structure; (iii) the energy consump-

tion. In general, the energy consumed in listening state is equal

to 50%-80 % [7] of that in transmitting state.

In this pap er, w e will generalize CACs and SCACs to

support g-robust property for any g, and further examine the

effects of synchronization on the maximal delay, average delay

and average energy consumption. A similar study on OOCs

based TTSs can be found in [4], but only focused on the

maximal delay.

The rest of this paper is organized as follows. After setting

up some notation and deﬁnitio ns in Section II, we in Section

III present a sufﬁcient combinatorial condition of g-robust

TTSs for each synchronization level. Section IV compares

lower bounds on the minimum schedule leng th, and Section V

compares maximal delays by CAC and SCAC constructions.

Section VI provides a performance study by simulation in

terms of average delay a nd average energy consumption. Fi-

nally, we close in Section VII with some concluding remarks.

II. NOTATION AND DEFINITIONS

For i = 1, 2, . . . , K, the binary sequence associated with

user i is speciﬁed by a row vector

:= [s

(0) s

(1) . . . s

(L − 1)],

and its Hamming weight is deﬁned as w(s) :=

L−1

t=0

s(t).

A sequence can also be deﬁned as the set of all time indices

in a period where the value of the protocol sequence is equal

to 1. Let Z

= {0, 1, . . . , L−1} be the set of integers reduced

modulo L. A subset I of Z

is associated with a binary

sequence s(t) of length L, by setting s(t) = 1 if and only

if t ∈ I.

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