IP TV Bandwidth Demand: Multicast and Channel Surfing

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1 This full text paper was peer reviewed at the direction of IEEE Communications ociety subect matter experts for publication in the IEEE INFOCOM 2007 proceedings. IP TV Bandwidth Demand: Multicast and Channel urfing Donald E. mith Verizon Laboratories Waltham, MA 0245 UA Abstract IP networks may soon become a delivery mechanism for broadcast television content. Multicast can reduce the steady state bandwidth demand on network links from one stream per viewer to one stream per watched program. owever, channel surfing at commercial breaks can periodically increase the bandwidth demand. In the channel change mechanism we study, surfers leave multicast groups and receive unicast streams at higher than usual bandwidth. This paper builds a mathematical model to determine the net bandwidth demand of multicast and surfing during commercial breaks. In one example, we find that the peak demand during a commercial break is twice the steady state multicast demand. Key Words Broadband access, capacity planning, IP TV, traffic analysis I. INTRODUCTION Fiber optic access networks (variants include fiber-to-thepremises or FTTP and fiber-to-the-node) have boosted individual users broadband access speeds into the tens of megabits per second. uch speeds enable Internet service providers to deliver video, one of broadband s principal applications. ome U.. telephone companies are pursuing a delivery mechanism called IP TV or switched digital video. IP TV encodes all video, whether broadcast or video-on-demand, into IP data packets and transmits them to subscribers over IP networks. Video packets may share portions of the IP network with data packets from web applications such as web surfing, online gaming, or peer-to-peer file transfers. Video threatens to consume large amounts of bandwidth in these IP networks. A standard definition (D) video stream typically runs at 3.75 megabits per second (Mbps), while a high definition (D) stream runs at 5 Mbps or more under MPEG-2 encoding. Any network link that handles many subscribers, each capable of demanding one or more IP TV video streams, must have enough bandwidth to meet the demand. A FTTP network provides several examples of such links. Fig. illustrates a portion of a FTTP network. Each node can serve multiple nodes of the type below it. The IP network core router and edge router at the top of the figure deliver content to the edge of the network. An Optical Line Terminal (OLT) forwards the content over a Passive Optical Network (PON) to an Optical Network Terminal (ONT) at each subscriber s premise. The PON typically serves up to 32 subscribers, while the OLT serves roughly 2000 subscribers. The link from the edge router to the OLT must deliver content to those 2000 subscribers. While not all of them may subscribe to IP TV, we can reasonably expect to find hundreds of IP TV subscribers on an OLT. ow big do these links need to be? As IP TV traffic will likely dominate other traffic, it will determine much of the answer. Analytical methods for engineering links often assume stationary (steady state) busy hour traffic. In the steady state, multicast reduces IP TV traffic volume: if two viewers watch the same broadcast program, the network needs to deliver only one video stream to the point (e.g., the OLT) where it must divide the stream in two. owever, steady state IP TV demand may not tell the whole story, for channel surfing disrupts the steady state at every commercial break. urfers start watching different programs. One way the network can make channel changes fast is to send surfers unicast (one per viewer) streams at higher than usual rates (see ec. IV). While surfing episodes may be short-lived (say, a minute), each episode superimposes a significant additional demand on top of the steady state demand. urfing s recurring nature means that capacity planning and engineering must include surfing s transient effects. This paper develops a model that quantifies the extra bandwidth that channel surfing consumes. It then combines this model with a model of the savings from multicast to analyze the net IP TV bandwidth demands due to multicast and channel surfing. The multicast model is the classical occupancy problem model [] (balls in cells) with the difference that cell probabilities are not uniform. The surfing model represents the PON Core Router Edge Router OLT ONT Figure. A portion of a fiber-to-the-premises network X/07/$ IEEE 2546

2 This full text paper was peer reviewed at the direction of IEEE Communications ociety subect matter experts for publication in the IEEE INFOCOM 2007 proceedings. surfing demand as a stochastic fluid flow, but the underlying modulating process is neither Markov nor stationary. Instead of using the eigenvalue methods of [2], we use a terminating renewal process [3]. When the renewal process is Poisson, we compute the renewal function explicitly. We illustrate our techniques with an example in which the channel surfing demand spikes at twice times the steady state demand (when all viewers have settled into channels and multicast gains are operative). II. DEMAND AUMPTION In both the multicast model and the channel surfing model, demand originates from a fixed population of users and from a single application, broadcast television over IP. The population consists of all video subscribers on an OLT or one OLT shelf. The entire OLT serves about subscribers, while one shelf serves roughly a third of that. Typically, only a subset of the subscribers on a shelf will subscribe to video. On the other hand, one subscriber may have several televisions or set top boxes in the home. We call each device capable of receiving an IPTV stream a viewer. We assume that each set top box always remains on and receives some video stream because there is as yet no reliable way to determine that no one is watching a given TV set. The link from an edge router to an OLT may carry other traffic types, including video on demand and data applications, such as web surfing, gaming, peer-to-peer file transfers, and so on. Engineering such a link requires a oint characterization of all applications; this paper attempts only to characterize broadcast IP TV s contribution. In the steady state, multicast requires the link to carry only one copy of each stream that viewers request. The steady state demand is therefore the total bandwidth of all broadcast streams in use. We characterize steady state demands in terms of channel popularity and the probability that a viewer will choose a given program definition (D or D). Zipf s law [4] asserts that if we rank programs in order of popularity, viewers are twice as likely to watch the most popular program than to watch the second most popular program, three times as likely to watch the most popular program than the third most popular program, and so on. The probability z i that a viewer will choose the ith most popular program is given by α z i = c / i, () where c is a constant that makes that the probabilities sum to and the exponent α is close to. In our description of Zipf s law above, α was exactly. This account of Zipf s law makes no reference to program definition. A channel may occur in D, D, or both. We will interpret Zipf s law to apply to channels, irrespective of definition. The only information about definition that we have is an estimate of the fractions p D and p D of broadcast streams that are D and D. To combine channel popularity and program definition, use the index i to label a channel. Index broadcast streams with a pair s = ( i,, where i is the channel number and d is the program definition. Denote by p ( s) = p( i, the steady state probability that a viewer will pick stream s = ( i,. This indexing allows for channels that are D, D, or both. For example, if channel i comes in both D and D, then p ( i, D) > 0 and p ( i, D) > 0. If channel i is available in only D, then p ( i, D) = 0. Our data about channel selection imposes two constraints on the marginal distributions of the probabilities p ( i. : p = ( i, D) + p( i, D) z i. and p i, = p d i (. (2) The easiest way to meet both constraints in (2) is to assume that p ( i, = z i p d, which we do when computing with our model. We do not use the implied independence of channel frequency and program definition in any essential way. In general, the bandwidth demand from multicast viewers is sensitive to those aspects of p ( i, that (2) does not constrain. For example, imagine that each channel were either D or D and the least popular channels were requested in D. Constraint (2) would imply that more D channels would be in use and the total multicast bandwidth would be higher than if the most popular channels were D. Note that we implicitly assume homogeneous viewers. That is, if 0% of stream requests are for D content, then each viewer requests D streams with probability 0%. In actuality, the 0% may come about because 20% of viewers subscribe to D and request D half the time. Although our homogeneity assumption makes the aggregate demand correct on average, since everyone can request D content, we may overestimate the tail of the aggregate demand. III. MULTICAT MODEL The multicast model predicts the steady state bandwidth demand from a population of m viewers watching broadcast streams over IPTV. The demand equals the sum of the streams in use times the bandwidth per stream. We model the viewers steady state choices of broadcast streams as m independent samplings from all streams according to the distribution p ( i,. A given channel is in use with the probability of least one success in m Bernoulli trials with success probability p ( i, [4], [6]. It turns out that 400 viewers, for example, will watch an average of only 54 different broadcast channels, which means that (momentarily ignoring which streams are D and which are D) multicast uses only 54/400 = 38% of the bandwidth that unicast would use. In other examples with fewer viewers or fewer channels (but still in the hundreds) channels in use divided by viewers is typically under 50%. 2547

3 This full text paper was peer reviewed at the direction of IEEE Communications ociety subect matter experts for publication in the IEEE INFOCOM 2007 proceedings. IV. CANNEL URFING MODEL. INGLE VIEWER Although multicast can cut the steady state bandwidth demand in half, commercial breaks disrupt the steady state. Viewers often surf through channels when commercials start. This section quantifies the bandwidth demand that would occur with one fast channel change mechanism [5]. Each viewer s set top box contains a playout buffer that receives bits from the network. The bit stream might not arrive to the playout buffer at a constant rate, as contention with other traffic in the network may create itter. As long as the itter is not too severe (greater than the buffer size in seconds), the buffer can play out the video stream at a constant rate and never empty out. The buffer initially has no bits belonging to the new stream when a viewer changes channels. One solution that allows both the buffer to fill and the viewer to begin viewing the new channel quickly involves what we will call a channel change server that transmits a new channel s content at a higher rate than usual. For example, a standard definition channel might be 3.75 Mbps; the channel change server might send a D channel at twice that rate or more (a guess on our part; [5] does not indicate rates). At the same time, the playout buffer will empty out the new channel s bits at the usual D rate of 3.75 Mbps. Once the buffer fills, the viewer can oin a multicast group running at the usual 3.75 Mbps. Channel surfing stresses the IPTV network in several ways. First, the network must temporarily carry any new channel at a higher than usual rate. econd, viewers typically surf through many channels. Third, many viewers are likely to surf simultaneously because commercial breaks are synchronized across channels. The remainder of this section quantifies the first two effects, while ec. V addresses the third. We expect channel surfing to last only a few minutes after a commercial break starts; therefore the scope of our model is only one commercial break. After the surfing associated with one break is over, the viewers enter a steady state until the next break, which, from the model s point of view, is far in the future. A. The Time to Fill the Playout Buffer We first model how long the channel change server must transmit at a higher than normal rate to fill the playout buffer. We will need the following notation (presented for D only; we have analogous definitions for D) r = rate at which D content plays out of buffer r C = rate at which channel change server delivers D content to the buffer for a channel change b = D buffer size in seconds. The product r is the D buffer size in megabits. b The bandwidth must stay at rate r C until the buffer fills after a channel change. Let t be the time it takes to fill the buffer at rate r C while simultaneously emptying it at rate r. Defining and so C f = rc r, t satisfies the relation f t = r b r t = b = b. (3) r r r / r C C Now make two simplifying assumptions. C b = b and r / r = r / r. From (3) and its analogue for D, it follows that t = t ; call the common value τ. It is the time the bandwidth must stay high after a single channel change. B. ingle Viewer Behavior Next, we model one viewer making multiple channel changes. Our goal is to compute the bandwidth the viewer demands at any given time. We call the demand (or rate) at time t R ( ); it is a random variable. t et time 0 to the time a commercial break begins. We represent a single viewer s channel changing behavior with a terminating renewal process [3]. The time between two renewal epochs represents the random amount of time the viewer stays on a given channel. Termination represents the viewer settling down to a steady state channel after some random number of renewals (channel changes). The renewal process evolves as follows. At time 0, the viewer is watching some steady state channel. e or she tosses a biased coin to decide whether to surf at all. If the coin comes up tails, the viewer does not surf. If the coin comes up heads, after some random amount of time, the viewer switches to another channel and repeats the coin toss, staying on that channel if the result is tails and otherwise changing channels after some random amount of time. This pattern continues until the coin comes up tails and the process terminates, with the viewer staying on the channel chosen last. Formally, denote by Y k, k = 0,, 2,, the times between renewals (channel changes). They are independent and have a common defective probability distribution. The word defective means that some Y k can be infinite, in which case the process terminates at the last finite renewal. Denote the renewal epochs by Tk = Y0 + + Yk, k =, 2, 3,. With this indexing, Y k is the time between renewals T k and T k +. Upon a channel change, the bandwidth umps to a high (relative to the steady state) rate r C or r C and stays there until either the playout buffer fills or the user changes channels again. Define = min(, τ ) for k. k Y k At renewal epoch T k, the rate becomes high until time T k + k, at which time it may become low or assume another high value if the viewer has again changed channels. To describe explicitly the bit rate the viewer demands, let D 0 be the definition (D or D) the viewer was watching at time 2548

4 This full text paper was peer reviewed at the direction of IEEE Communications ociety subect matter experts for publication in the IEEE INFOCOM 2007 proceedings. 0 and let D k, k =, 2, 3,, be the programming definition that the viewer switches to at time T k. ince we do not know how viewers will skip through channels, we track only the program definition in the surfing model. The rate the viewer demands at time t is then given by rd for t < T 0 R = rcd for Tk t < Tk + k, k (4) k rd for Tk + k t < Tk +, k k We put the subscript on R to indicate the first user. In ec. V we will consider multiple users. The rate function R ( ) can take only four possible values: r, r, r C, or r C t. Two things determine the value: the program definition at time t and whether the channel change server is still feeding the playout buffer at time t. If the channel change server is still working, we say the system is in a high state (t) ; in this case, the program definition determines whether the rate is r C or r C. If the channel change server is finished with this channel change, we say the system is in a low state L (t) ; again the program definition decides between r and r. We assume that the program definition is independent of the renewal process { ; k = 0,, 2, } ; this assumption is Y k possible because we assumed (right after (3)) that τ does not depend on the program definition. Were this not the case, the time structure of the renewal process would be linked to the program definition. As a result of the independence assumptions, the probability distribution of R ( ) is given by r L( D = D) r L( D = D) R( t) = (5) rc ( D = D) rc ( D = D) When the renewal process is a terminating Poisson process we can solve explicitly a renewal equation for P ( ( and get the distribution (5). t V. COMBINED MODEL. MULTIPLE VIEWER Combining the multicast and surfing models requires three steps. First we extend the surfing model to many active viewers. econd we extend the multicast demand to a timevarying number of viewers (those who are not surfing). Third we combine the two. Let a denote the number of active viewers. A viewer is active when someone is watching the associated device and idle if not. Only active viewers can surf. Although the number of active viewers may change during a commercial break, we ignore such changes and treat the number as constant. We also assume that commercial breaks on all channels begin at the same time and all active viewers begin surfing at the same time. tart at time 0 with a active viewers, indexed by a, each of whom behaves in a statistically identical fashion, but independently of the other viewers. Call viewer s demand (t). If we merely add up these (unicast) demands, the sum R R + + R ( ) would overstate the total demand because it a t neglects the fact the surfers eventually oin multicast groups. They may do so even while surfing if they remain on a channel long enough. In the interest of modeling simplicity we will ignore the latter possibility; we assume that a surfer receives a unicast stream until he or she stops surfing. urfing viewer changes channels for the last time at some time L (the termination epoch of the renewal process). If the active viewer surfs at all, then the viewer leaves the high state (t) for the last time (until the next commercial break, which is beyond our model s view) at time L + τ and oins a multicast group. Thus, viewer is a unicast viewer at time t if t L +τ and a multicast viewer if t L + τ. The exception < to this rule is the active viewer who does not surf at all. This viewer s L = 0 and the viewer never leaves a multicast group. ince (4) sets R (t) > 0 for all time, we use L to make viewer s demand zero when the viewer oins the multicast group. The total (unicast) demand from surfers is a BU = R L + τ > t) L > 0) ; = here, I denotes an indicator function. The first indicator takes care of surfers who oin a multicast group after time zero, while the second indicator zeroes out viewers who chose not to surf. The multicast demand B M (t) includes both idle viewers and active viewers who have stopped surfing or never started. The number N s (t) of viewers watching multicast stream s umps by whenever a surfer stops surfing and oins multicast group s. The total number of multicast viewers at time t is M = N s ; their total bandwidth demand is s BM rd N s > 0). d { D, D} s = The inner sums are the numbers of D or D streams in use; we multiply them by r = or r = 5 and add. Both M (t) and B M (t) are monotonically increasing step functions; the latter umps at epoch L d + τ if viewer chooses a stream not yet occupied, but otherwise does not ump. The total bandwidth demand, consisting of unicast streams to surfers and multicast streams, is given by 2549

5 This full text paper was peer reviewed at the direction of IEEE Communications ociety subect matter experts for publication in the IEEE INFOCOM 2007 proceedings. B = B B. U + VI. REULT We now illustrate the model and the simulation on an example with the following parameter values: m = 400 total viewers, a = 200 active viewers, 500 channels offered (all in D and D in accordance with (9)), r = 3. 75, r = 5, rc = 2. 5r, rc = 2. 5r, and b = second. Note that since a / m = ½, we are assuming that half the viewers are active. The playout buffer fill time when the channel change server is running is τ = seconds. The probability that a stream is D is p = 90% and a stream is D with p = 0%. D In the terminating Poisson process, the times between renewals (channel changes) follow an exponential distribution; the mean time between renewals is 4 seconds. At each renewal and at time 0, the viewer tosses a coin to decide whether to change the channel. We choose the mean number of channel changes to be 0, which makes the probability of heads in the coin toss 0.9. Note that r = 2. 5r implies r = Mbps, which is C high by today s broadband standards. If use instead r =. 67, we obtain a more tractable r = 25 Mbps. C r owever, the results described below change hardly at all. Fig. 2 shows the mean surfing demand E ( B U ( urfing ), the mean multicast demand E ( B M ( Mcast ), and and the mean total demand E ( B( Total ) over 00 seconds. The multicast demand increases as time progresses and surfers quit surfing and settle down into multicast groups. The urfing curve decreases as viewers stop surfing. The mean total bandwidth decays asymptotically to about 000 Mbps as a result of multicast savings. Fig. 2 makes clear the implications of surfing and multicast. As a reference point, if 400 viewers were watching unicast streams with average bandwidth per stream p r + p r C M D C D = Mbps, the mean total demand would be 950 Mbps. The asymptotic demand of about 000 Mbps in Fig. 2 shows that multicast cuts the demand in half. On the other hand, the maximum in Fig. 2 reaches almost to 700 Mbps. Channel surfing gives back nearly all multicast s gains. D Broadcast Demand (Mbps) urfing Total Time (seconds) VII. UMMARY AND CONCLUION We have developed a model of the extra demands IP TV viewers impose when they surf at commercial breaks. We then superimposed it on top of a multicast model to quantify bandwidth demand during the transition from surfing to steady state viewing. Our example with 400 viewers shows mean demand during surfing peaking at almost two times the steady state level if the service provider offers fast IP TV channel changes. REFERENCE Multicast Figure 2. urfing, multicast, and total mean demands [] W. Feller, An Introduction to Probability Theory and Its Applications 3rd ed., vol.. New York, Wiley, 968, pp [2] D. Anick, D. Mitra, and M. M. ondhi, tochastic theory of a datahandling system with multiple sources, Bell yst. Tech. J., vol. 6, no. 8, pp , October, 982. [3] W. Feller, An Introduction to Probability Theory and Its Applications 2 nd ed., vol. 2. New York, Wiley, 97, pp [4] D. T. vanveen, M. K. Weldon, C. C. Bahr, and E. E. arstead, An analysis of the technical and economic essentials for providing video over fiber-to-the-premises networks, Bell Labs Tech J., vol. 0, no., pp , [5] Delivering IPTV with the Windows Media Platform, Microsoft Corporation, Available from: 9aed-f25c73d6ac/Delivering_IPTV.doc [6] J. Weber and J. Gong, Modeling switched video broadcast services, Cable Labs,

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