Ad Hoc Networks 24 (2015) 109–120

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Ad Hoc Networks

journal homepage: www.elsevier .com/locate /adhoc

Source delay in mobile ad hoc networks

http://dx.doi.org/10.1016/j.adhoc.2014.08.0041570-8705/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author at:E-mail addresses: jtgao@is.naist.jp (J. Gao), ylshen@mail.xidian.edu.cn

(Y. Shen), jiang@fun.ac.jp (X. Jiang), lijie@cs.tsukuba.ac.jp (J. Li).1 Principal corresponding author.

Juntao Gao a,⇑, Yulong Shen b,c,1, Xiaohong Jiang d, Jie Li e

a Graduate School of Information Science, Nara Institute of Science and Technology, 630-0192, Japanb State Key Laboratory of Integrated Services Networks, Xidian University, Xian, Shaanxi 710071, PR Chinac School of Computer Science and Technology, Xidian University, Xian, Shaanxi 710071, PR Chinad School of Systems Information Science, Future University Hakodate, 116-2 Kamedanakano-cho, Hakodate, Hokkaido 041-8655, Japane Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba Science City, Ibaraki 305-8573, Japan

a r t i c l e i n f o

Article history:Received 21 November 2013Received in revised form 6 March 2014Accepted 9 August 2014Available online 19 August 2014

Keywords:MANETsPacket dispatchSource delayMeanVariance

a b s t r a c t

Source delay, the time a packet experiences in its source node, serves as a fundamentalquantity for delay performance analysis in networks. However, the source delay perfor-mance in highly dynamic mobile ad hoc networks (MANETs) is still largely unknown bynow. This paper studies the source delay in MANETs based on a general packet dispatchingscheme with dispatch limit f (PD-f for short), where a same packet will be dispatched outup to f times by its source node such that packet dispatching process can be flexiblycontrolled through a proper setting of f. We first apply the Quasi-Birth-and-Death (QBD)theory to develop a theoretical framework to capture the complex packet dispatchingprocess in PD-f MANETs. With the help of the theoretical framework, we then derive thecumulative distribution function as well as mean and variance of the source delay in suchnetworks. Finally, extensive simulation and theoretical results are provided to validate oursource delay analysis and illustrate how source delay in MANETs is related to networkparameters.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Mobile ad hoc networks (MANETs) represent a class ofself-configuring and infrastructureless networks withmobile nodes. As MANETs can be rapidly deployed, recon-figured and extended at low cost, they are highly appealingfor a lot of critical applications, like disaster relief, emer-gency rescue, battle field communications, environmentmonitoring, etc. [1,2]. To facilitate the application ofMANETs in providing delay guaranteed services in aboveapplications, understanding the delay performance ofthese networks is of fundamental importance [3,4].

Source delay, the time a packet experiences in its sourcenode, is an indispensable behavior in any network. Sincethe source delay is a delay quantity common to all MAN-ETs, it serves as a fundamental quantity for delay perfor-mance analysis in MANETs. For MANETs where a packetis transmitted only once by its source node (through eitherunicast [5,6] or broadcast [7]), the source delay actuallyserves as a practical lower bound for and thus constitutesan essential part of overall delay in those networks. Thesource delay is also an indicator of packet lifetime, i.e.,the maximum time a packet could stay in a network; inparticular, it lower bounds the lifetime of a packet and thusserves as a crucial performance metric for MANETs withpacket lifetime constraint.

Despite much research activity on delay performanceanalysis in MANETs (see Section 6 for related works), thesource delay performance of such networks is still largelyunknown by now. The source delay analysis in highly

110 J. Gao et al. / Ad Hoc Networks 24 (2015) 109–120

dynamic MANETs is challenging, since it involves not onlycomplex network dynamics like node mobility, but alsoissues related to medium contention, interference, packetgenerating and packet dispatching. This paper is devotedto a thorough study on the source delay in MANETs underthe practical scenario of limited buffer size and also ageneral packet dispatching scheme with dispatch limit f(PD-f for short). With the PD-f scheme, a same packet willbe dispatched out up to f times by its source node such thatpacket dispatching process can be flexibly controlledthrough a proper setting of f. The main contributions of thispaper are summarized as follows.

� We first apply the Quasi-Birth-and-Death (QBD) theoryto develop a theoretical framework to capture the com-plex packet dispatching process in a PD-f MANET. Thetheoretical framework is powerful in the sense itenables complex network dynamics to be incorporatedinto source delay analysis, like node mobility, mediumcontention, interference, packet transmitting andpacket generating processes.� With the help of the theoretical framework, we then

derive the cumulative distribution function (CDF) aswell as mean and variance of the source delay in theconsidered MANET. By setting f ¼ 1 in a PD-f MANET,the corresponding source delay actually serves as alower bound for overall delay.� Extensive simulation results are provided to validate

our theoretical framework and the source delay models.Based on the theoretical source delay models, we fur-ther demonstrate how source delay in MANETs isrelated to network parameters, such as packet dispatchlimit, buffer size and packet dispatch probability.

The rest of this paper is organized as follows. Section 2introduces preliminaries involved in this source delaystudy. A QBD based theoretical framework is developedto model the source delay in Section 3. We derive in

Fig. 1. An example of a cell partitione

Section 4 the CDF as well as mean and variance of thesource delay. Simulation/numerical studies and the corre-sponding discussions are provided in Section 5. Finally,we introduce related works regarding delay performanceanalysis in MANETs in Section 6 and conclude the paperin Section 7.

2. Preliminaries

In this section, we introduce the basic system models,the Medium Access Control (MAC) protocol and the packetdispatching scheme involved in this study.

2.1. System models

2.1.1. Network model and mobility modelWe consider a time slotted torus MANET of unit area.

Similar to previous works, we assume that the networkarea is evenly partitioned into m�m cells as shown inFig. 1a [8–11]. There are n mobile nodes in the networkand they randomly move around following the Indepen-dent and Identically Distributed (IID) mobility model[6,12,13]. According to the IID mobility model, each nodefirst moves into a randomly and uniformly selected cellat the beginning of a time slot and then stays in that cellduring the whole time slot.

2.1.2. Communication modelWe assume that all nodes transmit data through one

common wireless channel, and each node (say S inFig. 1a) employs the same transmission range r ¼

ffiffiffi8p

=mto cover 9 cells, including S’s current cell and its 8 neighbor-ing cells. To account for mutual interference and interrup-tion among concurrent transmissions, the commonly usedprotocol model is adopted [10,12,14,15]. According to theprotocol model, node i could successfully transmit toanother node j if and only if dij 6 r and for another simulta-neously transmitting node k – i; j; dkj P ð1þ DÞ � r, where

d MANET with a MAC protocol.

J. Gao et al. / Ad Hoc Networks 24 (2015) 109–120 111

dij denotes the Euclidean distance between node i and nodej and D P 0 is the guard factor to prevent interference. In atime slot, the data that can be transmitted during a success-ful transmission is normalized to one packet.

2.1.3. Traffic modelWe consider the widely adopted permutation traffic

model [10,12,13], where there are n distinct traffic flowsin the network. Under such traffic model, each node actsas the source of one traffic flow and at the same time thedestination of another traffic flow. The packet generatingprocess in each source node is assumed to be a Bernoulliprocess, where a packet is generated by its source nodewith probability k in a time slot [6]. We assume that eachsource node has a first-come-first-serve queue (calledlocal-queue hereafter) with limited buffer size M > 0 tostore its locally generated packets. Each locally generatedpacket in a source node will be inserted into the end of itslocal-queue if the queue is not full, and dropped otherwise.

2.2. MAC protocol

We adopt a commonly used MAC protocol based on theconcept of Equivalent-Class to address wireless mediumaccess issue in MANETs [10–12,15]. As illustrated inFig. 1b that an Equivalent-Class (EC) consists of a groupof cells with any two of them being separated by a horizon-tal and vertical distance of some integer multiple ofað1 6 a 6 mÞ cells. Under the EC-based MAC protocol(MAC–EC), the whole network cells are divided into a2

ECs and ECs are then activated alternatively from time slotto time slot. We call cells in an activated EC as active cells,and only a node in an active cell could access the wirelesschannel and do packet transmission. If there are multiplenodes in an active cell, one of them is selected randomlyto have a fair access to wireless channel.

To avoid interference among concurrent transmissionsunder the MAC–EC protocol, the parameter a should beset properly. Suppose a node (say S in Fig. 1b) in an activecell is transmitting to node R at the current time slot, andanother node W in one adjacent active cell is also transmit-ting simultaneously. As required by the protocol model, thedistance dWR between W and R should satisfy the followingcondition to guarantee successful transmission from S to R,

dWR P ð1þ DÞ � r: ð1Þ

Notice that dWR P ða� 2Þ=m, we have

ða� 2Þ=m P ð1þ DÞ � r: ð2Þ

Since a 6 m and r ¼ffiffiffi8p

=m; a should be set as

a ¼min dð1þ DÞffiffiffi8pþ 2e;m

n o; ð3Þ

where the function dxe returns the least integer valuegreater than or equal to x.

Remark 1. Notice that for a time slot and an active cell, therandom selection of one node from multiple nodes toaccess wireless channel can be implemented based on amechanism similar to DCF protocol [16,17]. At the begin-ning of the time slot, each node in the active cell first

initiates a backoff timer with backoff period drawnuniformly from ½0;CW � (CW represents the contentionwindow size), all nodes then begin to count down. Thenode whose timer reaches 0 first broadcasts a messageclaiming its access to the wireless channel, and all othernodes in the same active cell, after overhearing thebroadcasted message, stop their timers and remain silentin the time slot.

2.3. PD-f scheme

Once a node (say S) got access to the wireless channel ina time slot, it then executes the PD-f scheme (f P 1) sum-marized in Algorithm 1 for packets dispatch.

Remark 2. The PD-f scheme is general and covers manywidely used packet dispatching schemes as special cases,like the ones without packet redundancy [5,6,8] whenf ¼ 1 and only unicast transmission is allowed, the oneswith controllable packet redundancy [12,16,18] whenf > 1 and only unicast transmission is allowed, and theones with uncontrollable packet redundancy [7,19] whenf P 1 and broadcast transmission is allowed.

Algorithm 1. PD-f scheme.

1: if S has packets in its local-queue then2: S checks whether its destination D is within its

transmission range;3: if D is within its transmission range then4: S transmits the head-of-line (HoL) packet in its

local-queue to D;{source–destination transmission}

5: S removes the HoL packet from its local-queue;6: S moves ahead the remaining packets in its

local-queue;7: else8: With probability q (0 < q < 1), S dispatches the

HoL packet;9: if S conducts packet dispatch then10: S dispatches the HoL packet for one time;

{packet-dispatch transmission}11: if S has already dispatched the HoL packet

for f times then12: S removes the HoL packet from its local-

queue;13: S moves ahead the remaining packets in

its local-queue;14: end if15: end if16: end if17: else18: S remains idle;19: end if

3. QBD-based theoretical framework

In this section, a QBD-based theoretical framework isdeveloped to capture the packet dispatching process in a

Fig. 2. State transitions from state ðl; jÞ of the local-queue.

112 J. Gao et al. / Ad Hoc Networks 24 (2015) 109–120

PD-f MANET. This framework will help us to analyze sourcedelay in Section 4.

3.1. QBD modeling

Due to the symmetry of source nodes, we only focus ona source node S in our analysis. We adopt a two-tupleXðtÞ ¼ ðLðtÞ; JðtÞÞ to define the state of the local-queue inS at time slot t, where LðtÞ denotes the number of packetsin the local-queue at slot t and JðtÞ denotes the numberof packet dispatches that have been conducted for thecurrent head-of-line packet by slot t, here 0 6 LðtÞ 6M;0 6 JðtÞ 6 f � 1 when 1 6 LðtÞ 6 M, and JðtÞ ¼ 0 whenLðtÞ ¼ 0.

Suppose that the local-queue in S is at state ðl; jÞ in thecurrent time slot, all the possible state transitions that mayhappen at the next time slot are summarized in Fig. 2,where

� I0ðtÞ is an indicator function, taking value of 1 if S con-ducts source–destination transmission in the currenttime slot, and taking value of 0 otherwise;� I1ðtÞ is an indicator function, taking value of 1 if S con-

ducts packet-dispatch transmission in the current timeslot, and taking value of 0 otherwise;� I2ðtÞ is an indicator function, taking value of 1 if S con-

ducts neither source–destination nor packet-dispatchtransmission in the current time slot, and taking valueof 0 otherwise;� I3ðtÞ is an indicator function, taking value of 1 if S locally

generates a packet in the current time slot, and takingvalue of 0 otherwise.

From Fig. 2 we can see that as time evolves, the statetransitions of the local-queue in S form a two-dimensionalQBD process [20]

fXðtÞ; t ¼ 0;1;2; . . .g; ð4Þ

on state space

fð0;0Þg [ fðl; jÞg; 1 6 l 6 M;0 6 j 6 f � 1f g: ð5Þ

Based on the transition scenarios in Fig. 2, the overalltransition diagram of above QBD process is illustratedin Fig. 3.

Remark 3. The QBD framework is powerful in the sense itenables main network dynamics to be captured, like thedynamics involved in the packet generating process andthose involved in the source–destination and packet-dispatch transmissions (i.e., node mobility, medium con-tention, interference and packet transmitting).

3.2. Transition matrix and some basic results

As shown in Fig. 3 that there are in total 1þM � f two-tuple states for the local-queue in S. To construct the tran-sition matrix of the QBD process, we arrange all these1þM � f states in a left-to-right and top-to-down way asfollows: fð0;0Þ; ð1;0Þ; ð1;1Þ; . . . ; ð1; f � 1Þ; ð2;0Þ; ð2;1Þ; . . . ;

ð2; f � 1Þ; . . . ; ðM;0Þ; . . . ; ðM; f � 1Þg. Under such state

arrangement, the corresponding state transition matrix Pof the QBD process can be determined as

P ¼

B1 B0

B2 A1 A0

A2. .

. . ..

. ..

A1 A0

A2 AM

266666664

377777775; ð6Þ

where the corresponding sub-matrices in matrix P aredefined as follows:

� B0: a matrix of size 1� f , denoting the transition prob-abilities from ð0; 0Þ to ð1; jÞ;0 6 j 6 f � 1.� B1: a matrix of size 1� 1, denoting the transition prob-

ability from ð0;0Þ to ð0;0Þ.

Fig. 3. State transition diagram for the QBD process of local-queue. For simplicity, only transitions from typical states ðl; jÞ are illustrated for 1 6 l 6 M,while other transitions are the same as that shown in Fig. 2.

J. Gao et al. / Ad Hoc Networks 24 (2015) 109–120 113

� B2: a matrix of size f � 1, denoting the transitionprobabilities from ð1; jÞ to ð0;0Þ;0 6 j 6 f � 1.� A0: a matrix of size f � f , denoting the transition

probabilities from ðl; jÞ to ðlþ 1; j0Þ;1 6 l 6 M � 1;0 6 j; j0 6 f � 1.� A1: a matrix of size f � f , denoting the transition prob-

abilities from ðl; jÞ to ðl; j0Þ;1 6 l 6 M � 1;0 6 j; j0 6 f � 1.� A2: a matrix of size f � f , denoting the transition prob-

abilities from ðl; jÞ to ðl� 1; j0Þ;2 6 l 6 M;0 6 j; j0 6 f � 1.� AM: a matrix of size f � f , denoting the transition

probabilities from ðM; jÞ to ðM; j0Þ;0 6 j; j0 6 f � 1.

Some basic probabilities involved in the above sub-matrices are summarized in the following Lemma.

Lemma 1. For a given time slot, let p0 be the probability thatS conducts a source–destination transmission, let p1 be theprobability that S conducts a packet-dispatch transmission,and let p2 be the probability that S conducts neithersource–destination nor packet-dispatch transmission. Then,we have

p0 ¼1a2

9n�m2

nðn� 1Þ �m2 � 1

m2

� �n�1 8nþ 1�m2

nðn� 1Þ

( ); ð7Þ

p1 ¼qðm2 � 9Þa2ðn� 1Þ 1� m2 � 1

m2

� �n�1( )

; ð8Þ

p2 ¼ 1� p0 � p1: ð9Þ

Proof. See Appendix A for the proof. h

4. Source delay analysis

Based on the QBD-based theoretical framework devel-oped above, this section conducts analysis on the sourcedelay defined as follow.

Definition 1. In a PD-f MANET, the source delay U of apacket is defined as the time the packet experiences in itslocal-queue after it is inserted into the local-queue.

To analyze the source delay, we first examine the steadystate distribution of the local-queue, based on which wethen derive the CDF and mean/variance of the source delay.

4.1. State distribution of local-queue

We adopt a row vector p�x ¼ ½p�x;0 p�x;1 . . .p�x;M� of size1þM � f to denote the steady state distribution ofthe local-queue, here p�x;0 is a scalar value representingthe probability that the local-queue is in the state ð0;0Þ,while p�x;l ¼ ðp�x;l;jÞ1�f

is a sub-vector with p�x;l;j being theprobability that the local queue is in state ðl; jÞ;1 6 l 6M;0 6 j 6 f � 1.

For the analysis of source delay, we further define a rowvector p�X ¼ ½p�X;0 p�X;1 . . .p�X;M � of size 1þM � f to denotethe conditional steady state distribution of the local-queueunder the condition that a new packet has just beeninserted into the local-queue, here p�X;0 is a scalar valuerepresenting the probability that the local-queue is in thestate ð0;0Þ under the above condition, while p�X;l ¼ðp�X;l;jÞ1�f

is a sub-vector with p�X;l;j being the probabilitythat the local queue is in state ðl; jÞ under the above condi-tion, 1 6 l 6 M;0 6 j 6 f � 1. Regarding the evaluation ofp�X, we have the following lemma.

Lemma 2. In a PD-f MANET, its conditional steady local-queue state distribution p�X is given by

p�X ¼p�xP2

kp�xP11; ð10Þ

where 1 is a column vector with all elements being 1. Thematrix P1 in (10) is determined based on (6) by setting thecorresponding sub-matrices as follows:

114 J. Gao et al. / Ad Hoc Networks 24 (2015) 109–120

For M ¼ 1,

B0 ¼ 0; ð11ÞB1 ¼ ½1�; ð12ÞB2 ¼ c; ð13ÞAM ¼ 0: ð14Þ

For M P 2,

B0 ¼ 0; ð15ÞB1 ¼ ½1�; ð16ÞB2 ¼ c; ð17ÞA0 ¼ 0; ð18ÞA1 ¼ Q ; ð19ÞA2 ¼ c � r; ð20ÞAM ¼ 0: ð21Þwhere 0 is a matrix of proper size with all elements being 0,

c ¼ ½p0 . . . p0 p0 þ p1�T; ð22Þ

r ¼ ½1 0 . . . 0�; ð23Þ

Q ¼

p2 p1

p2 p1

. .. . .

.

p2 p1

p2

266666664

377777775: ð24Þ

The matrix P2 in (10) is also determined based on (6) bysetting the corresponding sub-matrices as follows:

For M ¼ 1,

B0 ¼ ½k 0 . . . 0�; ð25ÞB1 ¼ ½0�; ð26ÞB2 ¼ 0; ð27ÞAM ¼ kc � r: ð28Þ

For M P 2,

B0 ¼ ½k 0 . . . 0�; ð29ÞB1 ¼ ½0�; ð30ÞB2 ¼ 0; ð31ÞA0 ¼ kQ ; ð32ÞA1 ¼ kc � r; ð33ÞA2 ¼ 0; ð34ÞAM ¼ kc � r: ð35Þ

Proof. See Appendix B for the proof. h

The result in (10) indicates that for the evaluation of p�X,we still need to determine the steady state distribution p�xof the local-queue.

Lemma 3. In a PD-f MANET, its steady state distribution p�xof the local-queue is determined as follows:

For M ¼ 1,

p�x;0 ¼ p�x;0B1 þ p�x;1B2; ð36Þp�x;1 ¼ p�x;0B0 þ p�x;1AM; ð37Þp�x � 1 ¼ 1: ð38Þ

For M ¼ 2,

p�x;0 ¼ p�x;0B1 þ p�x;1B2; ð39Þp�x;1 ¼ p�x;0B0 þ p�x;1A1 þ p�x;2A2; ð40Þp�x;2 ¼ p�x;1A0 þ p�x;2AM; ð41Þp�x � 1 ¼ 1: ð42Þ

For M P 3,

½p�x;0;p�x;1� ¼ ½p�x;0;p�x;1�B1 B0

B2 A1 þ RA2

� �; ð43Þ

p�x;i ¼ p�x;1Ri�1; 2 6 i 6 M � 1; ð44Þp�x;M ¼ p�x;1RM�2RM; ð45Þp�x � 1 ¼ 1; ð46Þ

where

B0 ¼ ½k 0 . . . 0�; ð47ÞB1 ¼ ½1� k�; ð48ÞB2 ¼ ð1� kÞc; ð49ÞA0 ¼ kQ ; ð50ÞA1 ¼ ð1� kÞQ þ kc � r; ð51ÞA2 ¼ ð1� kÞc � r; ð52ÞAM ¼ A1 þ A0; ð53Þ

R ¼ A0½I� A1 � A0 � 1 � r��1; ð54Þ

RM ¼ A0½I� AM��1; ð55Þ

here c; r and Q are given in (22)–(24), respectively; I is anidentity matrix of size f � f , and 1 is a column vector of propersize with all elements being 1.

Proof. See Appendix C for the proof. h

4.2. CDF, mean and variance of source delay

Based on the conditional steady state distribution p�X ofthe local-queue, we are now ready to derive the CDF aswell as mean and variance of the source delay, as summa-rized in the following theorem.

Theorem 1. In a PD-f MANET, the probability mass functionPrfU ¼ ug, CDF PrfU 6 ug, mean U and variance r2

U of thesource delay U of a packet are given by

PrfU ¼ ug ¼ p�XTu�1cþ; u P 1; ð56ÞPrfU 6 ug ¼ 1� p�XTu1; u P 0; ð57Þ

U ¼ p�XðI� TÞ�2cþ; ð58Þ

r2U ¼ p�XðIþ TÞðI� TÞ�3cþ � U2; ð59Þ

where p�X ¼ ½p�X;1 p�X;2 . . .p�X;M � is a sub vector of p�X; cþ is acolumn vector of size M � f and T is a matrix of sizeðM � f Þ � ðM � f Þ determined as follows:

For M ¼ 1,

cþ ¼ c; ð60ÞT ¼ Q : ð61Þ

J. Gao et al. / Ad Hoc Networks 24 (2015) 109–120 115

For M P 2,

cþ ¼ ½c 0 . . . 0�T ; ð62Þ

T ¼

A1 A0

A2 A1 A0

. .. . .

. . ..

A2 A1 A0

A2 AM

266666664

377777775; ð63Þ

where

A0 ¼ 0; ð64ÞA1 ¼ Q ; ð65ÞA2 ¼ c � r; ð66ÞAM ¼ Q ; ð67Þ

here c; r and Q are given in (22)–(24), respectively, and 0 is amatrix of proper size with all elements being 0.

Proof. See Appendix D for the proof. h

Remark 4. As a packet will be dispatched out by its sourcenode for at least one time, the source delay under f ¼ 1actually serves as a lower bound for overall delay in PD-fMANETs.

(a) U versus (λ,M)

5. Numerical results

In this section, we first provide simulation results tovalidate the efficiency of our QBD-based theoretical frame-work and source delay models, and then illustrate howsource delay in a PD-f MANET is related to networkparameters.

5.1. Source delay validation

To validate the theoretical framework and source delaymodels, a customized C++ simulator was developed to sim-ulate the packet generating and dispatching processes inPD-f MANETs [21], in which network parameters, such asthe number of network nodes n, network partition param-

Fig. 4. The simulation and theoretical results on cumulative distributionfunction (CDF) of source delay.

eter m, local-queue buffer size M, packet dispatch limitf, packet dispatch probability q and packet generatingprobability k, can be flexibly adjusted to simulate sourcedelay performance under various network scenarios. Basedon the simulator, extensive simulations have been con-ducted to validate our QBD-based source delay models.For three typical network scenarios of n ¼ 100 (small net-work), n ¼ 200 (medium network) and n ¼ 400 (large net-work) with m ¼ 8; M ¼ 7; f ¼ 2; q ¼ 0:4 and k ¼ 0:001,the corresponding simulation/theoretical results on theCDFs of source delay are summarized in Fig. 4.

We can see from Fig. 4 that for all three network scenar-ios considered here, the theoretical results on the CDF ofsource delay match nicely with the corresponding simu-lated ones, indicating that our QBD-based theoreticalframework is highly efficient in modeling the source delaybehaviors of PD-f MANETs. We can also see from Fig. 4 thatthe source delay in a small network (e.g. n ¼ 100 here) isvery likely smaller than that of a large network (e.g.n ¼ 200 or n ¼ 400 here). This is because that for a givennetwork area and a fixed partition parameter m, as net-

(b) σU versus (λ,M)

Fig. 5. Source delay performance versus packet generating probability kand local-queue buffer size M.

116 J. Gao et al. / Ad Hoc Networks 24 (2015) 109–120

work size in terms of n decreases the channel contentionbecomes less severe and thus each source node has morechances to conduct packet dispatch, leading to a shortersource delay one packet experiences in its source node.

5.2. Source delay illustrations

With our QBD-based theoretical framework, we thenillustrate how source delay performance, in terms of its

mean U and standard deviation rU ¼ffiffiffiffiffiffir2

U

q, is related to

some main network parameters like packet generatingprobability k, local-queue buffer size M, packet dispatchlimit f and packet dispatch probability q.

We first illustrate in Fig. 5 how U and rU vary with kand M for a network scenario of n ¼ 200; m ¼ 16; q ¼0:6 and f ¼ 3. We see from Fig. 5a that for any givenM; U first increases as k increases until k reaches somethreshold value and then U remains almost a constant ask increases further beyond that threshold. On the otherhand, for a given k 2 ½0:0005;0:002�, as M increases U firstincreases and then remains constant, while for a given

(a) U versus (q, f)

(b) σU versus (q, f)

Fig. 6. Source delay performance versus packet dispatch probability qand packet dispatch limit f.

k 2 ½0:002;0:01�; U always increases as M increases.Regarding the standard deviation rU of source delay, wesee from Fig. 5b that for given M, as k increases from0.0005 to 0.01 rU first increases sharply to a peak value,then decreases sharply, and finally converges to a constant.It is interesting to see that the peak values of rU under dif-ferent settings of M are all achieved at the samek ¼ 0:0025. The results in Fig. 5b further indicate that forfixed k, as M increases rU always first increases and thengradually converges to a constant.

We then illustrate in Fig. 6 how U andrU vary with packetdispatch parameters q and f under the network scenario ofn ¼ 300; m ¼ 16; M ¼ 7 and k ¼ 0:002. From Fig. 6a and bwe can see that although both U and rU always decreaseas q increases for a fixed f, their variations with q change dra-matically with the setting of f. On the other hand, for a givenq 2 ½0:05;0:2�, as f increases both U and rU first increase andthen tend to a constant, while for a given q 2 ½0:2; ;1:0�, bothU and rU always monotonically increase as f increases.

6. Related works

A substantial amount of works have been devoted tothe study of delay performance in MANETs, which can beroughly divided into partial delay study and overall delaystudy.

6.1. Partial delay study

The available works on partial delay study in MANETsmainly focus on the delivery delay analysis [12,18,22–27]and local delay analysis [28–30], which constitutes only apart of the overall packet delay.

The delivery delay, defined as the time it takes a packetto reach its destination after its source starts to deliver it,has been extensively studied in the literature. For sparseMANETs without channel contentions, the Laplace–Stielt-jes transform of delivery delay was studied in [25]; later,by imposing lifetime constraints on packets, the cumula-tive distribution function and n-th order moment of deliv-ery delay were examined in [22,26]; the delivery delay wasalso studied in [18,23,27] under different assumptions oninter-meeting time among mobile nodes. For more generalMANETs with channel contentions, closed-form results onmean and variance of delivery delay were recentlyreported in [12]. Regarding the local delay, i.e. the time ittakes a node to successfully transmit a packet to its next-hop receiver, it was reported in [28] that some MANETsmay suffer from a large and even infinite local delay. Thework [29] indicates that the power control serves as a veryefficient approach to ensuring a finite local delay in MAN-ETs. It was further reported in [30] that by properlyexploiting node mobility in MANETs it is possible for usto reduce local delay there.

6.2. Overall delay analysis

Overall delay (also called end-to-end delay), defined asthe time it takes a packet to reach its destination after it isgenerated at its source, has also been extensively studied

Fig. B.7. Illustration for state transition from XðtÞ to Xðt þ 1Þ during timeslot ½t; t þ 1Þ.

J. Gao et al. / Ad Hoc Networks 24 (2015) 109–120 117

in the literature. For MANETs with two-hop relay routing,closed-form upper bounds on expected overall delay werederived in [6,16]. For MANETs with two-hop relay routingand its variants, approximation results on expected overalldelay were presented in [13,31]. For MANETs with multi-hop relay routing and simple linear network topology, ana-lytic results on expected overall delay and algorithm forcomputing expected overall delay were reported in[32,33] when the source there has only one packet to betransmitted to its destination; along this line, upperbounds on the cumulative distribution function of overalldelay and approximations to Laplace–Stieltjes Transformof overall delay were further explored in [34–36] whenthe source has multiple packets to be transmitted to itsdestination. For MANETs with multi-hop relay routingand non-linear network topology, some initial results onthe approximation of expected overall delay can be foundin [37]. Rather than studying upper bounds and approxi-mations on overall delay, some recent works exploredthe exact overall delay and showed that it is possible toderive the exact results on overall delay for MANETs undersome special two-hop relay routings [6,7].

7. Conclusion

This paper conducted a thorough study on the sourcedelay in MANETs, a new and fundamental delay metric forsuch networks. A QBD-based theoretical framework wasdeveloped to model the source delay behaviors under a gen-eral packet dispatching scheme, based on which the cumu-lative distribution function as well as the mean and varianceof source delay were derived. As validated through exten-sive simulation results, our QBD-based framework is highlyefficient in modeling the source delay performance in MAN-ETs. Numerical results were also provided to illustrate howsource delay is related to and thus can be controlled by somekey network parameters, like local-queue buffer size, packetdispatch limit, and packet dispatch probability.

Notice that we studied the source delay in MANETsunder the independent and identically distributed mobilitymodel, an interesting future work is to extend our theoret-ical model to analyze source delay for MANETs under otherpopular mobility models, like the random walk andrandom waypoint mobility models. Note also that the the-oretical framework developed in this paper concerns onlysource delay modeling, so another future research direc-tion is to generalize our theoretical framework to modelthe overall delay in MANETs.

Acknowledgment

This work is partially supported by JSPS Grant (B)24300026.

Appendix A. Proof of Lemma 1

The proof process is similar to that in [13,16]. We omitthe proof details here and just outline the main idea of theproof. To derive the probability p0 (resp. p1), we first dividethe event that S conducts a source–destination transmis-

sion (resp. packet-dispatch transmission) in a time slotinto following sub-events: (1) S moves into an active cellin the time slot according to the IID mobility model; (2) Ssuccessfully accesses the wireless channel after fair con-tention according to the MAC–EC protocol; (3) S selectsto conduct source–destination transmission (resp. packet-dispatch transmission) according to the PD-f scheme. Wecan then derive probability p0 (resp. p1) by combining theprobabilities of these sub-events.

Appendix B. Proof of Lemma 2

To derive the conditional steady state distribution p�X ofthe local-queue under the condition that a packet has justbeen inserted into the queue, we first study its correspond-ing transient state distribution pXðt þ 1Þ at time slot t þ 1.

Similar to the definition of p�X, we can see that theð2þ ðl� 1Þf þ jÞ-th entry of row vector pXðt þ 1Þ, denotedby ½pXðt þ 1Þ�2þðl�1Þfþj here, corresponds to the probabilitythat the local-queue is in state Xðt þ 1Þ ¼ ðl; jÞ in time slott þ 1 under the condition that a packet has just beeninserted into the local-queue in time slot t; 1 6 l 6M; 0 6 j 6 f � 1. The basic state transition from XðtÞ toXðt þ 1Þ is illustrated in Fig. B.7, where I0ðtÞ through I3ðtÞare indicator functions defined in Section 3.1, and I4ðtÞ isa new indicator function, taking value of 1 if the local-queue is not full in time slot t (i.e. the local-queue is insome state in fð0;0Þg [ fðl; jÞg; 1 6 l 6 M � 1; 0 6 j 6ff � 1g), and taking value of 0 otherwise.

From Fig. B.7 we can see that ½pXðt þ 1Þ�2þðl�1Þfþj is eval-uated as

½pXðt þ 1Þ�2þðl�1Þfþj ðB:1Þ¼ PrfXðt þ 1Þ ¼ ðl; jÞjI4ðtÞ ¼ 1; I3ðtÞ ¼ 1g ðB:2Þ

¼ PrfI4ðtÞ ¼ 1; I3ðtÞ ¼ 1;Xðt þ 1Þ ¼ ðl; jÞgPrfI4ðtÞ ¼ 1; I3ðtÞ ¼ 1g ðB:3Þ

¼ PrfI4ðtÞ ¼ 1; I3ðtÞ ¼ 1;Xðt þ 1Þ ¼ ðl; jÞgk � PrfI4ðtÞ ¼ 1g ; ðB:4Þ

where (B.4) follows because the packet generating processis a Bernoulli process independent of the state of the local-queue.

For the probability PrfI4ðtÞ ¼ 1g in (B.4), we have

PrfI4ðtÞ ¼ 1g ðB:5Þ¼Xðl0 ;j0 Þ

PrfI4ðtÞ ¼ 1;XðtÞ ¼ ðl0; j0Þg ðB:6Þ

¼Xðl0 ;j0 Þ

PrfXðtÞ ¼ ðl0; j0ÞgPrfI4ðtÞ ¼ 1jXðtÞ ¼ ðl0; j0Þg ðB:7Þ

where PrfI4ðtÞ ¼ 1jXðtÞ ¼ ðl0; j0Þg is actually the transitionprobability from state XðtÞ ¼ ðl0; j0Þ to states in

118 J. Gao et al. / Ad Hoc Networks 24 (2015) 109–120

fð0;0Þg[fðl; jÞg; 16 l6M�1; 06 j6 f �1f g. The matrix P1

of such transition probabilities can be determined basedon (6) by setting the corresponding sub-matrices accordingto (11)–(21). With matrix P1 and (B.7), we have

PrfI4ðtÞ ¼ 1g ¼ pxðtÞ � P1 � 1; ðB:8Þ

where pxðtÞ ¼ ðpx;l;jðtÞÞ1�M�f with px;l;jðtÞ being the proba-bility PrfXðtÞ ¼ ðl0; j0Þg.

For the numerator of (B.4), we have

PrfI4ðtÞ¼1; I3ðtÞ¼1; Xðtþ1Þ¼ðl;jÞg ðB:9Þ¼Xðl0 ;j0 Þ

PrfXðtÞ¼ðl0;j0Þ;I4ðtÞ¼1;I3ðtÞ¼1;Xðtþ1Þ¼ðl;jÞg ðB:10Þ

¼Xðl0 ;j0 Þ

PrfXðtÞ¼ðl0;j0Þg

�PrfI4ðtÞ¼1;I3ðtÞ¼1;Xðtþ1Þ¼ðl;jÞjXðtÞ¼ðl0;j0Þg; ðB:11Þ

where PrfI4ðtÞ ¼ 1; I3ðtÞ ¼ 1; Xðt þ 1Þ ¼ ðl; jÞjXðtÞ ¼ ðl0; j0Þgrepresents the transition probability from state XðtÞ ¼ðl0; j0Þ to state Xðt þ 1Þ ¼ ðl; jÞ, when events fI4ðtÞ ¼ 1g andfI3ðtÞ ¼ 1g also happen simultaneously. The matrix P2 ofsuch transition probabilities is determined based on (6)by setting the corresponding sub-matrices according to(25)–(34). With matrix P2 and (B.11), we have

PrfI4ðtÞ ¼ 1; I3ðtÞ ¼ 1;Xðt þ 1Þ ¼ ðl; jÞg¼ ½pxðtÞP2�2þðl�1Þfþj: ðB:12Þ

After substituting (B.8) and (B.12) into (B.4), we get

½pXðt þ 1Þ�2þðl�1Þfþj ¼½pxðtÞP2�2þðl�1Þfþj

kpxðtÞP11: ðB:13Þ

Thus, in vector form

pXðt þ 1Þ ¼ pxðtÞP2

kpxðtÞP11: ðB:14Þ

Taking limits on both sides of (B.14), we get the steadystate distribution p�X as

p�X ¼ limt!1

pXðt þ 1Þ ðB:15Þ

¼ limt!1

pxðtÞP2

kpxðtÞP11ðB:16Þ

¼ p�xP2

kp�xP11; ðB:17Þ

where

p�x ¼ limt!1

pxðtÞ: ðB:18Þ

This completes the proof of Lemma 2.

Appendix C. Proof of Lemma 3

Recall that as time evolves, the state transitions of thelocal-queue form a QBD process shown in Fig. 3. FromFig. 3, we can see that the QBD process has finite statesand all states communicate with other states, so theMarkov chain is recurrent. We also see from Fig. 3 thatevery state could transition to itself, indicating that theMarkov chain is aperiodic. Thus, the concerned QBD

process is an ergodic Markov chain and thus has a uniquelimit state distribution p�x defined in (B.18).

Notice that p�x must satisfy the following equation

p�x ¼ p�xP0; ðC:1Þ

where P0 is the transition matrix of the QBD process, whichcan be determined based on (6) by setting the correspond-ing sub-matrices according to (47)–(53). In particular, forM ¼ 1 and M ¼ 2, the transition matrix P0 is given by thefollowing (C.2) and (C.3), respectively.

P0 ¼B1 B0

B2 AM

� �; ðC:2Þ

P0 ¼B1 B0

B2 A1 A0

A2 AM

264

375: ðC:3Þ

Thus, under the cases of M ¼ 1 and M ¼ 2, p�x could be eas-ily calculated by Eqs. (36)–(42), respectively. Due to thespecial structure of the matrix A2, which is the product ofa column vector c by a row vector r [20], p�x under the caseM P 3 could be calculated by Eqs. (43)–(46).

Appendix D. Proof of Theorem 1

Suppose that the local-queue is in some state accordingto the steady state distribution p�X, then the source delay ofa packet (say Z) is independent of the packet generatingprocess after Z is inserted into the local-queue and is alsoindependent of the state transitions of the local-queueafter Z is removed from the local-queue. Such indepen-dence makes it possible to construct a simplified QBD pro-cess to study the source delay of packet Z, in which newpackets generated after packet Z are ignored, and once Zis removed from the local-queue (or equivalently thelocal-queue transits to state ð0;0Þ), the local-queue willstay at state ð0;0Þ forever.

For the above simplified QBD process, its transitionmatrix P3 can be determined based on (6) by setting thecorresponding sub-matrices as follows:

For M ¼ 1,

B0 ¼ 0; ðD:1ÞB1 ¼ ½1�; ðD:2ÞB2 ¼ c; ðD:3ÞAM ¼ Q : ðD:4Þ

For M P 2,

B0 ¼ 0; ðD:5ÞB1 ¼ ½1�; ðD:6ÞB2 ¼ c; ðD:7ÞA0 ¼ 0; ðD:8ÞA1 ¼ Q ; ðD:9ÞA2 ¼ c � r; ðD:10ÞAM ¼ Q : ðD:11Þ

By rearranging P3 as

J. Gao et al. / Ad Hoc Networks 24 (2015) 109–120 119

P3 ¼1 0cþ T

� �; ðD:12Þ

we can see that matrices cþ and T are determined as (60)–(63). With matrices cþ, T and p�X, the probability massfunction (56) and CDF (57) of the source delay followdirectly from the theory of Phase-type distribution [20].

Based on the probability mass function (56), the mean Uof the source delay can be calculated by

U ¼X1u¼1

u � PrfU ¼ ug ¼X1u¼1

up�XTu�1cþ

¼ p�XX1u¼1

uTu�1

!cþ ðD:13Þ

Let

f ðTÞ ¼X1u¼1

uTu�1; ðD:14Þ

and use f ðxÞ to denote its corresponding numerical series

f ðxÞ ¼X1u¼1

uxu�1 ðD:15Þ

¼ ð1� xÞ�2; for x < 1: ðD:16Þ

Since above simplified QBD process is actually anabsorbing Markov Chain with transition matrix P3, weknow from Theorem 11.3 in [38] that

limk!1

Tk ¼ 0: ðD:17Þ

Based on the property (D.17) and the Theorem 5.6.12 in[39], we can see that the spectral radius qðTÞ of matrix Tsatisfies following condition

qðTÞ < 1: ðD:18Þ

From (D.14), (D.16) and (D.18), it follows that thematrix series f ðTÞ converge as

f ðTÞ ¼ limg!1

Xg

u¼1

uTu�1 ðD:19Þ

¼ ðI� TÞ�2 ðD:20Þ

After substituting (D.20) into (D.13) and (58) thenfollows.

The derivation of the variance of source delay (59) couldbe conducted in a similar way and thus is omitted here.

References

[1] J. Andrews, S. Shakkottai, R. Heath, N. Jindal, M. Haenggi, R. Berry, D.Guo, M.J. Neely, S. Weber, S. Jafar, A. Yener, Rethinking informationtheory for mobile ad hoc networks, IEEE Commun. Mag. 46 (12)(2008) 94–101.

[2] A. Goldsmith, M. Effros, R. Koetter, M. MTdard, L. Zheng, BeyondShannon: the quest for fundamental performance limits of wirelessad hoc networks, IEEE Commun. Mag. 49 (5) (2011) 195–205.

[3] L. Hanzo II, R. Tafazolli, A survey of QoS routing solutions for mobilead hoc networks, IEEE Commun. Surv. Tutor. 9 (2) (2007) 50–70.

[4] L. Chen, W.B. Heinzelman, A survey of routing protocols that supportQoS in mobile ad hoc networks, IEEE Network 21 (6) (2007) 30–38.

[5] M. Grossglauser, D.N. Tse, Mobility increases the capacity of ad hocwireless networks, IEEE/ACM Trans. Network. 10 (4) (2002) 477–486.

[6] M.J. Neely, E. Modiano, Capacity and delay tradeoffs for ad-hocmobile networks, IEEE Trans. Inform. Theory 51 (6) (2005) 1917–1936.

[7] J. Gao, X. Jiang, Delay modeling for broadcast-based two-hop relayMANETs, in: 11th International Symposium on Modeling andOptimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt),2013.

[8] A.E. Gamal, J. Mammen, B. Prabhakar, D. Shah, Optimal throughput-delay scaling in wireless networks – Part I: The fluid model, IEEETrans. Inform. Theory 52 (6) (2006) 2568–2592.

[9] G. Sharma, R. Mazumdar, N.B. Shroff, Delay and capacity trade-offsfor mobile ad hoc networks: a global perspective, IEEE/ACM Trans.Network. 15 (5) (2007) 981–992.

[10] D. Ciullo, V. Martina, M. Garetto, E. Leonardi, Impact of correlatedmobility on delay-throughput performance in mobile ad hocnetworks, IEEE/ACM Trans. Network. 19 (6) (2011) 1745–1758.

[11] P. Li, Y. Fang, J. Li, X. Huang, Smooth trade-offs between throughputand delay in mobile ad hoc networks, IEEE Trans. Mobile Comput. 11(3) (2012) 427–438.

[12] J. Liu, X. Jiang, H. Nishiyama, N. Kato, Generalized two-hop relay forflexible delay control in MANETs, IEEE/ACM Trans. Network. 20 (6)(2012) 1950–1963.

[13] J. Liu, J. Gao, X. Jiang, H. Nishiyama, N. Kato, Capacity and delay ofprobing-based two-hop relay in MANETs, IEEE Trans. WirelessCommun. 11 (11) (2012) 4172–4183.

[14] P. Gupta, P. Kumar, The capacity of wireless networks, IEEE Trans.Inform. Theory 46 (2) (2000) 388–404.

[15] S.R. Kulkarni, P. Viswanath, A deterministic approach to throughputscaling in wireless networks, IEEE Trans. Inform. Theory 50 (6)(2004) 1041–1049.

[16] J. Liu, X. Jiang, H. Nishiyama, N. Kato, Delay and capacity in ad hocmobile networks with f-cast relay algorithms, IEEE Trans. WirelessCommun. 10 (8) (2011) 2738–2751.

[17] R.P. Liu, G.J. Sutton, I.B. Collings, A new queueing model for QoSanalysis of IEEE 802.11 DCF with finite buffer and load, IEEE Trans.Wireless Commun. 9 (8) (2010) 2664–2675.

[18] T. Small, Z. Hass, Resource and performance tradeoffs in delay-tolerant wireless networks, in: Proc. ACM SIGCOMM Workshop onDelay-Tolerant Networking (WDTN), 2005, pp. 260–267.

[19] B. Williams, T. Camp, Comparison of broadcasting techniques formobile ad hoc networks, in: MobiHoc, 2002.

[20] G. Latouche, V. Ramaswamy, Introduction to matrix analyticmethods in stochastic modeling, ASA–SIAM Series on Statistics andApplied Probability, 1999.

[21] C++ simulator for PD-f MANETs, 2013 <http://researchplatform.blogspot.jp/>.

[22] A.A. Hanbali, P. Nain, E. Altman, Performance of ad hoc networkswith two-hop relay routing and limited packet lifetime (extendedversion), Perform. Eval. 65 (6–7) (2008) 463–483.

[23] A. Panagakis, A. Vaios, I. Stavrakakis, Study of two-hop messagespreading in DTNs, in: WiOpt, 2007.

[24] M. Ibrahim, A.A. Hanbali, P. Nain, Delay and resource analysis inMANETs in presence of throwboxes, Perform. Eval. 64 (9–12) (2007)933–947.

[25] R. Groenevelt, P. Nain, G. Koole, The message delay in mobile ad hocnetworks, Perform. Eval. 62 (1–4) (2005) 210–228.

[26] A.A. Hanbali, A.A. Kherani, P. Nain, Simple models for theperformance evaluation of a class of two-hop relay protocols, in:Proc. IFIP Networking, 2007, pp. 191–202.

[27] T. Spyropoulos, K. Psounis, C.S. Raghavendra, Efficient routing inintermittently connected mobile networks: the multiple-copy case,IEEE/ACM Trans. Network. 16 (1) (2008) 77–90.

[28] F. Baccelli, B. Blaszczyszyn, A new phase transitions for local delaysin MANETs, in: INFOCOM, 2010.

[29] M. Haenggi, The local delay in poisson networks, IEEE Trans. Inform.Theory 59 (3) (2013) 1788–1802.

[30] Z. Gong, M. Haenggi, The local delay in mobile poisson networks,IEEE Trans. Wireless Commun. 12 (9) (2013) 4766–4777.

[31] J. Liu, X. Jiang, H. Nishiyama, N. Kato, X. Shen, End-to-end delay inmobile ad hoc networks with generalized transmission range andlimited packet redundancy, in: WCNC, 2012c.

[32] B. Blaszczyszyn, P. Muhlethaler, Stochastic Analytic Evaluation ofEnd-to-End Performance of Linear Nearest Neighbour Routing inMANETs with Aloha, Technical Report <http://arxiv.org/abs/1207.7219>.

[33] P. Nain, D. Towsley, A. Bar-Noy, P. Basu, M.P. Johnson, F. Yu,Estimating end-to-end delays under changing conditions, in: ACMMobiCom Workshop on Challenged Networks (CHANTS), 2013.

120 J. Gao et al. / Ad Hoc Networks 24 (2015) 109–120

[34] F. Ciucu, O. Hohlfeld, P. Hui, Non-asymptotic throughput and delaydistributions in multi-hop wireless networks, in: Annual AllertonConference on Communication, Control, and Computing (Allerton), 2010.

[35] F. Ciucu, Non-asymptotic capacity and delay analysis of mobilewireless networks, in: SIGMETRICS, 2011.

[36] A.A. Hanbali, R. de Haan, R.J. Boucherie, J.-K. van Ommeren, Delay ina tandem queueing model with mobile queues: an analyticalapproximation, Probab. Eng. Inform. Sci. 28 (03) (2014) 363–387.

[37] A. Jindal, K. Psounis, Contention-aware performance analysis ofmobility-assisted routing, IEEE Trans. Mobile Comput. 8 (2) (2009)145–161.

[38] C.M. Grinstead, J.L. Snell, Introduction to Probability, second reviseded., American Mathematical Society, 1997.

[39] R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University Press,1990.

Juntao Gao received his B.S. and M.S. degreesboth in Computer Science from Xidian Uni-versity, Xi’an, China, in 2008 and 2010,respectively, and received his Ph.D. degreefrom Graduate School of Systems InformationScience at Future University Hakodate, Japan,in 2014. He is an assistant professor at Grad-uate School of Information Science at NaraInstitute of Science and Technology, Japan. Hisresearch interests are in the areas of perfor-mance modeling and analysis, stochasticoptimization and control in wireless net-

works, queueing theory and its applications.

Yulong Shen received the B.S. and M.S.degrees in Computer Science and Ph.D. degreein Cryptography from Xidian University, Xi’an,China, in 2002, 2005, and 2008, respectively.He is currently an associate Professor at theSchool of Computer Science and Technology,Xidian University, China. He is also associatedirector of the Shaanxi Key Laboratory ofNetwork and System Security and a memberof the State Key Laboratory of IntegratedServices networks Xidian University, China.He has also served on the technical program

committees of several international conferences, including ICEBE, INCoS,CIS and SOWN. He is an IEEE and ACM member. Hiss research interest iswireless network security.

Xiaohong Jiang received his B.S., M.S. andPh.D. degrees all from Xidian University,China. He is currently a full professor ofFuture University Hakodate, Japan. He was anAssociate professor of Tohoku University,Japan, from February 2005 to March 2010, anassistant professor in Japan Advanced Insti-tute of Science and Technology (JAIST), fromOctober 2001 to January 2005. He was a JSPSresearch fellow at JAIST from October 1999 toOctober 2001. He was a research associate inthe University of Edinburgh from March 1999

to October 1999. His research interests include computer communica-tions networks, mainly wireless networks, optical networks, etc. He haspublished over 200 technical papers at premium international journals

and conferences, which include over 20 papers published in IEEE journalslike IEEE/ACM Transactions on Networking, IEEE Journal of Selected Areason Communications, etc. He was the winner of the Best Paper Award andOutstanding Paper Award of IEEE WCNC 2012, IEEE WCNC 2008, IEEE ICC2005-Optical Networking Symposium, and IEEE/IEICE HPSR 2002. He is aSenior Member of IEEE and a member of IEICE.

Jie Li received the B.E. degree in computerscience from Zhejiang University, Hangzhou,China, the M.E. degree in Electronic Engi-neering and Communication Systems fromChina Academy of Posts and Telecommuni-cations, Beijing, China. He received the Dr.Eng. degree from the University of Electro-Communications, Tokyo, Japan. He has beenwith University of Tsukuba, Japan, where he isa full Professor. His research interests are inmobile distributed multimedia computingand networking, OS, network security, mod-

eling and performance evaluation of information systems. He received thebest paper award from IEEE NAECON’97. He is a senior member of IEEEand ACM, and a member of IPSJ (Information Processing Society of Japan).

He has served as a secretary for Study Group on System Evaluation of IPSJand on several editorial boards for IPSJ Journal and so on, and on SteeringCommittees of the SIG of System EVAluation (EVA) of IPSJ, the SIG ofDataBase System (DBS) of IPSJ, and the SIG of MoBiLe computing andubiquitous communications of IPSJ. He has been a co-chair of severalinternational symposia and workshops. He has also served on the pro-gram committees for several international conferences such as IEEEICDCS, IEEE INFOCOM, IEEE GLOBECOM, and IEEE MASS.