efficient scheduling for video transmissions in maritime

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 9, SEPTEMBER 2015 4215

Efficient Scheduling for Video Transmissions inMaritime Wireless Communication Networks

Tingting Yang, Member, IEEE, Hao Liang, Member, IEEE, Nan Cheng, Student Member, IEEE,Ruilong Deng, Member, IEEE, and Xuemin (Sherman) Shen, Fellow, IEEE

Abstract—This paper develops a framework for vessel surveil-lance video uploading via maritime wideband communicationnetworks. A broadband wireless network utilizing a time-division-multiple-access (TDMA)-based media access control protocol isemployed to establish a shore-side network infrastructure, anda packet store–carry–forward routing mechanism is adopted toachieve intermittent network connectivity in maritime commu-nications. To provide high-quality videos to the administrativeauthority, a resource allocation problem is formulated to maxi-mize the throughput priority-based video transmission problem,subject to the intermittent network connections and the timeindexes such as the release time and deadline of each video packet.To reduce computational complexity, time-capacity mapping isapplied to transform the original resource allocation problem intoa two-machine nonpreemptive scheduling problem. Three offlinescheduling algorithms are proposed, namely, a time-capacity-mapping-based two-phase (TMTP) algorithm for a single ma-chine, a TMTP algorithm for two machines, and an intervalgraph-theory-based job relay selection (IGTJRS) algorithm. It ismathematically proved that the IGTJRS algorithm has an ap-proximation ratio (i.e., the ratio of the throughput of an optimalschedule to that of the IGTJRS algorithm) of 2 and time com-plexity of O(n2). Simulations results validate the performance ofthe proposed algorithms, based on real ship route traces obtainedfrom navigation software BLM-Shipping.

Index Terms—Job-machine scheduling, maritime widebandcommunication, time-capacity mapping, video transmission.

Manuscript received June 12, 2013; revised June 26, 2014 and August 26,2014; accepted August 28, 2014. Date of publication October 1, 2014; dateof current version September 15, 2015. This work was supported in part bythe China Postdoctoral Science Foundation under Grant 2013M530900, by theNatural Science Foundation of China under Grant 61401057, by the Scienceand Technology Research Program of Liaoning under Grant L2014213, bythe Natural Sciences and Engineering Research Council of Canada, by theResearch Funds for the Central Universities, by the China Postdoctoral Interna-tional Academic Exchange Fund, and by the Scientific Research Foundationfor the Returned Overseas Chinese Scholars from the Ministry of HumanResources and Social Security. This paper was presented in part at the IEEEGlobal Communications Conference, Atlanta, GA, USA, December 9–13,2013. The review of this paper was coordinated by N.-D. Dao.

T. Yang is with the Navigation College, Dalian Maritime University, Dalian116026, China, and also with the Department of Electrical and ComputerEngineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail:[email protected]).

H. Liang is with the Department of Electrical and Computer Engi-neering, University of Alberta, Edmonton, AB T6G 2V4, Canada (e-mail:[email protected]).

N. Cheng and X. Shen are with the Department of Electrical and ComputerEngineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada (e-mail:[email protected]; [email protected]).

R. Deng is with the School of Electrical and Electronic Engineer-ing, Nanyang Technological University, Singapore 639798 (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2014.2361120

I. INTRODUCTION

I T IS ENVISIONED that developing a maritime widebandcommunication system will greatly contribute to the mar-

itime distress, urgency, safety, and general communications [1].In particular, large capacity data such as surveillance videoscollected from bridge, engine room, or other critical regionsof a vessel can be efficiently delivered via such a system,which is crucial to maritime administrative authority on shore.Furthermore, safety-related information and multimedia datacould also be disseminated via this system. In other words, itextends wideband services from the land to the ocean.

The state-of-the-art maritime communication system, chris-tened as Global Maritime Distress and Safety System, com-prises of terrestrial and satellite systems [2]. For a satellitemaritime communication system, the advanced Fleet Broad-band (FBB) system can be enabled to establish wideband trans-missions with a data rate of up to 432 kb/s. Nonetheless, highcapital expenditure to launch satellites results in high servicecost (e.g., voice service costs 13.75 U.S. dollars per minute).Consequently, the cost of conveying large capacity videos couldbe prohibitive. On the other hand, existing terrestrial maritimecommunication systems cannot provide wideband services.Taking the legacy very-high-frequency communication systemas an example, the maximum data rate is merely 9.6 kb/s.Hence, it is an imperious demand to establish a maritimewideband communication system at low service expenditure. Itperfectly matches the emerging E-Navigation strategy initiatedby the International Maritime Organization, which is a led con-cept based on the harmonization of marine navigation systemsand supporting shore services driven by user needs [3].

The development of new maritime wideband networks hasattracted significant attention recently. In [4], Zhou et al. de-vised a cognitive maritime mesh/ad hoc network. The U.S.Navy ships have been getting advanced Fourth GenerationLong-Term Evolution (4G LTE) broadband service since 2011[5]. In Singapore, the project of wireless broadband access forSeaport (WISEPORT) achieves a wireless broadband accessrate of up to 5 Mb/s based on Worldwide Interoperability forMicrowave Access (WiMAX) technology [6]. Due to its highdata rate and large coverage area, WiMAX technology has beenapproved to be a candidate to satisfy the increasing demand ofwideband data traffic at sea [7]. However, its coverage rangeis still limited (e.g., with a range of approximately 20 nauticalmiles from the coastline). Moreover, the wireless channelsoccasionally deteriorate due to obstacles such as sea clutters,and the period of wireless connection is short because of a

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4216 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 9, SEPTEMBER 2015

limited number of infostations deployed on the shore side.Consequently, a continuous end-to-end path may not be avail-able in maritime environment. An innovative complementaryscheme is packet store–carry–forward routing in delay-tolerantnetworks (DTNs) [8], which can efficiently utilize node mobil-ity statistics and permit other nodes to store, carry, and forwarddata packets once a communication opportunity arises. Datadelivery can be achieved via infestations on the shore side,whereas the coverage provided by infostations might not beseamless due to long coastline and high deployment cost ofinfostations.

We design a broadband wireless network/store–carry–forward interworking maritime wideband communication sys-tem, which utilizes a time-division multiple access (TDMA)media access control (MAC) protocol widely used in WiMAXand LTE technology, explicitly devised to overcome the givenlimitations. We consider the vessel closed-circuit televisionsystems, which rigorously collect surveillance videos frombridge, engine room, deck, and/or other critical regions of themonitored vessel, under the control of elaborate intervalometercomponents [9]. Surveillance video clips are generated everyfixed interval, which are further divided into packets. Eachpacket has a release time, a deadline, and a weight, which areknown a priori, since the Electronic Chart Display and Infor-mation System [10] combined with Radio Beacon-DifferentialGlobal Positioning System onboard, Automatic IdentificationSystem (AIS), and predefined WiMAX TDMA protocol couldbenefit the prediction of global information under the premiseof the fixed routes scheduled in advance. For clarity, someterms used in this paper are defined as follows: Ship’s routemeans the lane at sea that is regularly used as the route forvessels; sailing schedule is defined as the exact planning of avessel’s travel between the origin port and the destination port,according to distance, speed, etc.; and actual trace representsthe real-time ship locations, speed, course, and other navigationdata detected by GPS and AIS on board. Weight is the quotientthat values its contribution to the importance of video clips orthe significance to the administrative authority. For instance,the packet with higher weight reflects the video informationpertinent to the crucial sections of a vessel, such as bridge,engine room, chart room, and cargo hold, other than galley,mess, accommodation, and game room [11]. When vessels passby infostations deployed along the shore side, i.e., the vesselsare in the transmission coverage of infostations, the infostationswill make an effort to upload video packets for vessels. Thevessel speed, distance between vessel and infostation determinethe contact period, which is defined as the time window withinwhich a vessel can transmit video packets to infostations.Due to the mobility, a vessel can only communicate withan infostation in its transmission range during the availabletime window. Hence, the resource allocation issues, referringto allocating transmission time slots for video packets in thetime windows of different infostations, are complicated andchallenging as the link from vessel to infostation is highlydynamic and subject to periodic disconnections as a vessel sailsen route. To transmit packets before the respective deadline andgain better video quality, which is determined by the weightof delivered packets, a cooperative transmission strategy can be

exploited. However, the scheduling of data packets to be relayedby other vessels still needs to be investigated. It should benoted that the scenario of maritime wideband communicationsutterly distinguishes from that of the existing data servicedelivery studied in vehicular networks [12] and high-speedtrains [13]. In vehicular networks, the traces of vehicles arenondeterministic and dynamically changing. In contrast, thetraces of vessels are deterministic or predictable since shiproutes1 are relatively stable and known a priori. In terms ofa high-speed train, the train schedule is deterministic, and thetrajectory is 1-D. However, the network topology in a maritimecommunication system could be either 1-D (without relay) or2-D (with relay). How to schedule video packets in 2-D andintermittently connected maritime communication system withdeterministic global knowledge is still an open issue.

In this paper, we are interested in transmitting critical videopackets to the administrative authority, i.e., throughput maxi-mization problem (TMP) based on the redefinition of through-put as the summation of weight of delivered packets. Wefirst formulate the packet scheduling problem, by taking intoaccount the intermittent network connectivity and cooperativetransmissions, and then mathematically transform this probleminto a job-machine problem. To reduce computational complex-ity, a time-capacity mapping method is applied to transform theoriginal resource allocation problem to a two-machine nonpre-emptive scheduling problem. Based on the knowledge of theschedules of vessels and the time indexes of jobs, we proposethree offline scheduling algorithms, namely, a time-capacity-mapping-based two-phase (TMTP) algorithm for a singlemachine, a TMTP algorithm for two machines, and an interval-graph-theory-based job relay selection (IGTJRS) algorithm.The performance of our proposed algorithms is demonstratedby simulations and comparisons with other classic schedulingalgorithms and existing maritime communication algorithms,under the real ship routes data obtained from navigation soft-ware BLM-Ship. This work targets to investigate the schedulingissues in a maritime communication system, which is featuredby the 2-D network topology, intermittent network connection,and deterministic global knowledge. Specifically, the contribu-tion of this paper is fourfold.

1) A time-capacity mapping technique is introduced totransform the original intermittent network connectivityscenario into a virtually continuous scenario. Thereby,the resource allocation issue could be converted fromtime-based scheduling to capacity-based scheduling overa continuous horizon to facilitate algorithm design.

2) Three offline scheduling algorithms, namely, a TMTPalgorithm for a single machine, a TMTP algorithm fortwo machines, and an IGTJRS algorithm, are proposed,respectively.

3) It is mathematically proved that the IGTJRS algorithmhas an approximation ratio (i.e., the ratio of the through-put of an optimal schedule to that of the IGTJRS algo-rithm) of 2 and time complexity of O(n2).

1We use the terms vessel and ship interchangeably.

YANG et al.: SCHEDULING FOR VIDEO TRANSMISSIONS IN MARITIME WIRELESS COMMUNICATION NETWORKS 4217

TABLE INOTATIONS AND DEFINITIONS

4) The simulations for the single-vessel, two-vessel, andmultivessel scenarios are performed using real vesseltraces obtained from BLM-Shipping navigation software.

The remainder of this paper is organized as follows. InSection II, we discuss some related works. System modeland problem formulation are presented in Sections III andIV, respectively. Three scheduling algorithms are proposed,and the performance analysis is corroborated in Section V.In Section VI, simulation results are given to demonstrate theperformance of our approaches. We conclude this paper withfuture work in Section VII. As many symbols are used inthis paper, some important notation definitions are tabulated inTable I.

II. RELATED WORK

In literature, there are several research works related tomaritime communication networks. The project TRITON [14]investigates a wireless mesh network to support multihop datatransmissions in maritime communications, and the perfor-mance of the MAC protocol is simulated. The ship mobilitymodel in terms of probability density function for ship speed ismodeled in [15]. In [16], the performance comparison of threeexisting routing protocols, i.e., optimized link state routing,ad hoc on-demand distance vector routing, and ad hoc on-demand multipath distance vector, in maritime networks isshown. In [17], Lin et al. explored the WiMAX-based meshtechnology for ship-to-ship communications with DTN featuresto provide less expensive wireless communication services atsea and compared the performance between regular routing pro-tocols and DTN routing protocols. In [18], a theoretical modelis developed to analyze the ships encounter probability distribu-tion, and the data delivery ratio from ships to the base station isderived. In [19], the performance of file delivery is investigatedthrough maritime DTNs. The proposed scheme integrates exist-ing oversea AIS to deal with mobility data of vessels, throughwhich the intervessel connection can be accurately predicted.The transmission opportunities are introduced only when twovessels are direct within the communication range of eachother, whereas in our work, we use DTN throw-box temporarily

storing data to enhance the transmission opportunity. In [20], adistributed adaptive time slot allocation scheme for a WiMAXmesh MAC protocol is proposed, considering the difference inmonitoring reception quality of an allocated time slot. In [21], anovel approach is proposed by utilizing multihop WiMAX andmesh network to provide Internet access to the MediterraneanSea without the assistance of a satellite. The MAC and routingschemes suitable for such a scenario are investigated, with thenetwork connectivity analysis. However, the Mediterranean Seacan be seen as a special scenario because the vessel density ishigh, and Internet access is assumed available anytime via themultihop mesh network. In [22], the maritime mesh networkbased on IEEE 802.16 mesh standards is developed to providemaritime communications with high bandwidth and accept-able quality of service. Different user requirements of overseacommunications are investigated, followed by the analysis ofconnectivity and design of scheduling and routing schemes. In[23], the maximum network capacity with a minimum voice-over-Internet-protocol cost flow is dimensioned over multihopmaritime networks. In addition, some other research issues areproposed for this special communication network application.They partially focus on ship–ship communication scenariothrough intervessel connectivity predictions and the evaluationof transmission performance in maritime DTNs [24]. Addi-tionally, few literature with emphasis on data transmissionscheduling problem in DTN maritime networks is presented.

With respect to data delivery, although there are very fewresearch works in the literature for maritime scenario, vehicle-assisted data delivery has been extensively studied. In [12],Yan et al. developed a theoretical model to compute the achiev-able throughput of cooperative mobile content distribution invehicular ad hoc networks. The IEEE 802.11p MAC proto-col is proposed for video broadcasting in a metro passengercommunication system, which is specially designed for high-speed trains with a speed of up to 360 km/h [25]. In [26],Khabbaz et al. provided the model and delay analysis of ve-hicular networks, investigating an information-delivery-delayminimization problem based on a probabilistic bundle re-lease scheme and a greedy bundle release scheme. In [27],Gozupek et al. addressed a throughput satisfaction-based


scheduling problem that maximizes the number of satisfiedusers for cognitive radio networks. In [28], Liang et al. pro-posed a semi-Markov decision-process-based service modelto manage interdomain resource allocation in mobile cloudnetworks. Cheng et al. proposed a vehicle-assisted data deliverymethod for smart grid applications. In [13], Liang and Zhuanginvestigated on-demand data services for high-speed trains. Anonline resource allocation algorithm based on Smith ratio andexponential capacity is proposed.

Regarding the job-machine scheduling problem, there existrelated works that target maximizing the weight of jobs be-fore their deadlines. Bar-Noy et al. [29] found combinatorialalgorithms for diverse types of machines (identical versus un-related) and the weight of the jobs (identical versus arbitrary).A ((1 + 1/k)k)/((1 + 1/k)k − 1) approximation algorithm isdeveloped for the R|rτ |

∑(1 − Uτ ) problem with arbitrary job

weight and k identical machines2. The approximation ratio ofan approximation algorithm denotes the ratio of the throughputof an optimal schedule to that of the approximation algorithmfor TMP. As k → ∞, the approximation ratio bound tends tobe (e/e− 1) ≈ 1.58198. A combinatorial algorithm labeledADMISSION is presented for the R|rτ |

∑wτ (1 − Uτ ) prob-

lem with an approximation ratio bound of 3 + 2√

2 ≈ 5.828,where wτ represents the weight of job τ . These are cases for anonpreemptive online scheduling algorithm. Nevertheless, thealgorithms are complex and slow. Following the nomenclatureof Lawler et al. [31], the special interval scheduling problemfor a single machine is expressed as 1|rτ |

∑wτ (1 − Uτ ) and

is NP-hard in general. Berman and Bhaskar [32] proposed a2-approximation algorithm, which is remarkably close to theoptimum value.

Abundant TMP algorithms recognize machine-independenttime indexes. Subject to time-window job availability andmachine downtime constraints, a mobile client may downloadwithin a machine-dependent contact time window. In [33],Lee and Sherali studied the unrelated machine scheduling prob-lem, which is machine dependent for the first time. The releasetime, deadline, and processing time are all machine dependent,with the goal of minimizing the total weighted flow timessubject to time-window job and machine downtime constraints.Chen et al. [34] are the primary antecedent to one class ofscheduling problems, in which jobs have machine-dependenttime indexes with the goal of throughput maximization, andproposed offline and online algorithms to address the problems.However, the scenario is different from ours since the coverageareas of access points are assumed to be consecutive, andeach client has only one job to convey. In [35], a two-phasealgorithm is leveraged in a joint timeslot, power control, andrate assignment problem in mobile wireless sensor networks.However, it is a parallel machine problem, without taking intoaccount the cooperation.

In this paper, we focus on designing ship-shore data trans-mission scheduling schemes in DTN maritime communication

2According to the standard notation of scheduling problems [30], R rep-resents unrelated parallel machines, Uτ denotes the number of late jobs,(1 − Uτ ) indicates the number of finished jobs, and rτ is the time prior towhich job τ cannot be processed.

Fig. 1. Network topologies.

networks, with the goal of throughput maximization throughcooperation among different vessels.

III. SYSTEM MODEL

We consider the scenario that a vessel generates surveil-lance videos periodically, within the duration of sailing. Videoclips are segmented to packets and uploaded to authoritiesvia infostations deployed along route line or stored in a DTNthrow-box (which is a small, stationary, and inexpensive deviceequipped with wireless interfaces and storage, acting as a relayto create more connection opportunities [36]) and then carriedand forwarded by other vessels.

A. Store–Carry–Forward Routing

Network topologies are shown in Fig. 1(a) and (b), for single-vessel and multivessel scenarios, respectively. A vessel sailsfrom an origin port to a destination port within time duration[TI , TO]. H infostations playing the roles of base stations aredeployed along the shore side intermittently. Moreover, the ves-sels are regarded as subscriber stations. A broadband wirelessnetwork utilizing a TDMA MAC protocol could provide seam-less coverages within the communication range of infostations.Each infostation has a transmission range according to wire-less propagation characteristics. A wireline/wireless networkassociates the infostations to content servers of administrativeauthorities via a backbone network. Vessels communicate withinfostations during the available time windows corresponding


Fig. 2. Video service.

to the mobility characteristic. Several vessels might pass acrossthe same rendezvous point, which is the cross point of routeswith DTN throw-box, presumably not at the same time. Ac-cordingly, vessels can participate in cooperative transmissionsfor data delivery via the DTN throw-boxes. All the channelsbetween vessels and DTN throw-boxes are assumed to be withno obstacles. Meanwhile, there are no capacity constraints thatall the data transmitted to DTN nodes could be stored. In thispaper, we consider passenger vessels and cargo vessels that sailon predetermined and fixed route lines, such that schedules ofvessels are relatively stable and known a priori. The analysis ofvessels with lower tonnage (such as fishing boats) may involvestochastic modeling and/or optimization and is left for ourfuture work.

B. Network Resources

The IEEE standard 802.16/TDMA MAC frame structure isutilized to provide high-bandwidth data services between thevessel and the infostations. The duration in which a vessel iswithin the coverage of the hth infostation is divided into frameswith equal duration TF , and correspondingly, the number offrames is given by Kh = [(T o

h − T ih)/TF ], where T i

h and T oh

are the times for a vessel to get into and come out of thecoverage of the hth (h ∈ [1, . . . , H]) infostation, respectively.The network resource is defined as frames, within which thevideo packets can be delivered.3 Let capacity Ah,k representthe maximum number of bytes that could be delivered withinthe kth frame of the hth infostation. We assume that themaritime wireless link connections are stable due to speciallydesigned antenna systems that may overcome sea wave move-ment and occlusion. Moreover, an omiantenna that can receive/transmit in 360◦ direction is employed. The beginning andending time of the kth frame during the hth infostation are T i

h +(k − 1)TF and T i

h + kTF , respectively. Fig. 2 shows networkresource and time-capacity mapping.

C. Video Service

Video clips (e.g., 10-min video) are partitioned into packets,and each packet has its release time, deadline, and weight.Weight values its contribution to the importance to adminis-trative authority. The profit of weight is obtained if the packetis delivered before its deadline. Denote rj , dj , bj , ej , wj , andpj as the release time, deadline, beginning time, ending time,weight, and processing time for job j, respectively. Let i, j ∈{1, . . . , n} denote jobs, n the number of jobs, bj ∈ {1, . . . , t}the beginning time of job j, and u ∈ {1, . . . , t} the beginningtime of another job, which is defined to avoid multiple jobs be-

3We use the terms frame and time slot interchangeably.

Fig. 3. Network resource and time-capacity mapping.

ing scheduled simultaneously on a single machine. Obviously,the time indexes should comply with rj ≤ bj and bj + pj ≤ dj .The time indexes are approximated to integers. Fig. 3 showsvideo service.

D. Time-Capacity Mapping

A time-capacity mapping technique is used to transform theoriginal scenario with intermittent network connectivity into avirtually continuous scenario [13]. We map the time indexesinto virtually cumulative capacity values, as shown in Fig. 2.The period [T o

h , Tih+1] is defined as the idle period, during

which a vessel is not within the coverage of any infostation.For example, t3 and t4 moments are in an idle period duringwhich no data are transmitted, thus corresponding to the samecumulative capacity c4. On the other hand, t1 and t2 are inthe coverage of infostations and are subsequently related totwo different cumulative capacity values c2 and c3, respec-tively. The time-capacity mapping function f(t) : [TI , To] →[0, 1, . . . ,

∑Hh=1

∑Kk=1 Ah,k] is given by

f(t)=

⎧⎪⎨⎪⎩

∑(t−T iht

)/TF

m=1 Aht,m

+∑ht−1

l=1

∑Kl

m=1 Al,m, if ht≥1 and T iht≤ t ≤ T o

ht∑ht

l=1

∑Kl

m=1 Al,m, otherwise(1)

where ht = argmaxh{T ih ≤ t}, if T i

ht≤ t ≤ T o

ht, and ht = 0

otherwise. Based on the time-capacity mapping, the resourceallocation issue could be converted from time-based schedulingto capacity-based scheduling over a continuous horizon [13],such that the job-machine scheduling theory can be appliedto solve the resource allocation problem at low computationalcomplexity, which will be discussed in the following section.

IV. PROBLEM FORMULATION

To achieve high-quality videos, i.e., maximizing the totalweight of delivered packets, we focus on scheduling datadelivery conducted by one vessel or cooperated vessels. Sinceship routes are relatively stable and the global information isknown a priori, offline scheduling algorithms are considered.Here, the problem of maximizing the total weight of delivered


packets is formulated as a vessel throughput maximizationproblem (VTMP), which is a 0-1 integer programming prob-lem. To solve the VTMP problem, a mathematic job-machinescheduling method is utilized to allocate resources (i.e., frames)to different video packets. In such job-machine schedulingmethod, vessels and video packets act as machines and jobs,respectively. The video packets transmitted by vessels resemblejobs that could be executed on machines. We consider jobsJ = {J1, . . . , Jn} that can be performed on machines M ={M1, . . . ,Mm}. For an arbitrary job, it corresponds to a family.A family is a set of job instances executed possibly withinrelease time and deadline. No more than one job instancecould be executed during this period [32]. Job instance Si isrepresented as a quadruple of the following variables: fam-ily, value, beginning, and ending, i.e., (i, wi, bi, ei), indicatinginteger time intervals during which a job may be executed.Each job instance in one family has the same weight wi. Atmost one job instance of one family can be scheduled. Problemformulations are based on the time-capacity mapping method,allowing multiple jobs being executed during the same periodon one machine. (That is, regarding the time domain, the or-thogonal frequency-division multiple-access technology couldachieve multijob transmission simultaneously. However, thejobs could not tolerate multijob transmission at the same timein the capacity domain.)

A. Formulation of Single-Vessel Delivery

In a single-vessel delivery scenario, the data can be deliv-ered when the vessel carrying the data is in the coverage ofinfostations, without cooperation among vessels. Through thetime-capacity mapping, the single-vessel data delivery becomesa single-machine scheduling problem. Define binary variablexjbj , which indicates whether job j is scheduled at interval[bj , bj + pj ] as follows:

xjbj =

{1, if job j is scheduled at interval [bj , bj + pj ]0, otherwise.

Then, the single-vessel VTMP is formulated as follows:

max

n∑j=1

dj−pj∑bj=rj

wj · xjbj (2)

s.t.n∑

j=1

u∑bj=u−pj+1

xjbj ≤ 1∀u (3)

dj−pj∑bj=rj

xjbj ≤ 1 ∀ j (4)

xjbj ∈ {0, 1} (5)

where n indicates the total number of jobs executed on a singlemachine. Constraint (3) is to avoid jobs to interfere with eachother on a single machine, whereas constraint (4) indicates thateach job can only be scheduled, at most, once. Therefore, theVTMP is a 0-1 integer programming problem.

To prove VTMP is NP-complete, we first transform it intoa decision problem (to be answered by “yes” or “no”) by

comparing the objective value with a threshold value. VTMP-DECISION is defined as

whether there exists {wj , xjbj} with⎧⎪⎪⎪⎨⎪⎪⎪⎩

∑nj=1

∑dj−pj

bj=rjwj · xjbj ≥ x (6a)∑n

j=1

∑ubj=u−pj+1 xjbj ≤ 1, ∀u (6b)∑dj−pj

bj=rjxjbj ≤ 1, ∀ j (6c)

xjbj ∈ {0, 1} (6d)

where x is a threshold value.Lemma 1: VTMP ∈ NP , i.e., VTMP-DECISION can be

verified in polynomial time.Proof: Consider that we are given coefficients wj , xjbj ,

and a threshold value x. We can verify in polynomial timewhether

•∑n

j=1

∑dj−pj

bj=rjwj · xjbj ≥ x;

•∑n

j=1

∑ubj=u−pj+1 xjbj ≤ 1 and

∑dj−pj

bj=rjxjbj ≤ 1. �

Lemma 2: VTMP is NP-hard, i.e., VTMP-DECISION canbe reduced from a known NP-complete problem in polyno-mial time.

Proof: The knapsack problem (KP) is a known NP-complete problem [37]. Define KP-DECISION as follows:

whether there exists xi with⎧⎨⎩

∑Ni=1 pixi ≥ p (7a)∑Ni=1 wixi ≤ c (7b)

xi ∈ {0, 1}. (7c)

To show the NP-hardness of VTMP, we reduce fromKP-DECISION. Restrict VTMP-DECISION by allowing eachjob j to have a specific starting time bj . We have the following:

whether there exists {wj , xj} with⎧⎨⎩

max∑n

j=1 wjxj ≥ x (8a)∑nj=1 xj ≤ 1 (8b)

xj ∈ {0, 1}. (8c)

Note that KP-DECISION has a feasible solution if the corre-sponding VTMP-DECISION has a feasible solution. Therefore,VTMP can be reduced from KP, and the reduction runs inpolynomial time. �

Theorem 1: VTMP is NP-complete.Proof: Since VTMP belongs to the class NP and is NP-

hard, it is concluded that VTMP is NP-complete [38]. �

B. Formulation of Multivessel Delivery

In a multivessel delivery scenario, the cooperation amongvessels can be utilized. A vessel, when passing by a DTN throw-box, can forward the data to it. When other vessels pass by, theycan carry the data and try to deliver. Multivessel delivery, whichcorresponds to multimachine scheduling, takes advantage ofthe different routes of vessels to enhance the chance of datadelivery. Denote rjm, djm, wjm, pjm, and bjm as release time,deadline, weight, processing time, and beginning time for job jon machine m, respectively, where j ∈ J represents jobs, andm ∈ M represents machines. Apparently, we have rjm ≤ bjmand bjm + pjm ≤ djm.


Let xjmbjm be the decision variable on whether job j isperformed at job interval [bjm, bjm + pjm], which is given by

xjmbjm

=

{1, if job j is performed at interval [bjm, bjm+pjm]0, otherwise.

Then, the multivessel VTMP is formulated as follows:

maxn∑

j=1

djm−pjm∑bjm=rjm

wjm · xjmbjm (9)

s.t.n∑

j=1

u∑bjm=u−pjm+1

xjmbjm ≤ 1∀m,u (10)

djm−pjm∑bjm=rjm

xjmbjm ≤ 1∀ j (11)

xjmbjm ∈ {0, 1} (12)

where n indicates the total number of jobs executed on multiplemachines.

Similar to Theorem 1, multivessel VMTP can be reducedfrom VMTP, and the reduction runs in polynomial time. There-fore, multivessel VMTP is also NP-complete.

C. Capacity-Based Formulation

To overcome the intermittent connectivity and achieve lowcomputational complexity, time-capacity mapping is utilizedto transform the original resource allocation problem into asingle-machine nonpreemptive scheduling problem and a two-machine nonpreemptive scheduling problem, respectively. Thetime indexes are required to be mapped into a capacity horizonapplying time-capacity mapping function f(·) in (1).

For a single-vessel delivery scenario, the job instances aredescribed as

Si = {[bi, bi + pi)|ri < bi and bi + pi < di} . (13)

Time indexes as bi, ei, ri, di, pi are all mapped by the time-capacity mapping to obtain capacity indexes b′i, e

′i, r

′i, d

′i, p

′i, re-

spectively, given by b′if← bi, e′i

f← ei, b′if← bi, d′i

f← di, p′if← pi.

Then, the job instances are expressed as

S ′i = {[b′i, b′i + p′i)|r′i < b′i and b′i + p′i < d′i} . (14)

For a two-vessel delivery scenario, the capacity indexesb′i, e

′i, r

′i, d

′i, p

′i,1 and bi

′′, e′′i , r′′i , d

′′i , p

′′i,2 are obtained by apply-

ing the mapping functions f1(·) and f2(·) on machine 1 andmachine 2, respectively. All the video packets could be trans-mitted by either vessel 1 or vessel 2. Then, the job instancesSi indicate the families of intervals during which jobs may beexecuted, i.e.,

Si = {[bi, bi + pi,m) + (m− 1)t|m ∈ [1, 2], ri < bi

and bi + p′i,m < di}. (15)

Here, m indicates machine 1 or machine 2. Time indexes

b′i, e′i, r

′i, d

′i, p

′i,1 are all mapped on machine 1, i.e., b′i

f1← bi,

e′if1← ei, r′i

f1← ri, d′if1← di, p′i,1

f1← pi,1. The job instances areexpressed as

S ′i =

{[b′i, b

′i + p′i,1)|r′i < b′i and b′i + p′i,1 < d′i

}. (16)

The corresponding latest deadline is t′ in the capacity domain.Time indexes b′′i , e

′′i , r

′′i , d

′′i , p

′′i,2 are all mapped on machine 2,

i.e., b′′if2← bi, e′′i

f2← ei, r′′if2← ri, d′′i

f2← di, p′′i,2f2← pi,2. Then, the

job instances can be expressed as

S ′′i =

{[b′′i , b

′′i + p′′i,2) + t′|r′′i < b′′i and b′′i + p′′i,2 < d′′i

}.(17)

Relatively, the latest deadline on machine 2 is t′′ in the capacitydomain. The job instances are expressed as

Si ={{

[b′i, b′i + p′i,1)|r′i < b′i and b′i + p′i,1 ≤ d′i

}∪{

[b′′i , b′′i + p′′i,2) + t′′|r′′i < b′′i and b′′i + p′′i,2 ≤ d′′i

}}. (18)

Based on the time-capacity mapping transformation, timeindexes are virtually transformed into the cumulative capacityvalues, over which the packet transmissions could be continu-ously scheduled. The following three algorithms are based onthe given capacity-based transformation.

V. PROPOSED ALGORITHMS

Toward effective resource allocation with low computa-tional complexity, we propose three offline algorithms to ad-dress VTMP, i.e., a TMTP algorithm for a single machine, aTMTP algorithm for two machines, and an IGTJRS algorithmthat leverages maximum weight 2-independent set (MW2IS)algorithm.

A. TMTP Algorithm for Single Machine

The two-phase algorithm is an offline algorithm [32], whichreveals a stack-based TMP algorithm with two phases, i.e., eval-uation phase and selection phase. In phase one, the algorithmpushes job instances in sequence of nondecreasing ending timeinto a stack, and only those job instances that have large enoughweight, compared with overlapping instances already in thestack, can enter the stack. In phase two, the algorithm pops jobinstances and arranges them into a nonconflicting schedule ininverted order. According to this rule, it could guarantee thatthe highest weight job instances with the earliest ending timesare chosen. Therefore, the total weight of scheduled jobs ismaximized.

Some useful definitions are given as follows. S is aninitially empty stack that could store intervals, which isapplied in the TMTP algorithm programming as previously de-scribed; L is a sequence that contains an instance (i, wi, bi, ei),for every integer i ∈ [1, n];TOTAL(i, b′i) is the total sumof values of those instances other than i on the stack Sthat have ending > b′i, where ending indicates the endingtime of job instance; total(i, b′i) is the total value of job in-stances that ending < b′i of family i. The latest deadline on


machine 1 is t and t′ in time and capacity horizon, respec-tively. Algorithm 1 shows a pseudo-polynomial algorithm.

B. TMTP Algorithm for Single Machine

We first consider the two-vessel case, which is a two-machinenonpreemptive scheduling problem, and then generalize theresults to the multivessel case.

Emergency Information Delivery Scenario: Consider anemergency information delivery case. In this case, vessel 1has emergency data to transmit, e.g., surveillance videos inthe warship. Vessel 2 is considered to have no data to deliverand acts a relay. On machine 1 (Vessel 1), let TOTAL(i, b′i)be the total sum of values of those instances other than i onthe stack S that have ending > b′i and total(i, b′i) be the totalvalue of job instances that ending < b′i of family i. The latest

deadline on machine 1 is t′ in capacity horizon. On machine 2(Vessel 2), TOTAL(i, b′′i ) and total(i, b′′i ) are the total sum ofvalues of those instances other than i that have ending > b′′i andthose instances of family i that have ending < b′′i , respectively.The latest deadline on machine 2 is t′′ in capacity horizon.

Algorithm 2 shows a pseudo-polynomial algorithm for thetwo-machine case [32]. A job only has one instance scheduledon machines 1 and 2. When vessel 1 reaches the rendezvouspoint, it transmits the video packets that need to be delivered bymachine 2, to the DTN throw-box.

Normal Information Delivery Scenario: We consider a nor-mal information delivery scenario in which both vessel 1 andvessel 2 have video packets with normal weight (rather thanemergency information) to deliver. We focus on the schedulingafter vessel 2 gets video packets from DTN throw-box. Itcan also be considered as a two-machine scheduling problem,which is solved by Algorithm 2. The remarkable difference isthat vessel 2 has its own videos to transfer. In this situation, withslight alteration, we use the TMTP algorithm of two machinesfirst. Then, we check whether the packets relayed from vessel 1conflict with the original packets on vessel 2. If they areconflicting, we propose the following feedback algorithm (seeAlgorithm 3) to avoid transmitting the overlapping packets,i.e., those packets that cannot be relayed to vessel 2, fromvessel 1 to DTN throw-box.

In Algorithm 3, set A includes all the overlapping packetsthat cannot be scheduled by vessel 1; A1 is the set of packetsin A that are transmitted to vessel 2 from vessel 1 (determinedby Algorithm 2); trelease and tdeadline denote the release timeand deadline of the corresponding packets, respectively; B1 isthe set of packets that are in set A1 and transmitted to vessel 2by using Algorithm 2; B is the original packet set of vessel 2;B′ is the set after B1 merges into B, i.e., the whole packetset of vessel 2 after receiving packets from vessel 1; B2 is theset of packets that cannot be scheduled on vessel 2; C is theintersection of B1 and B2.

Algorithm 3: Feedback Algorithm

1: B1 ← A1 : (trelease, tdeadline)2: B′ ← B1 ∪B3: Let B2 be the set of packets that cannot be scheduled on

vessel 24: C ← B1 ∩B2

5: A2 ← C : (trelease, tdeadline)6: A1 ← A1 \A2

In addition, since vessel 2 acts as a relay and vessel 1 cannotassist in the delivery of packets of vessel 2, we need to do somealterations to the original TMTP algorithm. When packets arereflected from vessel 2 to vessel 1, the ending time is set to e′ >t′ + δ, δ > 0. We have the following Lemma 3 with respect toAlgorithm 2.

Lemma 3: Using the TMTP algorithm to schedule the inter-secting jobs, the job instances with the earliest beginning timesare chosen.


Fig. 4. Case of multiple jobs with multiinterval intersection.

TABLE IITWO-PHASE PROCESS OF TMTP ALGORITHM

Proof: We first show the case that three jobs intersect witheach other, with w3 > w2 > w1. In Fig. 4, two job instancesare described, while the scheduling of more job instances couldbe easily extended. The calculation process is described inTable II. We judge whether the job instances should enter thestack in the left column and display the calculation process inthe right column, where ∗ means that the job instance is selectedin phase two. It is found that the total weight of job instancesthat enter the stack is just the weight of the last one job instance(e.g., after the first job instance of job 3 enters the stack, the totalweight of stack is (w3 − w2) + (w2 − w1) + w1 = w3. Whenevaluating whether the second job instance of job 3 enters thestack, we have (w3 − w3) = 0. The rest of more job instancescould be done in the same manner. The scheduling of morejobs and more job instances can be induced. Since the value ofjob n that enters the stack is v = wn − wn−1, the total weightof stack is (wn − wn−1) + (wn−1 − wn−2) + · · · (w3 − w2) +(w2 − w1) + w1 = wn. When evaluating whether the secondjob instance of job n enters the stack, we have (wn − wn) = 0.In other words, the job instances with the earliest beginningtimes are selected to enter the stack. It can be concludedthat the job instances with the earliest beginning times arechosen. Likewise, the deductions of other intersecting caseswith different weight values can obtain the same conclusion.

�

C. IGTJRS Algorithm

Based on the observations in Lemma 3, we propose a moreefficient IGTJRS algorithm (see Algorithm 4) to choose pack-ets to be delivered to vessel 2. First, time-capacity mapping isalso implemented to mitigate the intermittent connectivity.

Algorithm 4: IGTJRS Algorithm

1: Definition: the same as Algorithm 1, and M = ∅2: Detection whether two jobs intersect with each other:

3: for ∀ Ji ∈ J , ∀ Jj ∈ J \ Ji do4: Let bi ← {b1i , b2i , . . . bki } express beginning time of

job i intervals, bj ← {b1j , b2j , . . . bkj } express beginningtime of job j intervals

5: job instance kimin ← min{bki }, kjmax ← max{ekj },

α ← kbmini , β ← kemax

j

6: if eαi > bβj then7: Job i and j mutually intersect, Jj ← (j, wj , bjmin,

ejmin), Ji ← (i, wi, bimin, eimin)8: draw relative interval graph G(V,E), then use

Algorithm 5 to obtain two maximum weight intervalsetsQ′

u andQ′v to be delivered in vessel 1 and vessel 2

9: Q′ ← Q′m, Q′

m has the latest ending time, and m∈ {u, v}

10: vessel 2 ← DTN throw-box ← the set Q′

11: else12: Job i and j not mutually intersect, Find (j, wj ,

bj , ej), (i, wi, bi, ei) → M with minimum b

13: M ← M ∪ (j, wj , bj , ej) ∪ (i, wi, bi, ei)14: end if15: end for

Steps 3–7 are to judge whether jobs intersect with each other.When job instances ensure mutual exclusion, the algorithm candirectly schedule the packets on vessel 1, while choosing theinstances with earliest beginning times that guarantee nonover-lapping with each other, as shown in steps 12 and 13. However,we focus on packets with inevitable overlapping that could notbe fully scheduled on vessel 1. In steps 8–10, two sets of jobinstances are chosen, of which one is delivered by vessel 1 itselfand the other is transmitted to the DTN throw-box. In each set,job instances are nonoverlapping with each other.

To obtain the maximum total weight, we utilize the conceptof MW2IS in interval graph [39]. Interval graph is an inter-section graph of a multiset of intervals on the real line. It hasone vertex for each interval in the set, and an edge betweenevery pair of vertices corresponds to intervals that intersect[40]. According to the intersection between job instances, aninterval graph G(V,E) is obtained. Consequently, the job setselection issue, which is described in steps 8–10, could betransformed into the collection selection issue in the intervalgraph. In [39], the MW2IS algorithm gives a collection of twosets with maximum weight. However, the elements contained ineach set are not clear. We propose a modified MW2IS algorithm(see Algorithm 5) to obtain the maximum 2 independentsets Q′

u and Q′v as well as the elements in each set. For any

2-independent set Q of intervals I , MWQ(u, v) indicates anMW2IS, and w(u, v) denotes the weight of MWQ(u, v),which is a summation of the weight of all elements in the twosets. u and v are the largest indexes of the intervals in thetwo sets, respectively. In step 2, the algorithm computes thevalue of each w(u, v) based on the equation w(u, v) =w(ij) + max{{w(u, x)|bj > ex and u < x} ∪ {w(x, v)|bj >ex and x < v}}, if v > u, where the detailed algorithmMWIS_IN_INTERVALS is depicted in Algorithm 6; step 3 givesthe MW2IS Qmax2, without indicating the elements containedin each set; a backward interval selection procedure is described


in step 4 to give Q′u and Q′

v . Between Q′u and Q′

v , the one withthe latest deadline is chosen to be delivered to vessel 2.

Algorithm 5: Modified MW2IS Algorithm

1: Input: A set of weighted intervals I ← {i1, i2, . . . , in}and the sorted endpoint list L ← {e1, e2, . . . , e2n}.

2: Output: The MW2IS Qmax2 of I, two maximum weightinterval sets Q′

u, Q′v .

3: Step 1: Qmax2 ← ∅; Qu ← ∅; Qv ← ∅; Set the initialvalue of w(u, v), 0 ≤ u, v ≤ n, to be 0.

4: Step 2: Compute each value of w(u, v), 0 ≤u, v ≤ n, beginning from w(0, v), 0 ≤ v ≤ n, thenw(1, v), 0 ≤ v ≤ n, . . . , w(n, v), 0 ≤ v ≤ n, byalgorithm MWIS_IN_INTERVALS and formulaw(u, v) = w(ij) + max{{w(u, x)|bj > ex and u <x} ∪ {w(x, v)|bj > ex and x < v}}, if v > u.

5: Step 3: Let w(un−1, vn) ← ψ(I); Qmax2 ← Qmax2 ∪{iun−1

, ivn}; ψ(I) ← ψ(I)− (w(iun−1

) + w(ivn−1));

un−1 ← u1; vn ← v16: while ψ(I) > 0 do7: Select a pair of intervals (iu2, iv2) with the constraints

that max{eu2, ev2} < max{bu1, bv1}, min{eu2, ev2} <min{bu1, bv1}, and w(u2, v2) = ψ(I).

8: Qmax2 ← Qmax2 ∪ {iu2, iv2};9: ψ(I) ← ψ(I)− (w(iu2

) + w(iv2));

10: u1 ← u2; v1 ← v2;11: Qu ← Qu ∪ {iu1}; Qv ← Qv ∪ {iv1};12: end while13: Step 4: Let Qu ← {Qu1, Qu2, . . . , Qum}; Qv ←

{Qv1, Qv2, . . . , Qvm}; Q′u ← ∅; Q′

v ← ∅14: Q′

u ← Q′u ∪ {Qu1

}; Q′v ← Q′

v ∪ {Qv1}

15: for ← 1 to m do16: if bQui

> e′Qu(i−1)and bQvi

> e′Qv(i−1)then

17: Q′u ← Q′

u ∪ {Qui}; Q′

v ← Q′v ∪ {Qvi

},18: else19: Q′

v ← Q′v ∪ {Qui

}; Q′u ← Q′

u ∪ {Qvi}

20: end if21: end for

Algorithm 6 finds the maximum weight independent set(MWIS). Weight of MWS(c) is given by

χ(c) = wt(ic) + max {χ(x)|ex < bc} , for any 1 ≤ c ≤ n.(19)

temp_max is a temporary variable that represents the weightof MWIS; Smax1 represents an MWIS of intervals I;last_interval represents the largest index of the intervals [39].

Algorithm 6: MWIS_IN_INTERVALS

1: Input: A set of weighted intervals I = {i1, i2, . . . , in}and the sorted endpoint list L = {e1, e2, . . . , e2n}.

2: Output: The MWIS Smax1 of I.3: Step 1: temp_max ← 0; Smax1 ← ∅; last_interval ←

0;

4: for v ← 1 to n do5: χ(v) ← 06: end for7: Step 2:8: for i ← 1 to 2n do9: if ei is a left endpoint of interval ic then

10: χ(c) ← temp_max11: if ei is a right endpoint of interval ic then12: if χ(c) > temp_max then13: temp_max ← χ(c);14: last_interval ← c;15: end if16: end if17: end if18: end for19: Step 3: Smax1 ← Smax1 ∪ {ilast_interval};

temp_max ← temp_max− w{ilast_interval}20: for v ← last_interval− 1 to 1 do21: if χ(v) = temp_max and ev < alast_interval then22: Smax1 ← Smax1 ∪ {iv};23: temp_max ← temp_max−w{iv};24: last_interval ← v;25: end if26: end for

The given analysis focuses on the scenario in which each ves-sel only has one helper. The algorithm can be easily extendedto a multivessel scenario by repeating the TMTP or the IGTJRSalgorithm multiple times.

D. Performance Analysis

Here, we analyze the performance of the proposed algo-rithms, including the approximation ratio and time complexity.The approximation ratio is the ratio of the throughput of anoptimal schedule to that of the approximation algorithms.

Theorem 2: The approximation ratio of the IGTJRSalgorithm is 2.

Due to the page limitation, we omit the details of the proof.In terms of time complexity, it can be observed from

Algorithm 4 that the time complexity of the IGTJRS algorithmconstitutes three components.

i) Insert families: Sort list L of all the families by the earliestending time of the interval in this family. We adopt abinary search method on L in O(log n) time, where n isthe number of jobs.

ii) Judge intersection: Exploring linear search, time complex-ity O(n) for judgement is achieved.

iii) Job relay selection: MW2IS algorithm is adopted andsolved in O(n2) time [39].

Therefore, the IGTJRS algorithm runs in O(n2) time. Com-paratively, the TMTP algorithm runs in O(2tn log log(2t))time, where t is the latest job deadline. Typically, one joboccupies multiple timeslots, which indicates that t � n. Hence,the proposed IGTJRS algorithm has a more favorable timecomplexity performance than the TMTP algorithm.


TABLE IIITIME-POSITION TRACES OF VESSELS

Fig. 5. Traces of vessel Rainbow1.

VI. PERFORMANCE EVALUATION

The proposed algorithms are verified using simulations,based on the traces of vessels in an area of SingaporeHarbor obtained from BLM-Shipping navigation software [41].Table III lists the time-position information of some of therelated vessels. The video compression standard is based onH.264, with compressed video bit rate of 0.47 Mb/s [42].The arrival process of jobs (packets) of any specific videois deterministic based on the video bit rate. Fig. 5 showsthe trace of vessel “Rainbow1” as example. We consider thatthe infostations are uniformly deployed along the coastline. TheDTN throw-boxes are deployed at the rendezvous points ofvessel routes, which is known a priori. To estimate the framecapacity Ah,k for the offline scheduling, we utilize a two-raypropagation loss model to calculate the data transmission rateof vessels in different locations. The transmit power of vessel isdenoted by Ptx. At the beginning of a specific frame (denotedby tb), the distance between the vessel and the infostation is d.The receive power at the infostations can be calculated by

Prv

Ptx=

(λ

4πd

)2

× sin2(

2πhtxhrv

λd

)(20)

where λ is the transmission wavelength, and htx and hrv are therespective height of transmitting and receiving antennas [43].Thus, the instant transmission rate at tb can be estimated by

r = B ∗ log2(

1 +Prv

N

)(21)

where B is the bandwidth allocated to the vessel, and N is thenoise power. Assume that the channel is stable within one frameduration, and the capacity of the frame is Ah,k = (r ∗ Tf )/Sp,

TABLE IVSIMULATION PARAMETERS

where TF is the frame duration, and Sp is the packet size. Thesimulation parameters are listed in Table IV [14].

Using the BLM-Shipping navigation software, we identifyonly the discrete locations of vessels, not the particular traces.We use lines that connect the locations as the approximate trace.In other words, we consider a synthetic vessel trace method,assuming that vessels sail in straight line between two adjacentposition points. Curve fitting is implemented by undertakingthe straight-line hypothesis, based on the distance between anytwo contiguous locations. The following formulas calculatethe great circle distance S in navigation science, due to theEarth’s geographic characteristics. We define the locations oftwo vessels as (ϕ1, θ1) and (ϕ2, θ2), with ϕ and θ, respectively,expressing the latitude and longitude. Calculation formulas ofthe great circle distance are

cosS = sinϕ1 · sinϕ2 + cosϕ1 · cosϕ2 · cosDλ (22)

Dλ = θ2 − θ1. (23)

Consequently, we use S = arccos(cosS) as the great circle dis-tance [44], which is used to approximate the distance betweentwo adjacent position points.

We compare the proposed algorithms with some other mar-itime communication algorithms [15], [19] and classic schedul-ing algorithms, i.e., Deadline (the job with the earliest deadlineis scheduled first), First-Input First-Output (the job with theearliest release time is scheduled first), Weight (the job withthe largest weight is scheduled first), Single (noncooperativebetween two vessels, and only one vessel has packets to trans-mit), and Multisingle (noncooperative among multiple vessels).Here, the performance is evaluated by normalized throughput,indicating the ratio of the throughput of delivered packetsto the throughput of total packets. In [15], vessels are usingthe mesh network rather than DTN to transmit data. Thus,in the simulation, we assume that a vessel can transmit onlywhen it can directly communicate with an infostation and usesDeadline scheduling. In [19], the DTN scheme is utilized,where vessels can communicate with each other when possible


Fig. 6. Simulation results for a single-vessel scenario. (a) Normalizedthroughput versus number of infostations for a single vessel. (b) Normalizedthroughput versus size of job for a single vessel. (c) Normalized throughputversus job lifetime for a single vessel. (d) Normalized throughput versus jobinterarrival time for a single vessel.

and deliver the stored packets when they meet an infostation.However, since there are no DTN-boxes, the chances that datacan be successfully delivered may be less than our proposedframework.

We first investigate the single-vessel scenario, i.e., no relays.Fig. 6(a) shows the normalized throughput versus the numberof infostations, where the normalized throughput is definedas the ratio between the accomplished packet profits and thetotal weight of packets. The number of infostations varies from2 to 16 of the whole route line. It can be observed that thenormalized throughput of all four algorithms increases withthe increment of the infostations. Furthermore, the throughputof the TMTP algorithm obviously outperforms the others,and hence, the network performance is better. In Fig. 6(b),the normalized throughput versus the size of job (number ofpackets), for different schemes, is presented. For larger jobsizes, the total throughput becomes lower, because the numberof overlapping jobs increases. Fig. 6(c) shows the normalizedthroughput versus the job lifetime. The TMTP algorithm has asignificantly better performance than the other three algorithms.With a larger length of the job lifetime, the throughput of theTMTP algorithm becomes higher, since when the job lifetimeincreases, the probability of nonoverlapping job instances in-creases, and therefore, the performance of the TMTP algorithmis improved. In Fig. 6(d), the normalized throughput versus thejob interarrival time is shown. With a longer interarrival time,i.e., the granularity of interarrival time increases, the number ofoverlapping packets decreases. As a consequence, the achievedtotal profits increase.

Then, we study the two-vessel scenario, assuming that onlyvessel “Rainbow1” has packets to transmit and vessel “Secret”acts as a relay. In the TMTP algorithm, we assume that vessel“Secret” has all the packets that vessel “Rainbow1” may gener-ate and transmit at the beginning of the simulation, which is not

Fig. 7. Simulation results for a two-vessel scenario. (a) Normalized through-put versus number of infostations for two vessels. (b) Normalized throughputversus size of job for two vessels. (c) Normalized throughput versus job lifetimefor two vessels. (d) Normalized throughput versus interarrival time for twovessels.

realistic. Thus, the performance of TMTP can be considered asthe upper bound of all DTN algorithms. The Single algorithmcorresponds to a noncooperative scenario where the TMTPalgorithm is utilized for a single machine. In Fig. 7, it is obviousthat cooperative schemes IGTJRS and TMTP outperform thenoncooperative scheme Single. Moreover, the IGTJRS algo-rithm achieves nearly the same performance as the TMTP al-gorithm and obviously outperforms the other three cooperativealgorithms. The normalized throughput versus the number ofinfostations is shown in Fig. 7(a). As the number of infostationsincreases, the normalized throughput increases since there aremore transmission opportunities. The impact of the size of jobis demonstrated in Fig. 7(b). A larger size of job indicates thatone video packet needs more frame resource for transmission,which reduces the total weight of delivered packets. The nor-malized throughput versus job lifetime is described in Fig. 7(c).Longer job lifetime results in more nonoverlapping job intervalsand, thus, higher normalized throughput. In Fig. 7(d), we cansee that the normalized throughput increases as the job inter-arrival time increases, due to an increased number of nonover-lapping jobs.

The simulation results of a multivessel scenario are shownin Fig. 8. Each vessel has its own service and acts as a relayto assist in transmitting if possible. We compare our resultswith that in [15] and [19]. Similar to a two-vessel scenario,in the TMTP algorithm, the relaying vessels are assumed tocarry all the packets generated by the vessel they assist at thebeginning of the simulation. Thus, the TMTP algorithm canstill be considered to achieve the performance upper bound.The algorithm proposed in [15] does not perform as well asTMTP, IGTJRS, and that in [19] because it does not applya DTN mechanism. The algorithm proposed in [19] achievesbetter performance than that in [15]; however, it performsworse than TMTP and IGTJRS since it does not utilize theDTN throw-box. In Fig. 8(a), the normalized throughput versus


Fig. 8. Simulation results for a multivessel scenario. (a) Normalized through-put versus number of infostations for multiple vessels. (b) Normalized through-put versus size of job for multiple vessels. (c) Normalized throughput versusjob lifetime for multiple vessels. (d) Normalized throughput versus interarrivaltime for multiple vessels.

number of infostations is shown. It can be seen that thenormalized throughput increases with the increment of thenumber of infostations. The IGTJRS algorithm has nearlythe same performance as the TMTP algorithm and obviouslyoutperforms the other four algorithms, which coincides withthe performance analysis in Section V-D. Fig. 8(b) showsthe normalized throughput versus the size of job (number ofpackets). Moreover, the IGTJRS algorithm achieves almost thesame performance as the TMTP algorithm. As the job sizeincreases, the number of scheduled jobs decreases, and thethroughput decreases accordingly. In Fig. 8(c), the normalizedthroughput versus job lifetime is plotted. As the job lifetimeenlarges, the probability of nonoverlapping job intervals in-creases, and thus, the performance of IGTJRS and TMTPalgorithms is improved. In Fig. 8(d), the normalized throughputversus the job interarrival time is shown, where the granularityof interarrival time varies from 100 to 200 s. The normalizedthroughput of the network increases with the increment ofthe granularity, since the number of nonoverlapping jobs alsoincreases.

Through the simulations, we can draw the following con-clusions: 1) The TMTP algorithm for a single vessel offersimproved performance than the other classic scheduling algo-rithms; 2) compared with the TMTP algorithm, the IGTJRSalgorithm can efficiently solve the target problem with al-most the same performance; 3) comparing the existing mar-itime DTN/none-DTN algorithms in addition to some classicscheduling algorithms, the cooperative IGTJRS and TMTP al-gorithms outperform noncooperative algorithms; 4) the normal-ized throughput is increased with an increment in the numberof infostations, job lifetime, and granularity between jobs; and5) the normalized throughput decreases with the increased sizeof jobs.

VII. CONCLUSION

In this paper, we have shed light on the scheduling schemesin maritime wireless communication networks. To maximizethe weighted throughput of the delivered video packets, weutilize the job-machine scheduling method to solve the VTMP.Three offline scheduling algorithms, namely, the TMTP al-gorithm for a single machine, the TMTP algorithm for twomachines, and the IGTJRS algorithm have been proposed.We show that the IGTJRS algorithm has a 2-approximationratio and runs in O(n2) time. Simulation results indicate thatour proposed algorithms can achieve better performance thanseveral classic scheduling algorithms. For the future work,we will carry out the efficient scheduling for energy-constrainedinfostations and DTN throw-box with energy-harvesting tech-nologies. Additionally, stochastic models will be developedto investigate the scheduling problems for vessels with lowertonnage such as fishing boats. Moreover, an interrelatedthroughput–delay–fairness triplet will be also considered intothe maritime network scheduling.

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Tingting Yang (M’13) received the B.Sc. and Ph.D.degrees from Dalian Maritime University, Dalian,China, in 2004 and 2010, respectively.

She is currently an Associate Professor with theNavigation College, Dalian Maritime University.Since September 2012, she has been a VisitingScholar with the Broadband Communications Re-searchLaboratory,DepartmentofElectrical andCom-puter Engineering, University of Waterloo, Waterloo,ON, Canada. Her research interests include maritimewideband communication networks, delay-tolerant

networking, and green wireless communication.Dr. Yang serves as the Associate Editor-in-Chief for IET Communications

and the Advisory Editor for SpringerPlus. She is serving or has servedas a Technical Program Committee Member for the 2014 and 2015 IEEEInternational Conference on Communications, the 2014 IEEE InternationalConference on Smart Grid Communications, and the 2014 IEEE InternationalConference on Scalable Computing and Communications.

Hao Liang (S’09–M’14) received the Ph.D. degreein electrical and computer engineering from the Uni-versity of Waterloo, Waterloo, ON, Canada, in 2013.

From 2013 to 2014, he was a Postdoctoral Re-search Fellow with the Broadband CommunicationsResearch Laboratory and the Electricity Market Sim-ulation and Optimization Laboratory, University ofWaterloo. Since July 2014, he has been an As-sistant Professor with the Department of Electricaland Computer Engineering, University of Alberta,Edmonton, AB, Canada. His research interests in-

clude smart grid, wireless communications, and wireless networking.Dr. Liang was the System Administrator of the IEEE TRANSACTIONS

ON VEHICULAR TECHNOLOGY from 2009 to 2013. He served as a Tech-nical Program Committee Member for major international conferences inboth information/communication system discipline and power/energy systemdiscipline, including the IEEE International Conference on Communications,the IEEE Global Communications Conference, the IEEE Vehicular TechnologyConference, the IEEE Innovative Smart Grid Technologies Conference, and theIEEE International Conference on Smart Grid Communications. He receivedthe Best Student Paper Award from the IEEE 72nd Vehicular TechnologyConference (Fall 2010), Ottawa, ON, Canada.

Nan Cheng (S’13) received the B.S. and M.S. de-grees from Tongji University, Shanghai, China, in2009 and 2012, respectively. He is currently workingtoward the Ph.D. degree with the Department ofElectrical and Computer Engineering, University ofWaterloo, Waterloo, ON, Canada.

Since 2012, he has been a Research Assistant withthe Broadband Communication Research Group, De-partment of Electrical and Computer Engineering,University of Waterloo. His research interests in-clude vehicular communication networks, cognitive

radio networks, and cellular traffic offloading.


Ruilong Deng (S’11–M’14) received the B.Eng. andPh.D. degrees in control science and engineeringfrom Zhejiang University, Hangzhou, China, in 2009and 2014, respectively.

He was a Visiting Student with the Simula Re-search Laboratory, Oslo, Norway, in 2011 and theUniversity of Waterloo, Waterloo, ON, Canada, from2012 to 2013. He is currently a Postdoctoral Re-search Fellow with the School of Electrical andElectronic Engineering, Nanyang TechnologicalUniversity, Singapore. His research interests include

wireless sensor networks, cognitive radio, and smart grid.Dr. Deng served or will serve as a Technical Program Committee Member

for the 2013 IEEE International Conference on Smart Grid CommunicationsDemand Response Symposium; the 2015 IEEE International Conference onComputing, Networking, and Communications Mobile Computing and VehicleCommunications Symposium; and the 2015 IEEE International Conference onCommunications Quality of Service, Reliability, and Modeling Symposium. Hereceived a Student Travel Grant for the 2013 IEEE Global CommunicationsConference.

Xuemin (Sherman) Shen (M’97–SM’02–F’09) re-ceived the B.Sc. degree from Dalian Maritime Uni-versity, Dalian, China, in 1982 and the M.Sc. andPh.D. degrees from Rutgers University, NJ, USA, in1987 and 1990, all in electrical engineering.

He is a Professor and the University Re-search Chair with the Department of Electricaland Computer Engineering, University of Waterloo,Waterloo, ON, Canada. He was the Associate Chairfor Graduate Studies from 2004 to 2008. He is acoauthor/editor of six books and has published many

papers and book chapters in wireless communications and networks, control,and filtering. His research focuses on resource management in interconnectedwireless/wired networks, wireless network security, wireless body area net-works, and vehicular ad hoc and sensor networks.

Dr. Shen served as the Technical Program Committee Chair for the Fall 2010IEEE Vehicular Technology Conference (VTC), the Symposia Chair for the2010 IEEE International Conference on Communications (ICC), the TutorialChair for the 2011 Spring IEEE VTC and the 2008 IEEE ICC, the TechnicalProgram Committee Chair for the 2007 IEEE Global Communications Con-ference, the General Cochair for the 2007 International Conference on Com-munications and Networking in China and the 2006 International Conferenceon Quality of Service in Heterogeneous Wired/Wireless Networks, and theChair for the IEEE Communications Society Technical Committee on WirelessCommunications and Peer-to-Peer Communications and Networking. He alsoserves/served as the Editor-in-Chief for the IEEE NETWORK, Peer-to-PeerNetworking and Application, and IET Communications; a Founding Area Editorfor the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS; an Asso-ciate Editor for the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY,Computer Networks, and ACM/Wireless Networks; and the Guest Editor forthe IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, the IEEEWIRELESS COMMUNICATIONS, the IEEE COMMUNICATIONS MAGAZINE,and ACM Mobile Networks and Applications. He is a registered ProfessionalEngineer in Ontario, Canada, and a Fellow of the Canadian Academy of Engi-neering, a Fellow of the Engineering Institute of Canada, and a DistinguishedLecturer of the IEEE Vehicular Technology and the IEEE CommunicationsSocieties.

efficient scheduling for video transmissions in maritime

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