VIDEO streaming is becoming the dominate traffic in the

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1 2064 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 15, NO. 8, AUGUST 2016 Profit Maximization through Online Advertiing Scheduling for a Wirele Video Broadcat Network Wen Ji, Member, IEEE, Yingying Chen, Senior Member, IEEE, Min Chen, Senior Member, IEEE, Bo-Wei Chen, Member, IEEE, Yiqiang Chen, Member, IEEE, and Sun-Yuan Kung, Fellow, IEEE Abtract In thi paper, we addre the problem of how to make the wirele ervice provider (WSP) earn profit in a wirele video broadcat network with conideration of advertiement inertion. At the beginning, thi dy examine the profit component by analyzing traffic proviion and advertiement inertion. Thi dy conider uing two component for profit maximization one i the function for allocating video rate, and the other i the function for inerting advertiement duration. The maximum achievable profit depend on joint optimization of optimal video-rate vector and advertiement-duration vector, which are uually computationally intenive. To reolve uch a complexity problem, thi work alo propoe an effective algorithm for joint optimization. Firt, the overall profit i formulated a the olution of four local optimization problem through horizontal and vertical decompoition. Second, a theoretic polymatroidal framework i introduced in our work for optimization a thi framework i proved effective in profit maximization of multiuer ytem. Third, thi dy how that the overall profit can be maximized by finding the optimal profit point on the boundary of the rate and duration region. A a reult, the optimum point and the total profit can be obtained through a hierarchical greedy algorithm. Experimental reult demontrate that the propoed method i capable of making maximum profit for WSP in a wide range of broadcating rate. Index Term Video, broadcating, profit, polymatroid, advertiement Ç 1 INTRODUCTION VIDEO treaming i becoming the dominate traffic in the current and fure Internet and wirele network. The Cico Viual Networking Index predicted that video traffic accounted for 53 to 69 percent of the global mobile data traffic during 2013 to 2018 [1]. Although wirele erver provider (WSP) offer variou quality of ervice (QoS), mot uer till download video tream or watch on-line video for free. Conequently, it i deirable to capitalize the video traffic via advertiement in the fure. With the deregulation of telecommunication indutrie, fure wirele uer tend to chooe free ervice to obtain the cot-effective experience. Unlike conventional commercial broadcating on televiion or radio, which occupie the entire available ubbandwidth, the focu of wirele broadcating network i on the utilization of reource ince the W. Ji and Y. Chen are with the Beijing Key Laboratory of Mobile Computing and Pervaive Device, Intite of Computing Technology, Chinee Academy of Science, Beijing , P.R. China. {jiwen, yqchen}@ict.ac.cn. Y. Chen i with the Department of Electrical and Computer Engineering, Steven Intite of Technology, Catle Point on Hudon, Hoboken, NJ yingying.chen@teven.edu. M. Chen i with the School of Computer Science and Technology, Huazhong Univerity of Science and Technology, Wuhan , P.R. China. minchen2012@hut.edu.cn. B.-W. Chen and S.-Y Kung are with the Department of Electrical Engineering, Princeton Univerity, NJ dennibw@gmail.com, kung@princeton.edu. Manucript received 14 June 2015; revied 13 Sept. 2015; accepted 22 Sept Date of publication 2 Oct. 2015; date of current verion 29 June For information on obtaining reprint of thi article, pleae end to: reprint@ieee.org, and reference the Digital Object Identifier below. Digital Object Identifier no /TMC bandwidth i limited and hared. Accordingly, etting price for traffic proviion or advertiement draw much attention from WSP becaue uch a policy improve their profit. A recent work [2] howed that appropriate cheduling for targeted advertiement inertion i more beneficial and profitable for web-baed ervice provider. However, one particular challenge in wirele ytem i how to maximize the profit from advertiement and ervice proviion becaue exceive advertiement have a negative influence on the number of ubcriber. Hence, how to timulate more uer conumption while advertiement are inerted into the video content i critical to maintain the prior concern. 1.1 Background Conventionally, to cope with the varying characteritic of wirele channel in broadcat/multicat ervice, different method for increaing robutne and QoS were developed. On the ide of video ource, calable video coding (SVC) [3], layered video coding [4], [5], and adaptive video coding [6], [7], [8] with calable upport were widely employed to provide higher quality, flexiblilty, and calablity. Regarding the joint ource and channel ide, ince video data are enitive to tranmiion failure, treaming hould be more reliable. Therefore, joint coding [9], [10], [11] and optimal rate allocation [12], [13] technique become a feaible olution a thee approache provided variou protection level for video data generating, depending on importance and channel condition. On the joint modulation ide, SVC combined with adaptive modulation and coding cheme (MCS) [14], or combined with cooperative multiple-input-multiple-output (MIMO) [15], [16], [17], ß 2015 IEEE. Peronal ue i permitted, but republication/reditribution require IEEE permiion. See for more information.

2 JI ET AL.: PROFIT MAXIMIZATION THROUGH ONLINE ADVERTISING SCHEDULING FOR A WIRELESS VIDEO BROADCAST provided an effective cro-layer olution for video treaming in heterogeneou device under wirele broadcat/ multicat environment. A for quality-of-experience (QoE) upport, recent reearch on QoE-driven video broadcating [8], [12], [18], [19] howed better utilization of limited reource for multiuer heterogeneou requirement, with joint conideration of channel characteritic and current available reource. Mobile video broadcating ervice [20] are expected to become a popular application for wirele network operator. Unfornately, when it come to how to benefit from the wirele video traffic, few ytematic die have been conducted and publihed. Beide, profitdriven conideration were uually ignored in the related reearch on conventional wirele video broadcating. More pecifically, reearcher did not conider how to capitalize the video traffic via advertiement income. Recently, Li et al. [14] proved that when SVC wa applied to wirele broadcat/multicat treaming with conideration of heterogeneou characteritic, the total utility maximization of a broadcating ytem wa a nondeterminitic polynomial-time hard (NP-hard) problem. The author indicated that the olution for a profit-driven video broadcating depended on the following four factor available reource, the requirement for QoE, the channel condition of multiple end-uer (EU), and the profit generated baed on traffic proviion and advertiement inertion. Thee factor correpondingly deepened the difficulty of realizing a profit-driven wirele video broadcating ytem. To overcome uch difficulty, thi work propoe uing polymatroidal trucre for olving the profit-driven problem a the original problem i cloe to the problem of polymatroid interection. Furthermore, polymatroidal trucre have been proved effective [21], [22] a it can be eaily generalized when complex contraint are preent. Accordingly, polymatroidal trucre have been widely ued in dynamic reource-allocation problem, epecially in network and multiuer communication ytem [23]. 1.2 New Challenge In video broadcating ytem, advertiement inertion i attracting much attention from WSP becaue uch a policy improve their profit. However, it i till challenging how the QoE of EU i guaranteed, while divere requirement are jointly fulfilled. The following new challenge arie due to the preence of profit with advertiement inertion in wirele video broadcating ytem. In multivideo content broadcating, ince video content in different calable domain ha variou rate ditortion, a diverity of content rate during broadcating obviouly exit. In other word, if each video content i broadcated baed on a video rate, then when multicontent are broadcat, the ytem can build a hitogram or a vector of videorate ditribution. Allocation of reource according to uch video-rate vector apparently affect the profit performance. Typically, more broadcating content repreent more oppornitie for advertiement inertion. Although thi appear traightforward to implement, the acal profit model i more complicated than expected. For example, in multivideo content broadcating, it i difficult for a WSP to determine whether it hould inert more advertiement to enure profit or provide more content to retain ubcription. Thi i becaue there i a tradeoff between the number of content, the number of ubcribed uer, the quality of video ervice, and the profit of the WSP. In a multiuer environment, where video are broadcated over wirele channel, approache like forward error correction (FEC) and unequal error protection (UEP) are uually employed to provide QoS-guaranteed video tranmiion a channel condition change with time. Thu, it take additional effort for a WSP to impoe error protection to provide reliable tranmiion, which conequently reult in the increae of cot. In profit-driven video broadcating, the conflict between the economic efficiency and conumptive experience of uer uually exit. Thi i becaue, initively, EU alway wih to pay le for the ervice, wherea the WSP expect to earn a many revenue a poible. High price of traffic proviion however decreae the number of EU. A new profit model i therefore developed advertiement inertion. The growing popularity of online video ervice provide a good oppornity for advertier to reach their cutomer. Thi in rn increae the revenue for advertier and WSP a the ytem provider uually charge advertier baed on the number of EU. However, unlike the interactive advertiement in online video application, it i difficult to encourage more EU to watch advertiement voluntarily in wirele broadcating. Thu, long advertiement-duration inevitably decreae the number of EU. Therefore, there i a tradeoff between the advertiement duration and the number of EU. 1.3 New Formulation and Contribution Thi paper i around the above three challenge. In the following ection, we preent a olution for the problem of how to make the WSP maximize it profit through advertiement inertion with conideration of QoE guarantee. We conider a iation where the WSP ell limited wirele reource to heterogeneou uer who have freedom to chooe the ervice, while the WSP trie to make more profit through advertiement. We invetigate how EU pay for video ervice they purchae under a QoE meaure and how WSP et price for the traffic and advertiement inertion. We conider the general cae where heterogeneou EU have different experience and variou channel condition. The EU have the right to reject or keep receiving video ervice according to their willingne. Indeed, it i unclear how a wirele video broadcating ha maximum profit under dynamic EU connection condition. Thu, we firt give explicit definition to the above three challenge a follow. Firt, to tackle the diverity effectively in multivideo content broadcating, thi work propoe an approach coniting of joint profit optimization, ource adaptation, and advertiement cheduling for multiuer wirele broadcating. We formulate the profit maximization problem a a hierarchical optimization problem. By exploiting the content diverity of uer, the limited broadcating reource can be efficiently allocated. Furthermore, the aggregate profit of traffic proviion and advertiement inertion can be both maximized while the QoE requirement of heterogeneou uer are atified at the ame time. Second, for the conflict between the economic efficiency and conumptive experience of uer in multiuer

3 2066 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 15, NO. 8, AUGUST 2016 broadcating ytem, in thi work, the cot of traffic proviion i tated a a contraint. The goal i to find a olution that maximize collected profit o that traffic cot do not exceed a preet threhold. Furthermore, by analyzing the relation among video ource rate, additional error protection rate, and uer channel condition, the cot problem i tranformed to the problem of reliable video ervice proviion. A hybrid mechanim between profit maximization and reource allocation i propoed and etablihed to enure the feaibility of the olution. Third, for the profit-driven video broadcating, we carefully chooe the adjuting parameter to balance the relation among the profit, the rate, and cheduling region. Thi tradeoff become more important a the number of video EU increae. In thi work, profit maximization through advertiement inertion i died for video traffic-baed broadcating, where limited wirele reource are allocated to heterogeneou uer. Furthermore, thi work alo invetigate how EU elect video ervice under a QoE meaure and how WSP hould et price for the traffic proviion and advertiement inertion. Finally, a general cae i examined when EU have different QoE preference and channel condition. Thi ubection introduce a comprehenive polymatroidal trucre and ummarize how the overall profit can be maximized baed on the propoed idea. To the bet of our knowledge, thi i by far the firt attempt to combine both reource allocation and advertiement cheduling problem for wirele video broadcating. The contribution of thi work are ummarized a follow. Hybrid-domain profit framework. For a hybrid ytem with reource-allocation and advertiement cheduling, the exitence of optimal profit region depend on two factor. One i the video-rate allocation with conideration of the QoE of heterogeneou EU, and the other i the cheduling of advertiement inertion with conideration of the number of EU that are erviced. Thi dy how that the profit doe not alway increae the available bandwidth with the longer advertiement inertion, and/or better QoE proviion. To prove thi, an analytical optimal olution i provided in thi work. Profit optimization through hierarchical decompoition. Thi dy preent a dynamic profit-optimization approach that can imultaneouly model 1) the relation between advertiement inertion and ubcriber a well a 2) the aociation between the client and the cot of WSP. An objective function i therefore derived and propoed to expre thoe two relation in term of allocated broadcating rate and cheduled advertiement duration. Moreover, the contraint precribed by channel condition, available bandwidth, advertiement gro, and uer QoE are alo conidered in the propoed objective function. Our reult indicate that WSP can imply claify their EU into two group one prefer better QoE with hort-duration and fewer advertiement, and the other favor the lower and inexpenive bandwidth with a little bit more advertiement. Joint optimization through polymatroidal trucre. Thi dy develop a hybrid polymatroidal trucre for profit modeling that imultaneouly conider the factor of video-rate allocation and advertiement inertion. The profit can be maximized baed on the total rate and the total duration in the entire bandwidth by uing the polymatroid optimization. Alo, the maximum achievable profit can be explicitly obtained in a greedy manner by repectively finding the optimal rate vector (i.e., the rate ditribution of the current treaming video) and advertiementduration vector (i.e., the durational ditribution of the current treaming video) on the facet formed by the rate and the duration. The ret of the paper i organized a follow. Section 2 decribe the general framework of the profit model. Section 3 then decribe how to olve the profit maximization through hierarchical decompoition. In Section 4, the rate allocation and advertiement cheduling are formulated a a hybrid polymatroidal trucre. Section 5 how how to obtain the maximum profit by uing polymatroid optimization. Section 6 and 7 give the imulation reult and concluion. 2 SYSTEM MODEL Conider a ingle-cell broadcating network, where S video content (i.e., videotream) are being broadcat to N uer. The uer population i dynamic, and video on demand and advertiement inertion are both conidered in thi circumtance. Each video content i connected with N heterogeneou uer, whoe channel condition and creen feare are different. Notably, 2f1;...;Sg and P S ¼1 N ¼ N. Beide, reception performance of uer n i characterized a an eraure channel rate " n. To atify the requirement of heterogeneou EU, calable video coding i employed to provide layered and calable video upport. Typically, a video ervice i regarded a a ucceful tranmiion if an EU i atified with the received quality. The EU pay the WSP for the video ervice, and the WSP obtain the revenue by providing reliable ervice for multiple heterogeneou EU. To enure QoE, a broadcating ytem uually need to adapt the tranmiion to heterogeneou connecting environment by conidering the video quality, tranmiion rate, error protection, and traffic proviion trategie at the ame time. Thi correpondingly increae the cot of a WSP. What i more, to offer more choice to uer, the WSP ha to provide flexible video broadcating for heterogeneou EU by adopting joint SVC and adaptive layered broadcating. In uch a condition, even if the content that i being requeted i the ame, the erved quality i different from an EU to another, which therefore require an effective method for WSP to fully model the cot. The detailed model i depicted later in thi work. A advertiement inertion become a trend of buine model for WSP, thi work lay emphai on uch a topic. In thi dy, the behavior of advertiement inertion i modeled a a et of inertion S with finite lot t. The EU demand the video ervice by ending a requet to the WSP. If the WSP want to earn revenue by advertiement inertion, the WSP need to devie an appropriate way o that

4 JI ET AL.: PROFIT MAXIMIZATION THROUGH ONLINE ADVERTISING SCHEDULING FOR A WIRELESS VIDEO BROADCAST client can accept inertion. In our cenario, before advertiement are inerted into the S content at the advertiement lot (e.g., at the beginning of each content during playback), the broadcating ytem uually lice advertiement into egment and convert them into SVC tream. Therefore, all the propertie of the original SVC tream can be maintained in the content 1. Baed on uch a cenario, thi dy dicue how to maximize the profit by conidering the tradeoff between video traffic proviion and advertiement inertion, epecially when the limited available bandwidth and video-quality guarantee are required. To derive an objective function for profit maximization, thi dy analyze the major characteritic of the overall profit in wirele etting. Then, the profit region and broadcating model are built baed on thee characteritic in thi paper. 2.1 Revenue and Cot Analyi through Traffic Proviion The EU demand video content by making a requet to a ðr Þ be the revenue of the WSP when content i uccefully broadcat to EU n at a video rate r. Auming the WSP earn an average revenue per unit rate, we can expre the revenue in term of content price a (i.e., the price of content ubcription) a WSP. Let u WSPðrÞ ;n u WSPðrÞ ;n ðr Þ¼a r : (1) On the ide of EU, the video quality i uually defined a a utility function u EU ;n ðr Þ [24] u EU ;n ðr Þ¼u lnð1 þ r Þ; (2) where u repreent the willingne to pay of content. Theoretically, the ytem cot derive from the following four part [25], [26], [27]: i) Deployment cot becaue the WSP need to invet in infratrucre before operation, ii) operating expene due to the ervice proviion, iii) current uage-baed or congetion-baed degree, etc., and iv) maintenance expene a the broadcating ytem require management, adminitration, and long-term maintenance. Beide, the WSP need to provide the flexible protection for reliable video tranmiion in wirele environment. For implicity, we aume that the cot i dependent on the following factor the number of uer, the rate r of video data, and the rate g of error protection data. When the WSP provide a video ervice for an EU, the cot i given by c WSPðrÞ ;n ðr Þ¼w ðn Þðr þ g Þ; (3) where w ðn Þ i the cot between the WSP and n EU. The total profit of a WSP depend on many factor. Since it i difficult to accurately etimate all the cot aociated with carrying traffic, thi paper focue on the major factor that are related to the revenue generated from EU and the above cot of wirele video proviion. The total profitability generated from n EU baed on the th video i then decribed a Profit WSPðrÞ ;n ¼ u WSPðrÞ ;n ðr Þc WSPðrÞ ;n ðr Þ: (4) 1. Unlike the work in [2], thi dy doe not dicu the content of advertiement (i.e., targeted advertiement). In the wirele cenario, the tranmitter employ flexible FEC to provide reliable video tranmiion. Mot of the exiting literare focued on deviing effective protection trategie, uch a [28] and [11]. Rather than uing thoe protection trategie, thi work utilize Fountain code to provide flexible error protection in multiuer broadcating ytem. Let " ;n be the channel condition of EU n, who demand the content. With an appropriate deign [29], [30], the reliable video tranmiion condition in multiuer broadcating can be roughly etimated by g r ð 1þd 1^" ;n 1Þ, where d i a fixed mall poitive value, ^" ;n repreent the threhold. Such a function indicate that thoe EU, whoe channel tate atify " ;n ^" ;n, reliably receive video tream in a rate r. Then, for the wirele video broadcating ytem, the WSP can maximize it revenue by allocating the available bandwidth R among multicontent broadcating, on the premie of reliable traffic proviion and a certain quality u 0 guarantee. Equation (4) implie that Profit WSPðrÞ : X S X S X n ¼1 a r w ðn Þðr þ g Þ; (5) :t: u EU ;n ðr Þu 0 ; (6) ¼1 r þ g R Budget ; (7) r R ; (8) n N ; (9) 1 þ d g r 1 ; (10) 1 ^" ;n r ; g ; ^" ;n ;n 0; (11) where (6) indicate the quality guarantee level u 0 ; (7) give the available bandwidth budget R Budget ; (8) how that the ource-rate adaptation upported by the broadcating; (9) demontrate the baic condition in general multiuer communication, in which the acal number of EU being erviced might be fewer than the original number of EU requeting ervice; (10) pecifie the reliable multiuer broadcating condition. 2.2 Profit through Advertiement Inertion Nowaday, advertiing ha become the major income for mot ervice provider a the price of traffic gradually decreae. The WSP place advertiement in their channel and broadcat them to their EU. Then, the WSP charge their advertiement client baed on the broadcating frequency, the duration, and the chedule (i.e., prime time or fringe time). For example, the price of an advertiement inerted in a popular event or in a prime time i higher than that inerted in a uual event due to more audience and higher popularity. Notably, an advertiement ervice uually require the conent of EU. Accordingly, long-duration or high-frequent inertion reult in the decreaing number of EU. Baed on uch a concept, the revenue u WSPðAdÞ ;n ðt Þ gained from advertiement ervice can be characterized a

5 2068 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 15, NO. 8, AUGUST 2016 a function according to the advertiement duration t and the content price b (i.e., popular event or not): u WSPðAdÞ ;n ðt Þ¼b t : (12) The rik of advertiement ervice mainly come from the tolerance of the EU becaue comparing with the traffic proviion or broadcating, the cot of advertiement inertion can be ignored. Therefore, Profit WSPðAdÞ : :t: X S ¼1 X S ¼1 b t ; (13) t T budget ; (14) t T 0 ; (15) where (14) how that the amount of advertiement duration i limited to T budget. The condition (15) demontrate that the total duration for each content hould not exceed the utilization threhold T Propertie (1) Relation between n and t Obervation 1. Longer duration of advertiement t decreae the number of EU n. It i traightforward to ee that the long-duration advertiement lead to more content witching. The willingne of EU to wait for videoteaming and to keep watching advertiement apparently ha a tolerance degree. According to the work by Ha et al. [31], the number of EU, who tay ned while watching commercial in a time-frame t, can be calculated a follow: 8 < n ðt Þ¼ : N ; 1 r ð ttth t th þ1þ r N ; t t th ; t > t th ; (16) where r i a parameter that meaure uer patience, r denote an appropriate normalization contant, and N repreent the total number of EU, who demand the content. (2) Relation between w and n Obervation 2. The cot w increae dratically when the n i beyond a threhold N th. One example i howed in Fig. 2. The tranmiion capacity and correponding available bandwidth are uually limited. When ma EU demand a video ervice at the ame time, a large number of EU could tay in an extremely wore channel condition. If the tranmiion become unreliable, EU might loe their patience and quit. In thi cae, it i aumed that the broadcating ytem intend to keep a many uer a poible by broadcating it ervice at a high cot. Thu, the ervice capacity of a wirele broadcating ytem ha been limited to the arated number of EU. The aration condition i modeled a follow: ( w ðn Þ¼ w 0; n N th; n w 0 en th ; n >N th ; (17) where w 0 i an exponential parameter that meaure the cot of a normal cae, and N th preent the number of upporting EU when the broadcating ytem i initially operated. 2.4 Hybrid Model for Profit Maximization Formulation The total profit Profit WSP of a broadcating ytem can be built a a hybrid model that conider both traffic proviion profit Profit WSPðrÞ and advertiement inertion profit Profit WSPðAdÞ, baed on the aforementioned formulation: Profit WSP :max b XS t þ Xn a r w ðn Þðr þ g Þ ; (18) ¼1 X S :t: u EU ;n ðr Þu 0 ; (19) ¼1 r þ g R Budget ; (20) r R ; (21) n N ; (22) 1 þ d g r 1 ; (23) 1 ^" ;n X S ¼1 t T budget ; (24) t T 0 ; (25) r ; g ; ^" ;n ;n 0; (26) var: r; t: (27) 3 PROFIT MODEL AND DECOMPOSITION 3.1 Hierarchical Decompoition Thi ection introduce the decompoition method propoed by Palomar and Chiang [32] for analyzing the objective function in Eq. (18). Thi work adopt the idea of Palomar and Chiang with everal modification to upport hierarchical decompoition of the component trucre among profit. According to the theory by Palomar and Chiang, the component trucre can be divided into two ubproblem. Let Qðr; tþ ¼max r;t ½Profit WSP Š be the primal objective function, where t ¼½t 1 ;...; t S Š and r ¼½r 1 ;...;r S Š. Therefore, Qðr; tþ ¼Q ðadþ ðtþþq ðrþ ðrþ; (28) where Q ðadþ ðtþ ¼Profit WSPðAdÞ and Q ðrþ ðrþ ¼Profit WSPðrÞ. Obviouly, Q ðadþ ðtþ and Q ðrþ ðrþ are the individual reult of Eq. (13) and (5), repectively. The decompoed

6 JI ET AL.: PROFIT MAXIMIZATION THROUGH ONLINE ADVERTISING SCHEDULING FOR A WIRELESS VIDEO BROADCAST Fig. 1. Decompoition of profit maximization problem. ubproblem Q ðadþ ðtþ and Q ðrþ ðrþ repectively control the variable vector, i.e., t and r. According to the reliable broadcating condition in Eq. (10), the broadcating rate r received by n uer i differentiated by the threhold ^" ;n, which i determined by n. Baed on obervation 1 and 2, n can be formulated a a function of t. In the meantime, n and t affect the cot and the reulting profit Profit WSPðrÞ. Such contraint introduce the coupling effect to the profit maximization problem, o that the original problem can be olved by uing decompoition method. The reaon why thi paper applie hierarchical decompoition i it efficiency and effectivene. The illutration of the hierarchical decompoition i hown in Fig Hybrid-Domain Hierarchical Model Aume that there are two baic threhold in each broadcating video content One i uer aration N th, and the other i uer tolerance t th. To implify the expoition, the following content dicue the profit problem by introducing the aration domain and the tolerance domain firtly. The baic profit maximization problem can be claified into four dijoint domain: (1) Nonarated N N th and tolerable t t th. In thi condition, the number of total EU requeting ervice i not beyond the capacity of a broadcating ytem. At the ame time, the EU accept and tolerate a mall piece of advertiement inertion. Thi i the normal and ideal operational cenario for a broadcating ytem (ee Section 5.1). (2) Nonarated N N th and nontolerable t > t th. The duration of advertiement inertion i beyond the tolerance degree of uer. One cenario that frequently come up i, the WSP inert longduration commercial uch that uer witch the channel or quit the ervice. However, in uch a cae, there i till an optimal olution for profit maximization when uitable n and t are determined (ee Section 5.2). (3) Sarated N >N th and tolerable t t th. The number of total EU requeting ervice i beyond the erving capacity of the broadcating ytem. The broadcating ytem become overloaded uch that the cot increae rapidly when the N N th uer are erviced. Thi cae uually occur in popular event, uch a the world cup and top elling movie. Like (2), an optimal olution alo exit in thi cae (ee Section 5.3). (4) Sarated N >N th, nontolerable t > t th. A large number of EU are requeting the video ervice, but uer are not willing to tolerate advertiement during broadcating. When uch a circumtance occur, the ytem ue a mechanim to lower the number of uer requeting ervice by extending the duration of advertiement and increaing inertion (ee Section 5.4). The WSP maximize it profit by deigning an effective adjuting mechanim to manage the demand from EU. Since the WSP alway ha a limited bandwidth reource, it mut guarantee that the total demand from EU are not larger than it erving capacity. The mot important, the WSP can obtain the larget benefit with uch a mechanim. The following ection preent the olution domain by domain by exploiting the profit propertie of the polymatroidal trucre. 4 RATE ALLOCATION AND ADVERTISEMENT INSERTION SCHEDULING THROUGH HYBRID POLYMATROIDPROFIT STRUCTURE Obervation in [22], [23] howed that for a wide cla of multiuer ytem, particularly in wirele one, the entire or a ubet of the utility region formed an immanent polymatroidal trucre. Exploiting the polymatroidal trucre could implify the algorithmic treatment of broadcat/multicat rate region. In thi work, we oberve that profit region exhibit a polymatroidal trucre, and the following content then ue thi explicit characteritic of the profit region to create a hybrid trucre, which can acally olve practical problem in the real application. 4.1 Polymatroid Profit Strucre Analyi Conider a broadcating cenario, where a WSP remain profitable through adjuting the allocated rate and inerting advertiement. The profit region are repectively characterized through optimal rate allocation and cheduling policie. Let u denote R r a a rate-allocation policy, which i a mapping from the rate pace to R S þ. Beide, R r can be interpreted a the video rate allocated to all S content. Given the characteritic of EU, the profit region P WSPðrÞ ðr r Þ under policy R r how a polymatroidal trucre for our broadcating ytem. The following theorem ubtantiate uch an interpretation. Theorem 1. Given a policy R r, the achievable profit region of the ytem P WSPðrÞ ðr r Þ i a polymatroid, where P WSPðrÞ ðr r Þ¼ P WSPðrÞ 2 R S þ jpwspðrþ ðaþ XjAj X n ¼1 Proof. See Appendix A. a r w ðn Þðr þ g Þ;A S : (29)

7 2070 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 15, NO. 8, AUGUST 2016 Fig. 2. Performance comparion between the baeline and the propoed trategy for wirele video broadcating. Accordingly, let R t repreent a duration-allocation policy, which mean the total duration of advertiement cheduled to be inerted into all S content. The ubequent theorem how that the reulting profit region P WSPðaÞ ðr t Þ i alo a polymatroidal trucre. Theorem 2. Under a cheduling policy R t, the achievable profit region of the WSP P WSPðaÞ ðr t Þ i a polymatroid, where P WSPðaÞ ðr t Þ ¼ P WSPðaÞ 2 R Sþ jpwspðaþ ðbþ XjBj b t ;B S : (30) ¼1 Proof. The proof i imilar to that of Theorem 1 in Appendix A. Baed on Theorem 1 and 2, for the problem of Eq. (18), the total profit region for the WSP can be characterized by the following theorem. Theorem 3. Given policy ðr t ; R r Þ, the achievable hybrid profit region of the ytem P WSP ðr t ; R r Þ i a polymatroid, where P WSP ðr t ; R r Þ¼P WSPðaÞ ðr t ÞP WSPðrÞ ðr r Þ: (31) Proof. By direct verification.

8 JI ET AL.: PROFIT MAXIMIZATION THROUGH ONLINE ADVERTISING SCHEDULING FOR A WIRELESS VIDEO BROADCAST Profit Region via Hybrid Polymatroidal Profit Strucre Thi ubection introduce that for a multicontent video broadcating ytem, the profit region can be repreented by a broadcating function. Notably, the objective of thi ubection i to model P WSP. A the polymatroidal trucre of the broadcat function alo induce the polymatroidal trucre for the union profit region, the total profit region P WSP i the union of all the component P WSPðrÞ and P WSPðAdÞ. Thu, it i ufficient to firt conider the two component in term of polymatroidal trucre with the broadcating function. Such two component are repectively tated in the following theorem. Theorem 4. : When rate are dynamically allocated according to policy R 2 F, where F i the et of all feaible rate-control policie that atify the rate contraint FfR: ðrðaþ þ ðaþþ R budget ; 8g, the profit region with repect to traffic proviion can be defined a WSPðrÞ : P WSPðrÞ ðrþ ¼ [ R2F P WSPðrÞ ðrþ: (32) Proof. See Appendix B. Theorem 5. When the duration of advertiement i dynamically allocated baed on policy T 2 G, where G i the et of all feaible duration-control policie that atify the duration contraint GfT : ðtðp ÞT budget ; 8g, the profit region with repect to advertiement inertion i given by WSPðAdÞ : P WSPðAdÞ ðtþ ¼ [ T2GP WSPðAdÞ ðt Þ: (33) Proof. The proof i imilar to that of Theorem 4 in Appendix B. The following reult how that the total region (i.e., hybrid region) can be written a a union of the profit region with repect to traffic proviion and advertiement inertion. Theorem 6. The total profit region of the WSP i given by WSP : P WSP ðr; tþ ¼P WSPðrÞ ðrþp WSPðAdÞ ðtþ: (34) Proof. By direct verification. 4.3 Profit Maximization through Upper Boundary Surface Achieving Theorem 1, 2, and 3 prove that the total profit region P WSP ðr t ; R r Þ and it two component P WSPðrÞ ðr r Þ and P WSPðaÞ ðr t Þ exhibit polymatroidal trucre. Theorem 4, 5, and 6 give a hybrid profit region under the rateallocation and advertiement-cheduling policie. A the trucre of profit region i validated, in the following content, thi dy make ue of the polymatroidal trucre to characterize the boundary of the profit region. Although a imilar verion of the following reult wa obtained in [23], the difference between that paper and thi work i that the region P WSP of thi dy i controlled by both t and r. Definition 7. The boundary urface of P WSP ðt; rþ i the et of thoe rate-duration pair ðt; rþ uch that no component can be increaed while the other component remain fixed and in P WSP ðt; rþ. Let p be a permutation of the et E ¼f1;...;Sg, which repreent the element of the et E located in the i th poition after the permutation [33]. The olution to the optimization problem can be found by locating the extreme point of polymatroid and uing permutation [34], [23]. Baed on uch a concept, for the two trategie, rate allocation and duration cheduling, we have Permutation Baed on Rate P r ¼fp r ð1þ;...; p r ðsþg, where p r ðþ :¼ ða prðþ w p rðþ 1" prðþ ÞN and ða prð1þ w p rð1þ 1" prð1þ ÞN pð1þ > > ða prðsþ w p rðsþ 1" prðsþ ÞN pðsþ Permutation Baed on Advertiement P Ad ¼½p Ad ð1þ;...; p Ad ðsþš, where p Ad ðþ :¼ b pðþ and b pð1þ > >b pðsþ. Thu, the maximum of the profit lie at the point of the boundary urface becaue any other point in the profit region hould not fall outide the boundary urface. Then, the correponding optimal rate-control and duration-cheduling policie can be reduced to a boundary-achieving problem expreed in the following theorem. Theorem 8. The boundary urface of P WSP ðt; rþ i the cloure of all pair uch that ðt ; r Þ i a olution to the optimization problem max t;r PWSP 1 t 2 r :t: P WSP 2P WSP ðt; rþ: (35) Proof. See Appendix C. Conequently, there exit rate vector and duration vector in the polymatroid-baed broadcating network, which atifie Eq. (18). That i, the maximal broadcat profit can be found on the boundary urface. The rate vector and duration vector are from the um-profit facet of the polymatroid, and uch facet can be found by locating the extreme point. 5 POLYMATROIDPROFIT STRUCTURE ANDPROFIT MAXIMIZATION A the tranmiion capacity i uually limited, there i a maximum number of upporting EU for a general broadcating ytem. The ytem profit i an accumulative profit generated from P n EU, who demand divere video content and are already erviced. Therefore, uch a condition n N hold. Recall that the advertiement inertion affect n for all the S video ervice. Conequently, two interaction exit between the WSP and EU, which reult in n and the correponding aggregate profit. In Section 3.2, we characterize the interaction a

9 2072 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 15, NO. 8, AUGUST 2016 a hybrid-domain hierarchical model. Since the WSP i capable of controlling the acce of each EU, it i poible for the WSP to manage it profit by charging the EU that are already erviced. With the polymatroid profit trucre, the optimal olution can be found by adding more rate and more advertiement duration until the marginal profit become negative. Once the optimal olution i obtained, the WSP can determine which etting hould be elected by oberving thee two variable, t and r, with the highet marginal profit. The next dicuion analyze the ytem profit in four domain, repectively. 5.1 Domain 1: Nonarated N N th and Tolerable t t th The firt domain repreent that the broadcating ytem till ha available and ufficient reource o that the entire ytem i not overloaded. Therefore, the performance of video treaming i atifactory, and EU till have patience to wait for the ervice. The objective function in Eq. (18) become Profit WSP ¼ XS ¼1 ¼ XS ¼1 b t þ XN a r w ðn Þðr þ g Þ b t þ N a r w ðn Þðr þ g Þ : (36) Equation (36) can be further decompoed into the following independent bi-objective optimization problem: ( max XS ¼1 b t ; max N a r w ðn Þðr þ g Þ : (37) Equation (37) can be directly decompoed into eparate two objective (i) max P S ¼1 b t and (ii) max P S ¼1 N a r w ðn Þðr þ g Þ. Then, the original profit problem in Eq. (18) i rewritten a ubobjective optimization (i) and ubobjective optimization (ii) r maxq ðadþ ðtþ; (38) :t: t 1 T budget ; (39) t 0; (40) maxq ðrþ ðrþ; (41) :t: ðr þ gþ1 R budget ; (42) 1 þ d 1 1 ^" ;N g; 8 2f1;...;Sg; (43) r; g 0: (44) Thu, the profit can be maximized by directly olving the optimal reult in (i) and (ii) if the condition matche the firt domain. The following theorem ubtantiate uch an interpretation. Theorem 9. [Optimal Solution in the Firt Domain] The optimal olution ðt ; r Þ for Qðt; rþ in the firt domain i the global optimal olution to the entire problem. Therefore, uch a olution i alo the optimal olution (i.e., t and r ) to eparate ubproblem Q ðadþ ðtþ and Q ðrþ ðrþ, where Proof. See Appendix D. Qðt; rþ ¼Q ðadþ ðtþþq ðrþ ðrþ: (45) Define the marginal profit function of t and r a m ðadþ and m ðrþ repectively. Baed on Eq. (37) and Theorem 9, the marginal profit in the firt domain are calculated a m ðrþ ðr Þ¼ m ðadþ ðt Þ¼b ; (46) a w 0 N : (47) 1 " Example 1. Conider a typical multicontent broadcating ytem in the normal operation mode (i.e., the firt domain). Auming the S content atify the condition 8 2S, namely, N N th. Alo auming that for each broadcating content, the advertiement inertion atifie t t th. The maximum profit of broadcating can be achieved by the optimal permutation, which i hown in Algorithm 1. Algorithm 1. Optimal Permutation in the Firt Domain 1: Optimal permutation P Ad P Ad ¼½p Adð1Þ;...; p Ad ðsþš, where m ðadþ ðt pad ðþþ ¼b pad ðþ and b pad ð1þ > >b pad ðsþ 2: Optimal permutation P r P r ¼fp rð1þ;...; p r ðsþg, where m ðrþ ðr prðþþ ¼ aprð1þ w p rð1þ 1" prð1þ 3: Optimal permutation ðp Ad ; P r Þ a prðþ w p rðþ 1" prðþ N prðþ and Nprð1Þ > ::: > a prðsþ w p rðsþ 1" prðsþ NprðSÞ 5.2 Domain 2: Nonarated N N th and Nontolerable t > t th Since t can be rewritten a t ¼ t th þ Dt, the increae of Dt reult in the decreae of Dn and Profit WSPðrÞ. Further, Profit WSPðAdÞ increae a Dt rie. Thu, we can ue the incremental cheme to analyze the profit. Note that the original primal problem i decompoed into the component of fixed profit and dynamic profit, where the former i the reult of the t th advertiement inertion wherea the latter come from the flucation profit due to Dt. Conequently, the profit maximization problem i converted to how to utilize the profit flucation. The following lemma how that the primal profit problem i equivalent to the problem of fixed and dynamic profit. Lemma 10. When N max N th and t > t th, the olution for Profit WSP ðt ;N Þ i equivalent to the olution for Profit WSP ðt th ;N ÞþProfitWSP ðdt ; Dn Þ, where

10 JI ET AL.: PROFIT MAXIMIZATION THROUGH ONLINE ADVERTISING SCHEDULING FOR A WIRELESS VIDEO BROADCAST Profit WSP ðdt ; Dn Þ :¼ Profit WSPðAdÞ ðdt ;N Þ Profit WSPðrÞ ðdt ; Dn Þ: Proof. See Appendix E. (48) Conequently, the profit maximization ha a imple olution, and it can be olved by uing the dynamic profit optimization. The following lemma how the detail. Lemma 11. The optimal olution for Profit WSP ðdt ; Dn Þ i the ame a the optimal olution to Profit WSP ðt ;N Þ. Proof. By direct verification. The aforementioned two lemma imply an expendingwindow trategy, where the WSP can adjut the length of Dt to achieve the maximum profit. Algorithm 2 ummarize the expending-window trategy for computing the optimal Dt and Dn. Algorithm 2. Expanding-Window Strategy in the Second domain 1: Characterize the decrement of Dn via Eq. (16) Dn ¼ n 0 ðt ÞDt Profit WSP ¼ b Dt ðdt ; Dn Þ 1 1 rðdt þ1þ r 1 N r a w 1^" 2: Maximize Profit WSP ðdt ; Dn Þ through Lagrangian multiplier rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dt ¼ rþ1 N r a 1 w r 1^" rb 1 Dn ¼ n0 ðt Þj Dt Dt 3: Obtain the optimal profit through the polymatroidal trucre Profit WSP ¼ P S ¼1 b t th þ b Dt þ P N Dn a r w ðr þ g Þ Notably, during each increment Dt, the component Dn hould alway be increaed ince it lead to the larget profit of the objective function. Thu, the expending-window trategy i optimal. Theorem 12. [Optimal Solution in the Second Domain] The optimal olution ðt ; r Þ for Qðt; rþ in the econd domain i alo the optimal olution r for Q t ðrþ baed on Algorithm 1, where Proof. By direct verification. Q t ðrþ ¼Qðt th ; rþþqðdt; rþ: (49) Conequently, the marginal profit in the econd domain are m ðadþ ðt Þ¼b : (50) ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m ðrþ ðr Þ¼ n ða w 0 1^" Þ þ b n ða w 0 Þ: b r 1 " (51) Example 2. Conider a multicontent broadcating ytem, where the duration of an inerted advertiement i too long uch that EU begin to quit the ervice. The maximum profit of the broadcating ytem in thi cae i obtained through the following optimal permutation algorithm. Algorithm 3. Optimal Permutation in the Second Domain 1: Optimal permutation P r P r ¼½arg pð1þ Profit WSP pð1þ ;...; arg pðsþ Profit WSP pðsþ Š, where Profit WSP pðþ ¼ b pðþ t th þ b Dt þ PN pðþ Dn pðþ r pðþ apðþ w pðþ 1^", pðþ 8 2½1;SŠ 2: Optimal permutation P Ad P Ad ¼fp Adð1Þ;...; p Ad ðsþg, where p Ad ðþ :¼ t þ Dt 3: Optimal permutation ðp Ad ; P r Þ 5.3 Domain 3: Sarated N >N th and Tolerable t t th Since content of a popular event (e.g., FIFA world cup) uually reult in overloading iation, the cot N w ðn Þ¼w 0 en th increae for a practical video broadcating ytem. In thi cae, Eq. (18) i rewritten a Profit WSP ¼ XS N b t þ N a r w 0 en th ðr þ g Þ : (52) ¼1 If larger N lead to an overloaded ytem, the broadcating ytem uually increae the profit from the advertiement inertion. In other word, even when the cot increae due to overloading, the total profit can till be repectively increaed. The complete algorithm herein i imilar to the proce of the firt domain. The difference i the algorithm herein depend on the cot function. Algorithm 4 how the detail. Algorithm 4. Optimal Permutation in the Third Domain 1: Optimal permutation P Ad P Ad ¼½p Adð1Þ;...; p Ad ðsþš, where m ðadþ ðt pad ðþþ ¼b pad ðþ, b pad ð1þ > >b pad ðsþ 2: Optimal permutation P r P r ¼½arg pð1þ Profit WSP pð1þ ;...; arg pðsþ Profit WSP pðsþ Š, where Profit WSPðrÞ ¼ P S ¼1 N a r w 0 e N =Nth ðr þ g Þ, 8 2½1;SŠ 3: Optimal permutation ðp Ad ; P r Þ Similarly, the optimal proof follow Theorem 9. The marginal profit in the third domain are m ðadþ ðt Þ¼b ; (53) N m ðrþ ðr Þ¼ a w 0e 1 " N th N : (54) 5.4 Domain 4: Sarated N >N th and Nontolerable t > t th To enure the reception quality of each EU, the ytem hould be adapted to the wort cae becaue the rate allocation and advertiement cheduling are uceptible to uch a

11 2074 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 15, NO. 8, AUGUST 2016 condition when N >N th and t > t th occur. However, in thi cae, we have w ðn Þ¼w 0 e N =Nth 1, n ðt Þ¼ r ðt þ1þ r N, and t ¼ t th þ Dt. In other word, the bet profit can be obtained by computing a uitable Dt even in the wort cae. Like the econd domain, the Lagrangian multiplier can be ued in thi domain. The following algorithm lit the tep. Algorithm 5. Window Strategy for Wort Cae in the Fourth Domain 1: Characterize the decrement Dn via Eq. (16) Dn ¼ n 0 ðt ÞDt Profit WSP ðdt ; Dn Þ ¼ b Dt 1 1 rðdt þ1þ r N r a w 0 e N =Nth 1 1^" 2: Maximize Profit WSP ðdt ; Dn Þ by uing Lagrangian mutiplier ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dt ¼ N rþ1 N r a w 0 en th 1 r 1^" rb 1 Dn ¼ n0 ðt Þj Dt Dt 3: Obtain the optimal profit through the polymatroid trucre Profit WSP ¼ P S ¼1 b t th þ b Dt þ P N Dn a r w 0 e N =Nth ðr þ g Þ The profit maximization in the wort cae i obtained by applying the optimal permutation mentioned in Algorithm 3. The optimal proof follow Theorem 12, and the marginal profit in the fourth domain are the ame a thoe in the econd domain. 5.5 Greedy Procedure in the General Cae We now conider the general cae. Since the WSP i capable of controlling the acce of all EU, it mean that the WSP manage the n and the t by charging the EU that are already erviced. Thu, it i poible to decide which domain the content belong to. Thi dy ue the greedy algorithm (i.e., Algorithm 6) to olve the hybrid profit maximization mentioned in Eq. (18) by utilizing the polymatroidal trucre. Propoition 13. If Profit WSP ðr; tþ i a polymatroid in R þ, then Profit WSP i greedy. Thi propoition had been proved in [35]. Propoition 14. If Profit WSPðAdÞ i a polymatroid, Algorithm 6 give an optimum olution to Eq. (18). The proof i referred to the proof in [36]. Baed on the above-mentioned two propoition and the polymatroidal trucre, the greedy algorithm for optimal hybrid-domain allocation and cheduling can be derived. 6 NUMERICAL SIMULATION RESULTS Thi ection preent numerical example by analyzing a imple wirele broadcating network. Thi ection alo how how to obtain optimal bandwidth allocation and advertiement cheduling by uing the model propoed in the above-mentioned ection. Algorithm 6. Greedy (marginal) Algorithm in the General cae 1: Initialization: Define A i a a et of video content, where all the element fall in domain i and i=1,2,3,4, according to N and t. Partition S ¼f1;...;Sg into four ubet, i.e., A i. 2: Marginal Profit Computation: Switch A i do A 1 : Baed on Eq. (46) and (47), compute P Ad ¼ arg max 2A 1 ðb Þ P r ¼ arg max 2A 1 ðm ðrþ ðr ÞÞ P 1 ¼ P Ad þ P r A 2 : Baed on Eq. (50) and (51), compute rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 2 ¼ arg max n ða 2A 2 b w 0 1" Þ þ b r þ b n ða w 0 1" Þ A 3 : Baed on Eq. (53) and (54), compute P Ad ¼ arg max 2A 3 ðb Þ P r ¼ arg max 2A 3 ðm ðrþ ðr ÞÞ P 3 ¼ P Ad þ P r A 4 : Baed on Eq. (50) and (51), compute P 4 ¼ arg max 2A 4 b þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ða w 0e N=Nth 1" Þ b r þ b n ða w 0e N=Nth 1" Þ 3: Allocate Dr and Dt Calculate P ¼ maxfp 1 ; P 2 ; P 3 ; P 4 g If P i in the firt or third domain P Ad t þ Dt, P r r þ Dr ele if P i in the econd domain P 2 ele t þ Dt, P 2 r þ Dr P 4 t þ Dt, P 4 r þ Dr 6.1 Simulation Sep Conider a wirele network with video broadcating ervice. The video traffic and the connection of EU are et up by a WSP. The device of EU are heterogeneou in term of the content and channel condition, i.e. variou video content and difference ditance to the WSP. Thi imulation ue the H.264 extended SVC video encoder to generate layered video tream. Additionally, ratele error correction i ued to for variable channel condition. Aume that the ytem broadcat three tandard video equence City, occer, and harbor. Beide, the channel ta of the uer complie with the eraure-rate ditribution [11]. Mobile EU are requeting the ervice of different video content, where the number of EU and the number of video content are exogenou variable. The following part invetigate the profit performance when the following different trategie are applied: (i) Un_Weight Thi i a widely ued olution for reource allocation and cheduling. The broadcating ytem employ a uniform model, where the limited bandwidth i uniformly ditributed to S

12 JI ET AL.: PROFIT MAXIMIZATION THROUGH ONLINE ADVERTISING SCHEDULING FOR A WIRELESS VIDEO BROADCAST (ii) (iii) (iv) (v) content. The duration of each inerted advertiement in each video content i alo uniformly cheduled. Ad_Weight The allocation and cheduling follow the majority rule of bandwidth becaue the available bandwidth i the carce in wirele environment. The third-generation (3G) and the long-term evolution (LTE) till benefit mainly from the traffic proviion. Hence, the available bandwidth follow the common proportional allocation manner in thee typical cenario. EU_Weight The WSP earn profit mainly from the advertiement inertion. Free-WIFI acce i broadly ued in mot wirele broadcating ytem. In thi cenario, advertiement inertion become the major profit. The bandwidth allocation and advertiement cheduling depend on the number of EU. Weight_Ad_EU Mot WSP provide the flexible freemium mode, where part of ervice are free of charge wherea the other ervice are not. In thi mode, there i a tradeoff between the traffic proviion and advertiement inertion. Thi tradeoff i modeled a a weight policy, w 1 Ad Weight þ w 2 EU Weight. Propoed_Matroid. The propoed profit maximization baed on hybrid polymatroidal trucre. 6.2 Profit Analyi in Four Domain Thi ubection provide numerical example to quantize the key propertie of the propoed reource allocation trategy and the propoed advertiement-duration cheduling trategy Profit Comparion under Five Strategie We firtly analyze the total profit Profit WSP of a WSP baed on trategie (i)-(v) (ee Section 6.1) in the aforementioned four domain. The entire reult are repectively hown in Fig. 2a, 2d, 2g, and 2j. In the firt domain, a hown in Fig. 2a, the working mode i typical for general broadcating ytem, where the number of EU requeting ervice i not beyond the capacity of a ytem, and the advertiement duration i within a reaonable range. In thi cae, the profit Qðt ; r Þ i directly maximized through two eparate kind of optimization Q ðadþ ðt Þ and Q ðrþ ðr Þ. Thi i becaue the total profit i the ummation reult, Profit WSP ¼ Profit WSPðAdÞ þ Profit WSPðrÞ, and it doe not conflict with Profit WSPðAdÞ and Profit WSPðrÞ. Similar reult i found in the third domain (ee Fig. 2g). When the broadcating ytem become overloaded, it can adjut the operation mode through the control of n. Then, the profit i maximized by the boundary urface achieving. In thee two cae, the difficulty i to rapidly find the optimal vector r and t in variable circumtance. Through polymatroid modeling, the optimal reult can be explicitly obtained in a greedy manner by finding optimal permutation, illutrated in Algorithm 1 and 4. When advertiement duration t gradually increae, the WSP begin to loe their uer, which implie that n decreae. Interetingly, inflection point appear in both Fig. 2d and 2j, which repectively reflect the reult of the econd and fourth domain. In thee cae, the problem become how to determine Dt when the maximum profit occur. Rather than obtaining the maximum profit in the threhold t th or N th, the maximum profit i achieved when t > t th and n >N th hold. Thu, thi correpondingly indicate it i a hybrid-domain deciion between t and r. The optimization olution i found at the extreme point of the polymatroidal trucre after permutation i performed. Namely, the maximum profit olution i found by the boundary urface achieving. If the problem belong to the econd domain, the optimal r and t can be calculated by uing Algorithm 2 and 3. A for thoe in the fourth domain, Algorithm 5 become applicable during maximization. The profit under the policy (v) i larger than thoe under the other four policie becaue both Profit WSPðAdÞ and Profit WSPðrÞ in policy (v) are better than thoe in the other policie. The following two ubection how how the profit change when different policie are applied Profit Performance Comparion under Policy R r Fig. 2b, 2e, 2h, and 2k illutrate the Profit WSPðrÞ under five different policie. The profit performance of the WSP under the propoed cheme (v) outperform thoe under the other four cheme. Thee reult imply four concluion. 1) In multicontent broadcating, rate allocation hould conider not only the content but alo EU. Thi i becaue the reult under policy (v) how the bet profit in mot cae. 2) In multiuer ytem, profit are not improved with more conideration of EU requirement. Although, uer-centric deign typically dominate ervice provider, however, the reult under policy (iii) do not preent favorable performance compared with thoe under the other policie. Thi how that WSP cannot generate more benefit imply from EU atifaction becaue it i difficult to imultaneouly atify the divere demand from all EU. 3) In profit-driven ytem, advertiement inertion i the mot profitable mode becaue the policy (ii) i better than policie (i), (iii) and (iv). Thee reult alo demontrate how current mobile treaming ervice hould be operated Generate revenue primarily by delivering relevant and cot-effective online advertiing. 4) Suitable optimal trucre help improve the profit performance of the WSP. The propoed policy (v) how better performance in two apect. Firt, the propoed cheme keep the bet profit in a wide range of available bandwidth. Second, the propoed cheme can make the WSP obtain the profit quickly becaue the larget profit are achieved in a lower available broadcating rate Profit Performance Comparion under Scheduling Policy R t Fig. 2c, 2f, 2i, and 2l demontrate the Profit WSPðAdÞ under the five policie. The profit performance of the WSP under the propoed cheme (v) till exceed thoe under the other four cheme. Thee reult reflect two concluion. 1) To control the advertiement duration adaptively doe not alway improve the ytem profit becaue the reult under policy (ii) how wore profit in mot cae. The phenomenon reflect that profit from advertiement become complex in the wirele cenario becaue of the joint pricing

13 2076 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 15, NO. 8, AUGUST 2016 Fig. 3. Performance comparion for variable content for wirele video broadcating. between advertiement and traffic proviion. 2) Inertion of long-duration advertiement doe not improve the ytem profit, a hown in Fig. 2f and 2l. In thee two cae, t > t th lead to the rapid decreae of n uch that the profit Profit WSPðAdÞ alo reduce quickly. Conequently, there i an obviou optimum point between n and t. 3) Propoed polymatroid-baed method exhibit flexible performance becaue the reult under policy (v) how the bet profit in every domain even when t > t th. For the performance when the number of video content increae (Fig. 3), the main trend and concluion are imilar. Fig. 3 demontrate the total profit Profit WSP of a WSP, the repective profit Profit WSPðrÞ and Profit WSPðAdÞ under the S ¼ 2 (Fig. 3a, 3b, 3c) and S ¼ 4 (Fig. 3d, 3e, 3f). It i poible to oberve that, the propoed policy (v) keep the bet profit performance when the number of content increae and when the number of EU varie. 6.3 Complexity Analyi Thi ubection examine the complexity of the propoed approach. It invetigate whether it i efficient or not when polymatroid-baed approach i ued in the wirele video broadcating ytem. Generally peaking, one major advantage of the polymatroid-baed approach depend on it property. That i, each maximal independent et i alo the maximum independent et. Conequently, the optimal rate allocation and the advertiement cheduling in each domain can be explicitly obtained in a greedy manner. The next part analyze the complexity of the propoe approach in four domain. In the firt domain, for ubproblem Q ðadþ ðtþ, the computational complexity i OðS log SÞ becaue the computation mainly lie in the marginal profit permutation due to inertion of S advertiement. For the ubproblem Q ðrþ ðrþ, the computational complexity i alo OðS log SÞ becaue the permutation proce for S content i equivalent to marginal profit either for advertiement inertion or rate allocation. Thu, the overall computational complexity in the firt domain i OðSlog SÞ. In the econd domain, according to Algorithm 2, the rate i allocated into many window with the ize of Dt. Let R K ¼dmin Dt e be the upper bound of the number of window. In each window, the ytem rank the broadcating rate in order according to the marginal profit. Conequently, the major computation focue on the optimal permutation of rate allocation. The overall complexity of the propoed approach i no more than OðKS log SÞ. Like the reult in the previou two domain, the complexity in the third and the fourth domain i repectively OðS log SÞ and OðKS log SÞ. 7 CONCLUSION AND FUTURE WORK In order for the WSP to gain the maximum profit in advertiement inertion, thi dy analyze the interplay between traffic proviion and advertiement inertion. The maximum achievable profit depend on joint optimization of the optimal rate vector and the optimal advertiementduration vector. Optimization of thee two vector i uually computationally intenive. To reolve thi problem, thi dy firt formulate the overall profit a the olution to four uboptimization problem via horizontal and vertical decompoition. Then, by mean of a theoretic polymatroidal framework, thi dy how that the optimal profit point can be obtained by uing a hierarchical greedy algorithm. Simulation reult how that the propoed olution can improve the ytem profit effectively compared with the other four baeline. In the fure work, we plan to explore how to take into account uer preference in our optimization formulation. For example, uer profiling baed on peronalized advertiement inertion could lead to more efficient model and to yield more profit.

14 JI ET AL.: PROFIT MAXIMIZATION THROUGH ONLINE ADVERTISING SCHEDULING FOR A WIRELESS VIDEO BROADCAST APPENDIX A PROOF OF THEOREM 1 Under a given policy R r, r ¼½r 1 ;...;r S Š i then fixed. The reulting P WSPðrÞ i analyzed a follow. 1) It i normalized: Clearly, P WSPðrÞ (Ø) ¼ 0. 2) It i nondecreaing: Let T and T 0 be two finite et of element in E. Beide, T 0 T E ¼f1; 2;...;Sg. Then, 0 P WSPðrÞ ðt 0 Þ¼ XjT j 2jT 0 j P WSPðrÞ ðtþ ¼ XjT j 2jT j P WSPðrÞ : P WSPðrÞ P WSPðrÞ ðt 0 Þ: 0 ¼ XjT j 2jT 0 j P WSPðrÞ þ XjT j 2jTjjT 0 j P WSPðrÞ 3) It i ubmodular: Let T 0 and T 00 be any two finite et of element in E. Therefore, there are T 0 E ¼f1; 2;...;Sg and T 00 E ¼f1; 2;...;Sg. Then, P WSPðrÞ ðt 0 ÞþP WSPðrÞ ðt 00 Þ 0 ¼ XjT j ¼ ¼ 2jT 0 j jtx 0 \T 00 j P WSPðrÞ 2T 0 \T 00 P WSPðrÞ jtx 0 \T 00 j 2T 0 \T 00 P WSPðrÞ 00 þ XjT j 2jT 00 j P WSPðrÞ jt þ X 0 T 00 j jt þ X 0 [T 00 j 2T 0 T 00 P WSPðrÞ P WSPðrÞ 2T 0 [T 00 jt þ X 00 T 0 j ¼ P WSPðrÞ ðt 0 \ T 00 ÞþP WSPðrÞ ðt 0 [ T 00 Þ: P WSPðrÞ 2T 00 T 0 Thu, P WSPðrÞ atifie the ubmodular property. Thi complete the proof. APPENDIX B PROOF OF THEOREM 4 For any policy F k, where F k 2F, denote r k a the correponding allocated rate vector. The reulting profit can be written a P WSPðrkÞ ðrþ ¼ P WSPðrÞ : P WSPðrÞ ðr k Þ 1 r ðt þ 1Þ r N ða r k w 0ðr k þ gk ÞÞ; 8 2 S : The boundary urface of P WSPðrÞ ðrþ i P WSPðrÞ ðrþ [ P WSPðrkÞ ðrþ: R2F k Combining the above reult yield [ [ P WSPðrÞ ðrþ P WSPðrÞ ðrþ [ P WSPðrkÞ ðrþ: R2F k R2F R2F k S When k!1, R2F PWSPðrÞ ðrþ! S R2F PWSPðrkÞ ðrþ. Conequently, P WSPðrÞ ðrþ! S R2F PWSPðrÞ ðrþ. Thi complete the proof. APPENDIX C PROOF OF THEOREM 8 The original profit maximization problem can be rewritten a max P WSP :t: ðt; rþ 2ðt; rþ: (55) ðt;rþ Uing Lagrangian formulation yield ince P WSP ðt; rþ ¼ max P WSP 1 t 2 r: ðt;rþ [ P WSP ðt; rþ P P t: t t1r: r r1 [ ¼ P WSP ðt; rþ: t: P t ¼t1r: P r ¼r1 Denote pðkþ a the permutation of the component within a content vector in a decreaing order, where t k1 t k and r k1 r k. Therefore, P WSP pðkþ ¼ u WSPðAdÞ pðkþ ðt pðkþ Þ þ N pðkþ ðtþ X 2f1;...;Sg: u WSPðrÞ pðkþ;n ðr pðkþþe Then, Eq. (55) can be rewritten a X S max u WSPðAdÞ pðkþ ðt pðkþ Þ ðt;rþ k¼1 þ N pðkþ ðtþ X 2 r: u WSPðrÞ pðkþ;n ðr pðkþþe Thi complete the proof. N pðkþ ðtþ N 0 N pðkþ ðtþ APPENDIX D PROOF OF THEOREM 9 For the objective function in Eq. (18), there i Qðt ; r Þ¼ ðaþ max XS ¼1 ðbþ X S ¼ max b t ¼1 þ max XS N 0 ðr pðkþ þ g pðkþ Þ; 8k ðr pðkþ þ g pðkþ Þ 1 t b t þ Xn a r w ðn Þðr þ g Þ X n ¼1 ðcþ ¼ QðAdÞ ðt ÞþQ ðrþ ðr Þ: a r w ðn Þðr þ g Þ

15 2078 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 15, NO. 8, AUGUST 2016 (a) According to the definition of Qðr; tþ, Qðr; tþ ¼ max r;t ½Profit WSP Š. (b) In the firt domain, a the variation of t and r do not affect n, ubequently g ¼ r ð 1þd 1^" ;n 1Þ according to Eq. (23). (c) Baed on the definition of Q ðrþ ðrþ and Q ðadþ ðtþ, we obtain Q ðrþ ðrþ ¼max r ½Profit WSPðrÞ Š and Q ðadþ ðtþ ¼ max t ½Profit WSPðAdÞ Š. Thi complete the proof. APPENDIX E PROOF OF LEMMA 10 Let t ¼ t th þ Dt. Combining Eq. (16) with Eq. (18) yield Profit WSP ðr; tþ ¼ XS ¼ XS ¼1 ¼ XS ¼1 þ XS ¼1 b t th þ b Dt þ X b t þ Xn ðtþ a r w ðr þ g Þ NDn a r w ðr þ g Þ b t th þ XN a r w ðr þ g Þ b Dt XDn a r w ðr þ g Þ ¼1 ¼ Profit WSP ðt th ; NÞþProfit WSP ðdt; DnÞ: Thi complete the proof. ACKNOWLEDGMENTS Thi work wa upported by the National Naral Science Foundation of China ( ) and by the China Scholarhip Council. REFERENCES [1] Cico Viual Networking Index: Global Mobile Data Traffic Forecat Update, [Online]. 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16 JI ET AL.: PROFIT MAXIMIZATION THROUGH ONLINE ADVERTISING SCHEDULING FOR A WIRELESS VIDEO BROADCAST [33] M. Maddah-Ali, A. Mobaher, and A. Khandani, Fairne in multiuer ytem with polymatroid capacity region, IEEE Tran. Inf. Theory, vol. 55, no. 5, pp , May [34] J. Edmond, Submodular function, matroid and certain polyhedra, in Proc. Int. Symp. Combinatorial Struct., Jun. 1969, pp [35] F. Duntan and D. Welh, A greedy algorithm for olving a certain cla of linear programme, Math. Program., vol. 5, no. 1, pp , Dec [36] U. Faigle and S. Fujihige, A general model for matroid and the greedy algorithm, Math. Program., vol. 119, no. 2, pp , Mar Wen Ji (M 09) received the MS and PhD degree in communication and information ytem from Northwetern Polytechnical Univerity, China, in 2003 and 2006, repectively. She i currently an aociate profeor in the Intite of Computing Technology, Chinee Academy of Science, Beijing, China. From 2014 to 2015, he wa a viiting cholar in the Department of Electrical Engineering, Princeton Univerity. Her reearch interet include multimedia communication and networking, video coding, channel coding, information theory, optimization, network economic, and pervaive computing. She i a member of the IEEE. Yingying Chen received the PhD degree in computer cience from Rutger Univerity. She i currently an aociate profeor in the Department of Electrical and Computer Engineering, Steven Intite of Technology. Her reearch interet include cyber ecurity and privacy, mobile and pervaive computing, and mobile healthcare. She ha publihed more than 80 journal and referred conference paper in thee area. Prior to joining Steven, he wa with Alcatel-Lucent. She received the US NSF CAREER Award and Google Faculty Reearch Award. She alo received the NJ Inventor Hall of Fame Innovator Award, and the Bet Paper Award from ACM International Conference on Mobile Computing and Networking (Mobi- Com) She alo received the IEEE Outtanding Contribution Award from IEEE New Jerey Coat Section each year in Her reearch ha been reported in numerou media outlet including MIT Technology Review, Wall Street Journal, and National Public Radio. She i on the editorial board of the IEEE Tranaction on Mobile Computing, IEEE Tranaction on Wirele Communication, and IEEE Network Magazine. She i enior member of the IEEE. Min Chen (M 08-SM 09) received the BSc, MEng, and PhD degree in electrical and information technology from the South China Univerity of Technology, Guangzhou, China, in 1999, 2001, and 2004, repectively. He i currently a profeor in the School of Computer Science and Technology, Huazhong Univerity of Science and Technology. He i Chair of IEEE Computer Society Special Technical Communitie on Big Data. He wa an aitant profeor in the School of Computer Science and Engineering, Seoul National Univerity, from September 2009 to February He i a guet editor for IEEE Network, IEEE Wirele Communication Magazine, etc. He i co-chair of IEEE ICC 2012-Communication Theory Sympoium, and co-chair of IEEE ICC 2013-Wirele Network Sympoium. He ha more than 260 paper publication, including 100+ SCI paper, 50+ IEEE Tranaction/Journal paper, ix ISI highly cited paper, and one hot paper. Hi Google Scholar Citation reached 5,100+ with an h-index of 34. Hi top paper wa cited 621 time, while hi top book wa cited 420 time a of Augut Hi reearch interet include Internet of thing, mobile cloud, body area network, emotion-aware computing, healthcare big data, cyber phyical ytem, and robotic. He i a enior member of the IEEE. Bo-Wei Chen (M 14) received the PhD degree from the Department of Electrical Engineering, National Cheng Kung Univerity (NCKU), in He erved a a volunteer in IEEE R10 between 2010 and He alo worked a a potdoctoral reearch fellow in the Department of Electrical Engineering, NCKU, for four year. He i currently a potdoctoral reearcher at Princeton Univerity. He i the chair of Signal Proceing Chapter, IEEE Harbin Section. Hi reearch interet include big data analyi, machine learning, ocial network analyi, audioviual enor network, emantic analyi, and information retrieval. He i a member of the IEEE. Yiqiang Chen (M 03) received the BASc and MA degree from the Univerity of Xiangtan, China, in 1996 and 1999, repectively, and the PhD degree from the Intite of Computing Technology (ICT), Chinee Academy of Science (CAS), Beijing, China, in In 2004, he wa a Viiting Scholar Reearcher in the Department of Computer Science, Hong Kong Univerity of Science and Technology, Hong Kong. Currently, he i a Profeor and Director of the pervaive computing reearch center at ICT, CAS. Hi reearch interet include artificial intelligence, pervaive computing, and humancomputer interface. He i a member of the IEEE. Sun-Yuan Kung (F 88) i currently a profeor in the Department of Electrical Engineering, Princeton Univerity. Hi reearch area include VLSI array proceor, ytem modeling and identification, machine learning, wirele communication, enor array proceing, multimedia ignal proceing, and genomic ignal proceing and data mining. He wa a founding member of everal technical committee of the IEEE Signal Proceing Society, and wa appointed a the firt aociate editor in VLSI Area (1984) and later the firt aociate editor in Neural Network (1991) for the IEEE Tranaction on Signal Proceing. Since 1990, he ha been the editorin-chief of the Journal of VLSI Signal Proceing Sytem. He wa a recipient of IEEE Signal Proceing Society Technical Achievement Award for the contribution on parallel proceing and neural network algorithm for ignal proceing (1992), and a recipient of the IEEE Third Millennium Medal (2000). He ha been a fellow of the IEEE ince " For more information on thi or any other computing topic, pleae viit our Digital Library at