移动自组织网络的吞吐量-延迟权衡分析

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"具有参考点组移动性的移动自组织网络的吞吐量和延迟权衡" 在移动自组织网络（MANET）的研究中，理解和优化网络性能的关键因素之一是吞吐量与延迟之间的权衡。这篇由Jiajia Liu、Nei Kato、Jianfeng Ma和Toshikazu Sakano等人发表于2015年《无线通信 transactions on wireless communications》第14卷第3期的研究论文，深入探讨了在参考点组移动模型下这一问题。论文首先介绍了研究背景，即在网络节点按照随机方向模型以速度υ（υ∈[0,1]）移动的情况下，网络的吞吐量和延迟的相互影响。在这种情况下，网络中的n个节点被均匀地划分为Θ(nα)个小组，其中α属于[0,1]区间，每个小组的中心按照随机方向移动。作者的目标是确定每个节点的吞吐量和平均延迟的可达成区域（在阶的概念下），并揭示它们之间的权衡关系。对于υ=0的情况，即节点不移动时，论文证明了每个节点的吞吐量容量是Θ(n^(-α/2))。接着，他们提出了一种路由策略，该策略能够在保持这种吞吐量的同时，实现平均延迟为Θ(max{n^(1/2), n^(1-α)})的性能，这一结果适用于所有α∈[0,1]的范围。当υ>0时，即节点有移动时，论文进一步证明吞吐量容量可以提高到Θ(1)，这意味着即使在网络节点移动的情况下，也可以实现相对稳定的传输速率。然而，这种改进的吞吐量通常会带来更高的延迟成本，因此，作者可能也讨论了如何在保持网络稳定性的同时优化延迟性能。通过这些发现，研究者提供了对MANET在实际移动环境下的性能优化策略的见解，对于设计高效、动态的路由算法和网络管理策略具有重要的理论和实践意义。这篇论文不仅深化了我们对MANET性能理解，还为未来的研究提供了有价值的理论基础和方法论。

1268 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 14, NO. 3, MARCH 2015

left edge is attached the right one such that the border effects

can be avoided in the performance analysis. Furthermore, we

assume that all n nodes are evenly divided into m =Θ(n

)

groups, α ∈ [0, 1], and time is divided into slots of equal

duration for packetized transmission. Note that for a source-

destination pair, say S and D, the probability that S and D

are located in the same group is Θ(n

−α

), a small value which

approaches 0 very quickly as n scales up for 0 <α≤ 1.In

other words, for 0 <α≤ 1, S and D are located in different

groups with a probability of asymptotically approaching 1.

Therefore, neglecting the case of S and D locating in the same

group will not affect the scaling laws of throughput, delay, and

their tradeoffs, and hereafter we consider only the case that S

and D are located in different groups. Note also that the results

obtained in Sections IV and V still hold for the special case of

α =0, i.e., all nodes are divided into one group.

To characterize the correlation among nodes, we assume that

in any time slot all nodes of one group are constrained to stay

within the same portion of network area, i.e., a group region,

which is deﬁned as a disk area with radius R. To exclusively

explore and clearly illustrate the i mpact of correlated mobility

on throughput and delay performance, we maintain an average

node density n in each group region. As each group contains

Θ(n/n

)=Θ(n

1−α

) nodes, we can easily see that the radius

of each group region is determined as R =Θ(

√

1−α

· n

−1

Θ(n

−α/2

B. Correlated Mobility Model

For a node i,weuseG(i) to denote the group that i belongs

to, i.e., i ∈G(i). In a time slot t, the position of node i is

given by (X

(t),X



(t)), where X

(t) denotes the central point

position of the group region associated with G(i) and X



(t)

denotes the relative position of node i within its group region.

For any two nodes j = i, we always have X

(t)=X

(t) as

long as G(i)=G(j). Without incurring any ambiguity, in the

following we refer to “the central point of a group region” as

“the central point of a group”, or simply “group center”.

The Reference Point Group Mobility (RPGM) model, which

was ﬁrst introduced in [22], is adopted here to model the cor-

related mobility. Speciﬁcally, for a node i ∈G(i), its mobility

process {(X

(t),X



(t)); t =0, 1,...} is deﬁned as follows.

We ﬁrst introduce the movement of group center for G(i),

i.e., {X

(t); t =0, 1,...}. As shown in Fig. 1, a group center

moves according to a random direction mobility model [23],

[24] with a speed of no more than υ ∈ [0, 1]. Therefore, for any

time s lot t, we always have |X

(t) − X

(t +1)|≤υ, where |·|

denotes the Euclidean distance. With such a model, initially

all group centers are uniformly distributed and for each time

slot each group center then moves across the network with a

speed and a direction uniformly selected from [0,υ] and [0, 2π),

respectively. There exists no correlation among the movements

of different group centers, and thus the moving speed (and also

the moving direction) of each group center is i.i.d. For a group

center, its movement among different time slots is also i.i.d.

Now we proceed to deﬁne the relative movement of node

i within its group region, i.e., {X



(t); t =0, 1,...}.During

a time slot t, once the position X

(t) of group center is

determined, all nodes belonging to G(i) will concurrently move

into the disk area centered at X

(t) due to the correlated node

mobility. Note that according to the network model, under most

settings (except for the case α =0), all nodes belonging to

G(i) have to reside in a disk area of Θ(n

−α

) during each time

slot. Thus, we assume that each node moves within its group

region according to the i.i.d. mobility model [15], [25], [26],

which indicates that given the group center X

(t), node i may

uniformly appear at any place in its group region centered at

(t).

Remark 1: Note that the mobility of group regions will

unavoidably lead to their overlapping. Therefore, it is possible

to reform the group members within the overlapping area, so

as to achieve better performances of throughput, delay, or the

tradeoff. For example, consider a source-destination pair, say

S and D, which initially belong to two different groups, say

source group and destination group, respectively. When the

source group and the destination group meet together and S

(resp. D) is just located within in the overlapping area, S

(resp. D) may enter the destination group (resp. source group)

by changing its membership. By utilizing the member reform-

ing in group overlapping area, it changes the S-D trafﬁc ﬂow

from inter-group to intra-group, which enables a much better

throughput, delay, and their tradeoff to be achieved for the S-D

trafﬁc.

However, as the group overlapping behavior involves a lot

of factors, such as the moving speed and moving direction of

group center, the node mobility within group region, the num-

ber of overlapping groups, the shape and area of overlapping

area, etc., it is very difﬁcult (if not impossible) to quantita-

tively analyze the probability of member reforming i n group

overlapping area. Note that the main focus of this paper is to

explore the throughput-delay tradeoff under correlated mobility

with a general setting of moving speed, and to explicitly show

the impact of node transmission range on throughput, delay

and their tradeoffs. As a very initial step and also to keep the

analysis tractable, we assume in this paper a simple scenario

where the case of group region overlapping was not considered,

similar to that in available works [20], [21].

Remark 2: Actually, it is very challenging to accurately

characterize the heterogeneous random node mobility patterns

in MANETs. In particular, the node movements may be identi-

cally distributed and independent of each other or be correlated

to each other; may be able to visit the whole network region or

just a very limited area; may have different moving speeds; may

be partially predictable (e.g., on-road vehicles) or totally unpre-

dictable (e.g., animals); etc. So far, a lot of analytical models

have been proposed to characterize the MANETs mobility,

such as the i.i.d. model, random walk model, random waypoint

model, Brownian model, the Levy walk model, home-point

mobility, reference point group mobility, nomadic community,

etc. (see [27] for a survey). Note that all the available mobility

models can only be able to represent partial typical features

of real node mobility in MANETs. It still remains an open

problem to devise a general mobility model which is able to

match the heterogeneous node mobility in MANETs.

Different from previous works focusing on independent

node movements, we considered in this paper MANETs with

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