Source delay in mobile ad hoc networks

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<ul><li><p>Ad Hoc Networks 24 (2015) 109120Contents lists available at ScienceDirect</p><p>Ad Hoc Networks</p><p>journal homepage: www.elsevier .com/locate /adhocSource delay in mobile ad hoc networkshttp://dx.doi.org/10.1016/j.adhoc.2014.08.0041570-8705/ 2014 Elsevier B.V. All rights reserved.</p><p> Corresponding author at:E-mail addresses: jtgao@is.naist.jp (J. Gao), ylshen@mail.xidian.edu.cn</p><p>(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 eaGraduate 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, Japana r t i c l e i n f o</p><p>Article history:Received 21 November 2013Received in revised form 6 March 2014Accepted 9 August 2014Available online 19 August 2014</p><p>Keywords:MANETsPacket dispatchSource delayMeanVariancea b s t r a c t</p><p>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.</p><p> 2014 Elsevier B.V. All rights reserved.1. Introduction</p><p>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.</p><p>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</p><p>http://crossmark.crossref.org/dialog/?doi=10.1016/j.adhoc.2014.08.004&amp;domain=pdfhttp://dx.doi.org/10.1016/j.adhoc.2014.08.004mailto:jtgao@is.naist.jpmailto:ylshen@mail.xidian.edu.cnmailto:jiang@fun.ac.jpmailto:lijie@cs.tsukuba.ac.jphttp://dx.doi.org/10.1016/j.adhoc.2014.08.004http://www.sciencedirect.com/science/journal/15708705http://www.elsevier.com/locate/adhoc</p></li><li><p>110 J. Gao et al. / Ad Hoc Networks 24 (2015) 109120dynamic 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.</p><p> 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.</p><p> With the help of the theoretical framework, we thenderive the cumulative distribution function (CDF) aswell as mean and variance of the source delay in theconsidered MANET. By setting f 1 in a PD-f MANET,the corresponding source delay actually serves as alower bound for overall delay.</p><p> Extensive simulation results are provided to validateour 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.</p><p>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 inFig. 1. An example of a cell partitioneSection 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.</p><p>2. Preliminaries</p><p>In this section, we introduce the basic system models,the Medium Access Control (MAC) protocol and the packetdispatching scheme involved in this study.</p><p>2.1. System models</p><p>2.1.1. Network model and mobility modelWe consider a time slotted torus MANET of unit area.</p><p>Similar to previous works, we assume that the networkarea is evenly partitioned into mm cells as shown inFig. 1a [811]. 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.</p><p>2.1.2. Communication modelWe assume that all nodes transmit data through one</p><p>common wireless channel, and each node (say S inFig. 1a) employs the same transmission range r </p><p>ffiffiffi8</p><p>p=m</p><p>to cover 9 cells, including Ss 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 1 D r, whered MANET with a MAC protocol.</p></li><li><p>J. Gao et al. / Ad Hoc Networks 24 (2015) 109120 111dij 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.</p><p>2.1.3. Traffic modelWe consider the widely adopted permutation traffic</p><p>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 &gt; 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.</p><p>2.2. MAC protocol</p><p>We adopt a commonly used MAC protocol based on theconcept of Equivalent-Class to address wireless mediumaccess issue in MANETs [1012,15]. 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 ofa1 6 a 6 m cells. Under the EC-based MAC protocol(MACEC), the whole network cells are divided into a2</p><p>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.</p><p>To avoid interference among concurrent transmissionsunder the MACEC 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 nodeW 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,</p><p>dWR P 1 D r: 1</p><p>Notice that dWR P a 2=m, we have</p><p>a 2=m P 1 D r: 2</p><p>Since a 6 m and r ffiffiffi8</p><p>p=m; a should be set as</p><p>a min d1 Dffiffiffi8</p><p>p 2e;m</p><p>n o; 3</p><p>where the function dxe returns the least integer valuegreater than or equal to x.</p><p>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 firstinitiates a backoff timer with backoff period drawnuniformly from 0;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</p><p>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.</p><p>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 1 and only unicast transmission is allowed, the oneswith controllable packet redundancy [12,16,18] whenf &gt; 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.</p><p>1: if S has packets in its local-queue then2: S checks whether its destination D is within its</p><p>transmission range;3: if D is within its transmission range then4: S transmits the head-of-line (HoL) packet in its</p><p>local-queue to D;{sourcedestination transmission}</p><p>5: S removes the HoL packet from its local-queue;6: S moves ahead the remaining packets in its</p><p>local-queue;7: else8: With probability q (0 &lt; q &lt; 1), S dispatches the</p><p>HoL packet;9: if S conducts packet dispatch then10: S dispatches the HoL packet for one time;</p><p>{packet-dispatch transmission}11: if S has already dispatched the HoL packet</p><p>for f times then12: S removes the HoL packet from its local-</p><p>queue;13: S moves ahead the remaining packets in</p><p>its local-queue;14: end if15: end if16: end if17: else18: S remains idle;19: end if3. QBD-based theoretical framework</p><p>In this section, a QBD-based theoretical framework isdeveloped to capture the packet dispatching process in a</p></li><li><p>Fig. 2. State transitions from state l; j of the local-queue.</p><p>112 J. Gao et al. / Ad Hoc Networks 24 (2015) 109120PD-fMANET. This framework will help us to analyze sourcedelay in Section 4.</p><p>3.1. QBD modeling</p><p>Due to the symmetry of source nodes, we only focus ona source node S in our analysis. We adopt a two-tupleXt Lt; Jt to define the state of the local-queue inS at time slot t, where Lt denotes the number of packetsin the local-queue at slot t and Jt denotes the numberof packet dispatches that have been conducted for thecurrent head-of-line packet by slot t, here 0 6 Lt 6M;0 6 Jt 6 f 1 when 1 6 Lt 6 M, and Jt 0 whenLt 0.</p><p>Suppose that the local-queue in S is at state l; j in thecurrent time slot, all the possible state transitions that mayhappen at the next time slot are summarized in Fig. 2,where</p><p> I0t is an indicator function, taking value of 1 if S con-ducts sourcedestination transmission in the currenttime slot, and taking value of 0 otherwise;</p><p> I1t 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;</p><p> I2t is an indicator function, taking value of 1 if S con-ducts neither sourcedestination nor packet-dispatchtransmission in the current time slot, and taking valueof 0 otherwise;</p><p> I3t is an indicator function, taking value of 1 if S locallygenerates a packet in the current time slot, and takingvalue of 0 otherwise.</p><p>From Fig. 2 we can see that as time evolves, the statetransitions of the local-queue in S form a two-dimensionalQBD process [20]</p><p>fXt; t 0;1;2; . . .g; 4</p><p>on state space</p><p>f0;0g [ fl; jg;1 6 l 6 M;0 6 j 6 f 1f g: 5</p><p>Based on the transition scenarios in Fig. 2, the overalltransition diagram of above QBD process is illustratedin Fig. 3.</p><p>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 sourcedestination and packet-dispatch transmissions (i.e., node mobility, medium con-tention, interference and packet transmitting).3.2. Transition matrix and some basic results</p><p>As shown in Fig. 3 that there are in total 1M f two-tuple states for the local-queue in S. To construct the tran-sition matrix of the QBD process, we arrange all these1M f states in a left-to-right and top-to-down...</p></li></ul>

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