Pricing Considerations in Video-on-Demand Systems*
`
`Prithwish Basu
`Dept. of Electrical and Computer Engg.
`Boston University
`8 Saint Mary's St., Boston, MA, USA
`pbasu@bu.edu
`
`Thomas D.C. Little
`Dept. of Electrical and Computer Engg.
`Boston University
`8 Saint Mary's St., Boston, MA, USA
`tdcl@bu.edu
`
`ABSTRACT
`Video-on-demand (VoD} has been an active area of research
`for the past few years in the multimedia research community.
`However, there have not been many significant commercial
`deployments of VoD owing to the inadequacy of per user
`bandwidth and the lack of a good business model. 1 Signif(cid:173)
`icant research efforts have been directed towards reduction
`of network bandwidth requirements, improvement of server
`utilization, and minimization of start-up latency. In this par
`per, we investigate another aspect of VoD systems which has
`been largely neglected by the research community, namely,
`pricing models for VoD systems. We believe that the price
`charged to a user for an on-demand video stream should in(cid:173)
`fluence the rate of user arrivals into the VoD system and
`in turn should depend upon quality-of-service (QoS) factors
`such as initial start-up latency. We briefly describe some
`simple pricing models and analyze the tradeoffs involved in
`such scenarios from a profit maximization point of view. We
`further e>cplore secondary content insertion (ad-insertion)
`which was proposed elsewhere [1] not only as a technique
`for reducing the resource requirements at the server and the
`network, but also as a means of subsidizing VoD content to
`the end user. We treat the rate of ad insertion as another
`QoS factor and demonstrate how it can influence the price
`of movie delivery.
`
`Keywords
`Video-on-demand, pricing models, service aggregation
`
`INTRODUCTION
`1.
`With the explosive growth of the Internet and broad(cid:173)
`band cable networks in the mid- and late nineties, inter-
`
`*This work is supported by the NSF under grant No. NCR-
`9523958.
`'Several VoD field trials have been conducted in the US
`and elsewhere [5], but most of them have been reported to
`be unsuccessfuf ttom a business point of view, so far.
`
`Pcnnission to make digital or hard copies of all or part of this work for
`personal or classroom use is granted without fee provided that copies
`ure not made or distributed for profit or commercial advantage and that
`copies bear this notice and the full citation on the first page. To copy
`otherwise, to republish, to post on. servers or to redistribute to lists,
`requires prior specific permission and/or a fee.
`ACM Multimedia 2000 Los Angeles CA USA
`Copyright ACM 2000 1-58113-198-4/00/10 ... $5.00
`
`active video-on-demand (VoD) had been touted to be one of
`the most promising future applications for such networks.
`Unfortunately, inadequacy of bandwidth for serving a sig(cid:173)
`nificant user population has stymied the growth in deploy(cid:173)
`ment of VoD on a large scale. Hence, lot of research ef(cid:173)
`forts have been directed towards finding a scalable solu(cid:173)
`tion to the bandwidth problem using different techniques
`for serving aggregates of users [2, 3, 4). These techniques
`use CATV broadcast or IP multicast as dissemination mech(cid:173)
`anisms. One aspect of VoD systems that has been largely
`neglected by the research community is pricing of VoD ser(cid:173)
`vices. In this paper we briefly investigate several factors that
`can affect the price of a video stream delivered to the user
`and also analyze some economic tradeoffs that exist in that
`context. Such an analysis can help in establishing a sound
`economic basis for a large scale deployment of VoD.
`We develop models for pricing three different types of VoD
`service. First, in Sec. 2, we start with a simple interac(cid:173)
`tive VoD system which provides each user with a dedicated
`channel and show how an optimal price can be calculated
`for maximization of profit. In Sec. 3, we describe how a
`QoS factor like start-up latency can affect the price of an
`on-demand movie in a staggered broadcast delivery system,
`and then we again show how profits can be maximized in
`such a setup. In Sec. 4, we describe how ads can be used to
`subsidize VoD to users, and speculate how varying degrees
`of ad insertion can affect the price and the interest of the
`users. We also demonstrate how profits can be maximized
`in such a scenario. Sec. 5 concludes the paper and gives
`some directions of future work.
`
`2. OPTIMAL PRICE SELECTION
`A VoD system consists of a video server which can serve
`users on N channels at any point of time. Users arrive into
`the system with an average rate of .\ per unit time. For
`simplicity, suppose that the VoD system is not aggregation
`based, i.e., each channel supports only one user, because the
`service is fully interactive. Suppose that the movie is L time
`units long, and that the users remain in the system for some
`
`more vi~eo time n... > 0, on average, due to pauses and
`
`rewinds. We can treat the system as an M/GfN queue,
`where M stands for Poisson arrivals, G stands for a general
`service time which has a deterministic part L and a stochas(cid:173)
`tic part T;,., (T. = L+T;,.,), and N stands for the number of
`servers. For stability of the queue, i.e., for bounded waiting
`
`2 A lar~e numb~ of fast forw~d interactions may result in
`Tint bemg negative, but that IS unlikely in a paid service.
`
`359
`
`

`

`Mean
`Arrival
`Rote
`
`p
`
`Price
`or
`Movie
`
`L
`
`Start-up Latency
`
`(a) .\ vs. Price
`
`(b) Price vs. Latency
`
`Figure 1: Interdependence of Parameters
`
`times, the condition .\T, < N must hold, hence N should
`be chosen properly.
`Now suppose each user is charged a price p for viewing a
`movie. Intuitively, the mean arrival rate .\ will depend on
`the price of the movie as depicted by Fig. l(a). However,
`the exact function .\(p) can only be known from marketing
`experiments such as user polls and surveys. Suppose the
`VoD service provider (VoDSP) incurs a cost b per ch8Jlnel
`per unit time. Therefore in time T, the cost incurred will be
`NbT. In that time the VoDSP will receive .\T user requests.
`If no user is rejected (by bounding of waiting time due to ap(cid:173)
`propriate selection of N), the revenue earned will bep.\(p)T.
`The profit per unit time is given by P = p.\(p)- Nb. Now,
`we have an optimization problem at hand given by:
`Maximize: P(p, N) = p.\(p)- Nb
`Subject to: (1) p > 0 and (2) N > .\(p)T,
`Optimality is achieved when the second constraint has an
`equality, and the optimal price p• is given by the solution to
`the the equation: (bT, -p•).\'(p") = .\(p"). We should point
`out here that there is an issue with the above analysis: when
`the second constraint is relaxed to an equality, the variabil(cid:173)
`ity in arrivals may result in larger waiting times, and hence
`the assumption that the waiting times are low and do not
`affect user arrival, may fail. However, by over-engineering
`the system (i.e., by allocating a larger N than predicted by
`the optimal solution), we can approach a near-optimal solu(cid:173)
`tion. Also, if the function P(p, N) is not convex, then first
`derivative techniques may be inadequate to solve the opti(cid:173)
`mization problem. However, since the function is bounded,
`it will have a maxima, and that can be found using other
`more sophisticated (perhaps numerical) techniques.
`
`3. BROADCAST DELIVERY SYSTEMS
`Recently, staggered broadcast delivery systems have be(cid:173)
`come popular with researchers in this area since they can
`be used to provide VoD service over CATV networks to a
`large user population with a constant number of "staggered"
`broadcast channels per movie. The basic idea is to divide
`the whole movie into a constant number of smaller segments
`and then broadcast each smaller segment repeatedly on a
`different channel. The client listens on one or more of these
`channels for downloading the video data before consump(cid:173)
`tion. The simplest scheme which does not need any buffer(cid:173)
`ing on the clients is to distribute a movie of length L into an
`equal number of parts. In this case, the worst case start-up
`latency, t,1 is inversely proportional to the total number of
`broadcast channels, n (n = -1£ ). The worst case start-up la-
`••
`tency is a QoS parameter which can affect the price that is
`charged to a user by the VoDSP. We show by simple analysis
`
`..
`
`how this parameter can be adjusted by the VoDSP for max(cid:173)
`imizing their profits. More sophisticated broadcast schemes
`like Skyscraper Broadcast [4] can reduce the startup latency
`by dividing the movie into segments of increasing size and by
`intelligent use of client buffering. However, the basic pric(cid:173)
`ing model is similar in that case as n can be expressed as a
`function of t,,.
`As in the previous section, let us assume that the VoDSP
`incurs a cost b per video stream per unit time. Since they
`,,
`allocate n = ,£ streams for a movie, the total cost incurred
`by the VoDSP in timeT is f-bT. Suppose the mean arrival
`rate into the system is .\ per unit time. Hence the total
`number of users that have arrived in the system in time T
`is .\T. Suppose the price p charged to a user varies with t,,.
`We depict the price by some function p(t,,) which intuitively
`should be a decreasing function of t,, (a possible function is
`depicted graphically in Fig. 1(b)). As in Sec. 2, the exact
`shape of this curve too can be characterized by marketing
`techniques such as polls and surveys. The revenue earned
`by the VoDSP in timeT is .\Tp(t,,), and the profit per unit
`time, P is given by P = .\p(t,,) -
`tL b. P is maximized at
`••
`to~= topt when P'(t,,) = 0, i.e., .\p'(topt) + #--b = 0. If the
`opt
`equation has multiple roots, then the VoDSP can choose ei(cid:173)
`ther of those operating points depending upon other factors
`like viewer utility, which we do not consider in this paper.
`
`4. AD-INSERTION BASED SYSTEMS
`Secondary content insertion (or ad insertion) has been
`proposed for reduction in server and network bandwidth re(cid:173)
`quirements, and for subsidizing the cost of VoD to the end
`user [1]. First, we consider ads only as a means of subsidiz(cid:173)
`ing the cost to the user. We consider a scenario where all
`users are uniformly shown ads at a rate a (0 ~ a: ~ 1).3
`Intuitively, the price of a movie, p to a user should be a de(cid:173)
`creasing function of a:. If a ~ ao, the movie is streamed to
`the users for free. Price p should be maximum when no ads
`are shown, i.e., a = 0. An interesting topic to study is how
`the price varies with a in the interval [0, ao]. Two possible
`curves have been shown as I and II in Fig. 2(a).
`Initially, let us suppose that the mean arrival rate .\ is
`constant, and hence the number of movie channels needed
`to support that rate (N) is also constant. In this case, the
`VoDSP has two sources of revenue, namely, a broadcast ad(cid:173)
`vertisement channel, and the price of movies that it charges
`its users. If a video server can stream out N streams con(cid:173)
`currently, 4 and if b is the cost per stream per unit time, the
`cost incurred in timeT is NbT. If the VoDSP charges a per
`unit time to the advertisers, the revenue earned from the ad
`channel in timeT is aT. Since the advertisers are willing to
`pay more money if they know that more people are watch(cid:173)
`ing ads at any point of time, a can be represented as an
`increasing function of a. With respect to the above model,
`the profit per unit time is given by P = .\p(a) +a( a)- Nb,
`and it is maximized at a = a• which satisfies the equation
`.\p1 (a*)+ a'(a*) = 0.
`Now we consider the case when the mean arrival rate may
`be influenced by the price p and the quality of service factor
`a. Fig. 2(b) shows a tentative schematic of the effect of a on
`
`3a = A Am+~ , where Ama• is the maximum continuous
`mu.•
`Tnin
`ad time and Vmin is the minimum video time between ads.
`4 For bounded waiting time: .\L < N.
`
`360
`
`

`

`P{a)
`
`•
`
`<(a)
`
`(a) Price
`
`(b) Arrival Rate
`
`(c) Number of channels
`
`Figure 2: Effect of Ad-Ratio
`
`the arrival rate of users into the system in the steady state. 5
`As mentioned previously, these functions can be character(cid:173)
`ized more exactly by conducting marketing experiments. As
`a increases, the price drops and hence more people are at(cid:173)
`tracted to the system. But for a > a~, the high rate of ad
`insertion acts more as a deterrent, and A decreases. Also, in
`this case, the number of channels that are needed to support
`a particular arrival rate is lower bounded by N(a) > A(o:)L.
`Therefore we have an optimization problem akin to the one
`discussed in Sec. 2:
`Maximize: P(o) = A(o)p(a:) + a(o:)- N(O<)b
`Subject to: (1) 0 :Sa< o:o and (2) N(a) > A(a)L
`P is maximized for a particular value of "' = a:•, where
`a• is a root of the following equation:
`p1(a)A(O<) +a'(a) + {p(a)- L)A1(a) = 0
`Stream Merging Based Systems. Constrained ad inser(cid:173)
`tion has been proposed for reducing the server and network
`bandwidth requirements by reducing the temporal skews be(cid:173)
`tween adjacent streams receiving the same content [1]. Es(cid:173)
`sentially, a leading stream is put onto a multicast ad channel
`for AmG~ time units and then is shown video for Vmin time
`units, in a cyclic manner, while a trailing stream continu(cid:173)
`ously receives video until it merges with the leading stream.
`The merging algorithm ensures that no stream receives ads
`at a rate greater than a.
`In order to support users arriving into the system at a
`rate A( a), in steady state, the number of channels needed
`is given by Nm(a) which is an decreasing function of a: for
`a constant arrival rate A. However, since the arrival rate
`is influenced by the ad ratio, Nm (a) may not be a strict
`decreasing function. For a > a_x, Nm(a) drops due to the
`drop in the arrival rate, and due to greater ad insertion.
`But for 0 :S a :S O<>., Nm (a:) is dictated by two opposing
`behaviors: increase in arrival rate (which tends to increase
`N m) and greater ad insertion (tends to decrease N m). Hence
`the cumulative effect of these two forces may result in either
`an increasing or a decreasing function of a. It is very hard to
`characterize Nrn(a) analytically, but it can be characterized
`by simulations. Two curves that could possibly characterize
`Nm(O<) are shown in Fig. 2(c). Again, we are faced with a
`profit maximization problem as before:
`Maximize: P(a:) = A(a)p(a:) +a( a)- Nm(a)b
`Subject to: (1) 0 $a< ao
`P is maximized for a = a• where a• is a root of the
`following equation:
`p'(a:)A(O<) + p(a)A'(a) + a'(a)- bN;,(a) = 0
`"a(.) may not be an increasing function in this case.
`
`5. CONCLUSION AND FUTURE WORK
`We investigated pricing related tradeoffs involved in dif(cid:173)
`ferent types of VoD system deployments. Three different
`settings were analyzed: (1) a simple interactive VoD system
`with a dedicated channel per user, (2) a staggered broadcast
`delivery system, and (3) an aggregation system based on ad(cid:173)
`insertion. We demonstrated in this paper how a multitude of
`factors such as price, QoS level (start-up latency and ad ra(cid:173)
`tio), and user arrival rates can influence each other, and how
`the optimal price of a VoD service can be obtained (from a
`profit maximization perspective) in each of the above set(cid:173)
`tings. We believe that such an analysis of pricing models
`can help in establishing a sound economic basis for wide
`deployment of VoD in future.
`There are some open issues that need investigation. Wait(cid:173)
`ing times in VoD systems due to queueing (we have ad(cid:173)
`dressed waiting times due to hatching) can be another QoS
`factor for pricing. 6 Also, a good model of user behavior with
`respect to factors such as price is needed (by extensive sur(cid:173)
`vey) for proper characterization of the functions mentioned
`in this paper.
`
`6. REFERENCES
`[1] P. Basu, A. Narayanan, W. Ke, T. D. C. Little, and
`A. Bestavros. Optimal scheduling of secondary content
`for aggregation in video-on-demand systems. In
`Proceedings ICCCN •gg, Boston-Natick, MA, pages
`104-109, October 1999.
`[2) A. Dan, P. Shahabuddin, D. Sitaram, and D. Towsley.
`Channel allocation under hatching and VCR control in
`video-on-demand systems. Journal of Parallel and
`Distributed Computing, 30(2):168-179, November 1995.
`[3] L. Golubchik, J. Lui, and R. Muntz. Adaptive
`piggybacking: A novel technique for data sharing in
`video-on-demand storage servers. A OM/Springer
`Multimedia Systems, 4:140-155, 1996.
`[4] K. A. Hua and S. Sheu. Skyscraper broadcasting: A
`new broadcasting scheme for metropolitan
`video-on-demand systems. In Proceedings ACM
`SIGCOMM '97, Cannes, France, pages 89-100,
`September 1997.
`[5) Interactive TV trials. URL -
`http://www.teleport.com/~samcfcable4.html.
`
`6Large waiting times can result in loss of revenue due to
`reneging.
`
`361
`
`