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1 Threshold-Based Multicast for Continuous Media Delivery y Lixin Gao? Department of Electrical and Computer Engineering University of Massachusetts Amherst, Mass , USA lgao@ecs.umass.edu Don Towsley Department of Computer Science University of Massachusetts Amherst, Mass , USA towsley@cs.umass.edu Abstract In this paper, we propose and evaluate the performance of a continuous media delivery technique, called threshold-based multicast. Similar to patching, threshold-based multicast allows two clients that request the same video to share a channel without having to delay the earlier request. It ensures sharing by permitting the client with the later arrival time to join an ongoing multicast session initiated for the earlier request. However, threshold-based multicast does not allow a later arriving client to always join an ongoing multicast session. If it has been some time since the ongoing multicast session was started, a new multicast session is initiated. That is, a threshold is used to control the frequency at which new multicast sessions are started. We derive the optimal threshold that minimizes the server bandwidth required. Our analytical result shows that threshold-based multicast significantly reduces the server bandwidth requirement. Furthermore, we perform a simulation study demonstrating the performance gain of continuous media delivery by threshold-based multicast. Keywords Multicast, Video-On-Demand, Multimedia. EDICS: 2-ALAR - y A shorter version of this paper was presented at the IEEE Multimedia Computing and Systems, June Lixin Gao was supported in part by the National Science Foundation under Grant No. ANI and NSF CAREER Grant ANI Don Towsley was supported in part by the National Science Foundation under Grant No. ANI Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.? Corresponding author 1

2 1 Introduction Streaming continuous media is one of the most promising services in emerging broadband integrated service digital networks. New technologies such as ADSL and cable modems have increased the interest in developing high-quality video streaming services. In order to guarantee continuous playback at a client, a video server has to reserve a sufficient amount of network-i/o bandwidth for the video stream before serving the client s request. Due to the high bandwidth requirement of video stream, the most expensive resource in the delivery of continuous media streams is the server network-i/o bandwidth [7]. Therefore, efficient utilization of the server network-i/o bandwidth plays a crucial role in the delivery of continuous media streams. Existing schemes for allocating server network-i/o resources can be broadly classified into user-centered and data-centered approaches [5, 3, 6]. In a user-centered approach, for each client request, server eventually dedicates network-i/o resources to solely use for the delivery of requested video stream. Efficient usercentered scheduling algorithms have been studied extensively (see [16] and references therein). In the data-centered approach, the server network-i/o resources are dedicated to video objects rather than to users. This approach allows users to share a video stream through the multicast facility of modern communication networks [14, 15, 17]. The server accommodates numerous concurrent user requests with one video stream. For example, if two clients request the same video at about the same time, both requests can be satisfied by one video stream, thereby reducing the demand for both network and server I/O bandwidth. The key advantage of the data-centered approach is its scalability. Four types of data-centered approaches have been proposed in the literature [13]. Server-initiated. Here, the server multicasts video objects periodically via dedicated server network- I/O resources. Clients join an appropriate multicast group to receive desired video data. The serverinitiated scheme can guarantee a maximum service latency independent of the arrival time of the request. For example, the simplest server-initiated scheme is to start a multicast of an object at a fixed time interval (say t minutes) [9]. This scheme guarantees a maximum service latency of t minutes independent of the arrival time of the request. Therefore, it is more efficient for hot videos than for cold videos. Server-initiated-with-prefetching. Here, a video object is divided into segments, each of which is multicast periodically via a dedicated multicast group. The client prefetches data from one or several multicast groups for later playback. Prefetching is done in such a way as to ensure the continuous playback of the video. We refer to these broadcast schemes as Server-Initiated-With-Prefetching (SIWP) schemes. Recently, a number of innovative server-initiated schemes [3, 5, 6, 11] have been proposed. 2

3 A SIWP scheme takes advantage of resources (e.g., disk storage space and network bandwidth) at the client end, and therefore significantly reduces the server network-i/o resources required. Like serverinitiated schemes, such a scheme guarantees a maximum service latency independent of the arrival time of the request and performs the better for hot videos than for cold videos. Client-initiated. Here, a client makes a request for a video and waits until that video is eventually multicast. When a channel becomes available, the server selects a batch of pending requests for a video according to some scheduling policy. Efficient batching policies are studied in [9, 10, 4]. While batching reduces demand for server network-i/o bandwidth, it does so at the cost of introducing service latency and there is no maximum service latency guarantee. Client-initiated-with-prefetching. Here, two clients that request the same video can share a multicast stream without delaying the earlier arrival client. For example, consider two requests spaced 5 minutes apart for a 90 minutes long video. The server multicasts the entire video in order to satisfy the first request. The second request is satisfied by transmiting the first five minutes of the video while requiring the client to prefetch the remaining 85 minutes of the video from the first multicast group. Because the second client is five minutes behind, it continually buffers five minutes of the video for much of the time. Like SIWP, CIWP takes advantage of the resources (such as disk storage space and network bandwidth) at the client side to save server network-i/o bandwidth by multicasting segments of video data. Note that with the low cost of disks and the advent of access technologies such as cable modems (with up to 27Mbps downstream [2]), it is reasonable to assume that clients have sufficient disk space and can receive two MPEG-2 streams at the same time. Serveral CIWP schemes have been proposed in [7, 19]. In this paper, we present a CIWP scheme called threshold-based multicast which improves on the basic CIWP algorithm in [7, 19] by introducing a threshold to control the frequency that a complete video stream is delivered. In other words, threshold-based multicast does not always allow a client to share a segment of a complete video stream. Instead, if it has been some time since the most recent complete transmission of the video, the server will initiate a new complete video transmission. We analyze the threshold-based multicast and derive the optimal threshold that minimizes the server network-i/o bandwidth requirement. Our analytical results show that the server network-i/o bandwidth requirement is reduced significantly by using the optimal threshold. Specifically, in the basic CIWP, the server network-i/o bandwidth requirement for a video is a linear function of the request rate times the video length, whereas, in the threshold-based multicast, the server network-i/o bandwidth requirement for a video is a linear function of the square root of the request rate times the video length. Furthermore, we perform simulation studies on a set of videos and show convincingly that even if the client disk storage is as small as 150 Mbytes, threshold-based multicast 3

4 outperforms the basic CIWP significantly. In addition, we explore a hybrid of CIWP and SIWP scheme. We use threshold-based multicast for lukewarm or cold objects and a SIWP scheme for hot objects. Since SIWP performs best for hot objects, by systematically combining the two schemes, we show by simulation that the hybrid scheme can further improve the overall performance of the video delivery system. The rest of this paper is organized as follows. In Section 2, we overview the problem. Section 3 describes the server and client algorithms in the threshold-based multicast scheme. In Section 4, we analyze thresholdbased multicast and derive the optimal threshold. Section 5 describes the results of our evaluation study of threshold-based multicast using simulation. In Section 6, we propose a hybrid of CIWP and SIWP and present performance results for it. Finally, Section 7 summarizes the paper. 2 Overview of the Problem Client SCHEDULER CONTROL CHANNEL Client Client DATA SERVER VIDEO STORAGE CHANNEL1 CHANNEL2 CHANNEL3 Network Client DISK Video Server DISPLAY Figure 1: An overview of video delivery system architecture. A video delivery system consists of a video server, a high-speed network, and clients (Figure 1). A client requests a video of his/her choice from the video server and the server delivers the video stream via the highspeed network. The client request is transmitted via a low bandwidth control channel to the server scheduler, which determines when and on which channel it will deliver the requested video stream to the client. This information is sent to the client via the control channel. We refer to the server and network resources required ffor delivering one video stream as a logical channel. The data server retrieves data from the video storage and transfer it to each logical channel in an order determined by the scheduler. The video storage contains N videos. The ith video is L i minutes long. 4

5 Each client contains a set-top box, a disk, and a display monitor. A client is connected to the network via a set-top box, which selects one or more network channels to receive video data according to instructions from the server. The received video data are either stored on the disk or sent to the display monitor for immediate playback. The display monitor can either retrieve stored data from the disk or receive data directly from a channel. We assume that the client can store B minutes of video data. The service latency or waiting time experienced by a client is the amount of time that the client has to wait to start the playback once he/she requests a video. The server network bandwidth is divided into control channels and data delivery channels. Each data delivery channel is capable of delivering a video stream at its playback rate b. We assume that there are C data delivery channels in the server. The server delivers the video data to clients through either a unicast or a multicast connection. With a unicast connection, the server and network dedicates a single video stream to each client. A multicast connection permits the server to deliver one video stream to a group of clients in the network using a single data delivery channel. For example, in IP multicast, each data delivery channel can be implemented using a multicast group. A client that needs to retrieve data from a logical channel can join the corresponding multicast group. We use the term multicast group and channel interchangably in this paper. Since data delivery requires the most network and server resources, we focus on minimizing the network and server resource required by data delivery throughout this paper. Table 1 summarizes the notation introduced in this section. N: number of videos L i : length of video i B: client disk size (in minutes of video data) b: video playback rate C: number of logical channels in the server Table 1: Notation. 3 Threshold-Based Multicast As described in Section 1, threshold-based multicast is a CIWP scheme that employs a threshold to control the frequency at which a complete video stream is multicast. Figure 2 shows the benefit of having a threshold to control the initiation of a complete stream. For ease of the explaination, we assume that there are an infinite number of data delivery channels. Client 1 requests video i at time 0 and is the first client requesting the video. A complete video stream is multicast at time 0. A request from Client 2 for the the video arrives at time t 1. Now the server transmits the first t 1 minutes of the video for Client 2 to catch up with the complete 5

6 Client 1 arrives Complete Stream Li Client 2 arrives Partial Stream t1 Client 3 arrives Partial Stream Complete Stream Li/2+t2 Li Client 4 arrives Partial Stream t3-t2 Partial Stream Li/2+t3 0 t1 Li/2+t2 Li/2+t3 Threshold-based Multicast basic CIWP time Figure 2: An overview of threshold-based multicast. video stream. However, after some time, the benefit of piggybacking the complete stream started at time 0 diminishes. For example, suppose that Client 3 arrives at time L i =2+t 2 and Client 4 arrives at time L i =2+t 3. If the server transmits the partial streams for Client 3 and 4, the total length of the two partial streams is L i + t 2 + t 3. Instead, if the server transimts a complete stream for Client 3 and a partial stream of length t 3? t 2 for Client 4, the total length of the two streams is L i + t 3? t 2. Therefore, the network bandwidth requirement is reduced if a new complete stream is initiated for Client 3. Let T i denote the threshold that controls the frequency at which a complete stream of video i is delivered. The key idea of the thresholdbased multicast is as follows. When the first request for video i arrives at time t, the scheduler immediately schedules a complete video stream of video i on a channel, say MG. Any subsequent request for video i prefetches data from channel MG so long as the request arrives within T i minutes from the starting time of the previous complete transmission of video i (which is time t in this case). Otherwise, the request is served by initiating a new complete transmission of video i. This process repeats forever. We derive an optimal value for T i in Section 4. In the rest of this section, we describe the algorithm for the scheduler to implement threshold-based multicast given a fixed number of server channels. For the sake of completeness, we describe the algorithms for the client, the data server, and the scheduler and the interaction among them. Since the server has a fixed number of channels, a client s request might not be satisfied as soon as the client arrives. The server scheduler has to keep track of channel usage and inform clients which channels to retrieve data and inform data server 6

7 Scheduler (MG c,mg p, VLength) VId Video Lists Client MG p Data Server MGc data packets of video VId Figure 3: Interaction among client, data server, and scheduler. the data to be delivered on each channel. Figure 3 shows the interaction between the client and the server. When a client arrives, it sends a message to the scheduler indicating its desired video, V Id. The scheduler determines the channels that the client should join to receive the video data. This information is embedded in a triple (MG c ; MG p ; V Length) sent from the scheduler to the client, where MG c and MG p are the channels that deliver the complete and partial stream respectively, and V Length is the number of packets that the client will receive from MG p. The scheduler maintains a schedule in an array of video lists. The m-th video list represents the video data to be delivered to multicast group m. Each entry in the list consists of a pair (V Id; V Length) which indicates the first V Length packets of video V Id. Finally, the data server delivers video data indicated by the video list for each channel. 3.1 Client Algorithm The client s set-top box contains a main control thread, a complete video stream receiver thread, and a partial video stream receiver thread. The main control thread requests a video by sending V Id indicating its desired video to the server. It then waits to receive a message (MG c ; MG p ; V Length) from the server. Once it has recorded the information in this message, the client starts the complete and partial video stream receiver threads. The complete stream receiver thread retrieves video V Id data from multicast group MG c and starts to save the data to the disk after receiving a packet with sequence number V Length. The partial stream receiver thread is responsible for both receiving data and rendering data to the monitor. If MG p is not null, it receives the video data from multicast group MG p and immediately starts the playback of the video. After receiving V Length packets, it leaves multicast group MG p. Finally, it starts to playback the video data from the disk. Figure 4 shows the client algorithm. Note that we assume loss-free and ordered delivery of packets from the network. We further assume that each packet includes a sequence number and video ID so that the client can identify its desired data. This can be accomplished if a transport protocol such as the Real Time Transport Protocol (RTP) is used as it includes 7

8 Client Main Control Thread: 1. Send a message V Id to the server. 2. Wait for the message (MG c, MG p ; V Length) from the server. 3. Start both the complete and partial stream receiver threads. Complete Stream Receiver Thread: 1. Join channel MG c. 2. Start to receive data from MG c 3. Start to save the received data to buffer after receiving a packet with a sequence number > V Length. 4. Leave multicast group MG c when receiving a packet with sequence number 0, i.e., the complete stream ends. Partial Stream Receiver Thread: 1. If MG p is not null, 2. Join channel MG p. 3. Process received packets until a video V Id packet with sequence number 0 is received. 4. Playback received data until a packet with sequence number V Length is received. 5. Leave multicast group MG p. 6. Playback the saved data until no more data in the disk. Figure 4: Client algorithm. a sequence number of the video in each packet. 3.2 Server Scheduler Algorithm The key function of the scheduler is to determine the channels that a client has to join on order to receive the video data and video data delivery schedule for each channel in the form of video lists. The main idea of the scheduler algorithm is given in Figure 2 assuming that there are an infinite number of server channels. However, the server has a fixed number of channels. Therefore, a client s request might not be satisfied immediately after its arrival. The simplest scheduler can satisfy a client s request by scheduling a partial or complete stream (according to threshold T i ) at the earliest time that a channel is available. However, we can reduce the client startup latency by greedily piggbacking scheduled streams. In other words, the scheduler can let a client piggyback a complete or partial stream for the same video if there is a stream scheduled to start after the client s arrival. Therefore, when a client request for video i arrives, there are four potential avenues to satisfy the client; 1. batch the request with a complete stream of video i that is scheduled to start later. 8

9 2. prefetch from an on-going complete stream of video i and batch a partial stream of video i scheduled to start later by expanding the partial stream. 3. prefetch from an on-going complete stream of video i and schedule a partial stream of video i at the earliest possible time. 4. schedule a complete stream of video i at the earliest time possible. The scheduler tries each avenue in order so that it conserves the network bandwidth. Furthermore, it schedules (partial or complete) streams in a First-Come-First-Serve order. Specifically, it uses the first avenue if a complete stream of video i is scheduled to start later, i.e., the latest starting time of the complete stream of video i is after the current time. Otherwise, it uses the second avenue if the threshold constraint is satisfied and there is a partial stream of video i that is scheduled to start after the current time and that can be expanded without delaying any client s playback. Otherwise, the scheduler uses the third avenue provided that the most recent on-going stream started within T i minutes from the arrival of the request. For both the second and the third avenues, the client greedily shares the complete stream. In other words, if prefetching data from the complete stream overflows the disk, we let the client receive the last B minutes of the video data from the complete stream to maximize sharing. Finally, the fourth avenue is used if all of the above avenues fail. Figure 5 gives detailed descriptions of the scheduler algorithm. To simplify the description of the scheduler algorithm, we assume that the network delay and join latency are negligible. We can easily add a conservative estimate of the delay and latency to the algorithm if the network delay or join latency is substantial. 3.3 Data Server Algorithm The data server multicasts the video data to each channel according to the schedule determined by the server scheduler. The schedule for each channel is given by the scheduler as a video list. The data server has one data delivery thread for each multicast group. Each data delivery thread multicasts the video data according to the video list for the multicast group, i.e., the video data represented by the (V Id; V Length) in order. Figure 6 shows a formal description of the data server delivery thread for a multicast group. 4 Optimal Threshold As discussed in Section 3, the selection of the threshold is the key in determining the performance of thresholdbased multicast. In this section, we derive the optimal threshold that minimizes the server network-i/o bandwidth requirement. We focus on video i and assume that requests for video i are generated by a Poisson process with mean interarrival time 1= i. For simplicity of exposition, our analysis assumes that there are 9

10 Notations: t curr : current time. T i : threshold for video i. t i : latest starting time of the complete stream of video i in the schedule MG i : multicast group that starts to deliver the complete stream of video i at t i. MG e : multicast group that is available the earliest time. t e : the earliest time that channel MG e becomes available after current time. MG p : channel that starts to deliver a partial stream of video i the latest time and whose video list ends with the partial stream of video i. t p : starting time that channel MG p delivers the partial stream of video i. Scheduler Algorithm: 1. When a client requesting video i arrives, 2. if t curr t i, i.e., it is possible to piggyback the complete stream, 3. Send the client message (MG i, null; 0). 4. else if t p? t i < T i and t p t curr, i.e., threshold constraint is satisfied and it is possible to piggback a partial stream, 5. if minft p? t i ; L i? (t curr? t i )g B, i.e., there is sufficient disk space to piggyback the complete stream, 6. Expand this partial stream to satisfy the client by modifying the entry for this partial stream in the video list to (i; t curr? t i ). 7. Send the client message (MG i, MG p, t curr? t i ). 8. else 9. Expand this partial stream to satisfy the client by modifying the entry for this partial stream in the video list to (i; L i? B), i.e., piggyback only the last B minutes of the complete video stream. 10. Send the client message (MG i, MG p, L i? B). 11. else if t e? t i < T i, i.e., threshold constraint is satisfied, 12. if minft e? t i ; L i? (t curr? t i )g B, i.e., there is sufficient disk space to piggyback the complete stream, 13. Schedule a partial stream for video i at the earliest time that a channel becomes available by appending (i, t curr? t i ) to MG e s video list. 14. Send the client message (MG i, MG e, t curr? t i ). 15. else 16. Schedule a partial stream for video i at the earliest time that a channel becomes available by appending (i, L i? B) to MG e s video list, i.e., piggyback only the last B minutes of the complete video stream. 17. Send the client message (MG i, MG e, L i? B). 18. else 19. Schedule a complete stream for video i at the earliest time that a channel becomes available by appending (i, L i ) to MG e s video list. 20. Send the client message (MG e ; null; 0). Figure 5: Server scheduler algorithm 10

11 Data Delivery Thread for Multicast Group MG: 1. Repeat forever, 2. While MG s video list is not empty, 3. Remove the first pair (V Id; V Length) from MG s video list. 4. Multicast the first V Length packets of video V Id to multicast group M G. Figure 6: Data delivery thread. infinite number of server channels, i.e., each request is immediately satisfied and no request is batched with previous requests. Note that a video server typically stores many videos and all videos share the server channels. Effectively, a video can use more server bandwidth than its average share at a particular time. Over the long run, a video uses only its average share of the server bandwidth. Therefore, for one video, it is reasonable to assume that there is an infinite number of server channels for one video and use the average server bandwidth requirement as the performance parameter. We will show by simulation in Section 5 that videos of various popularity can achieve good multiplexing effect on the server channel usage. We derive the optimal threshold by modeling the system as a renewal process. We are interested in the process fs(t) : t > 0g where S(t) is the total server bandwidth used from time 0 to t. In particular, we are interested in the average server bandwidth C = lim t!1 S(t)=t. Let ft j g 1 j=0 (t 0 = 0) denote the times at which the system schedules a complete stream for video i. These are renewal points in the sense that the behavior of the system for t t j does not depend on past behavior. We consider the process fs j ; N j g where S j denotes the total server bandwidth used and N j the total number of clients served during the j-th renewal epoch, [t j?1; t j ). Because this is a renewal process, we will drop the subscript j. We have the following result. C = i E[S]=E[N ] Hence, it remains to determine E[S] and E[N ]. E[N ] is given by E[N ] = 1 + i T i : First, we assume that the client disk is sufficiently large. Note that when a client requesting video i arrives t minutes after a complete stream of video i starts, the client retrieves t minutes of the video data from the complete stream and L i? t minutes of the video data from a partial stream. Therefore, the client needs a buffer to store at least minft; L i? tg minutes of the video data. Therefore, if B L i =2, the buffer size is not a constraint. We first assume that B L i =2. Consider E[S]. Let K denote the number of arrivals in an interval of length T i. It has the distribution P [K = k] = ( i T i ) k e? it i =k!. Focus on E[SjK = k]. We have 11

12 E[SjK = k] = (L i + kt i =2)b: This comes as a consequence of the fact that k Poisson arrivals in an interval of length T i are equally likely to occur anywhere within the interval. Removal of the conditioning yields E[S] = 1X k=1 = bl i + b 2 ( i T i ) k e? it i E[SjK = k] k! 1X k=1 = bl i + i bt 2 i =2: ( i T i ) k e? it i kt i k! Therefore, C = C 1 (T i ) def = i b 2L i + i Ti 2 2( i T i + 1) The value of T i that minimizes this expression is T i = p 2Li i + 1? 1 i (1) The corresponding value of the average number of busy channels C is p C = ( 2L i i + 1? 1)b: (2) Now, suppose that the client can store at most B < L i =2 minutes of the video data. Then the above analysis is modified as follows. Case A. B T i, Using the same analysis as above, we have C = C 1 (T i ). Case B. B < T i L i? B, E[S] = (L i + i B 2 =2 + i (T i? B)(L i? B))b: The first two terms represent the total channel busy time from serving clients that arrive between time 0 and B, and their derivation is identical to that of E[S] for B L i =2. The last term is the total channel busy time for those requests that arrive between time B and T i and only piggyback the last B minutes 12

13 of data, since i (T i? B) is the expected number of arrival during time interval of length (T i? B) and L i? B is the length of the partial stream scheduled for each request. Therefore, C = C 2 (T i ) def = i b L i + i B 2 =2 + i (T i? B)(L i? B) i T i + 1 Case C. T i > L i? B, E[S] = (L i + i B 2 =2 + i (L i? 2B)(L i? B))b + 1X k=1 ( i (T i? L i + B)) k e? i(t i?(l i?b)) k(l i? B + T i )b=2 k! = (L i + i B 2 =2 + i (L i? 2B)(L i? B) + i (T i? L i + B)(L i? B + T i )=2)b = (L i + i ((L i? 2B) 2 + T 2 i )=2)b The first three terms represent the total channel busy time from serving clients that arrive between time 0 and L i?b, and their derivation follows from Case B. The last term is the total channel busy time for those requests that arrive between time L i? B and T i. Its derivation is similar to Case A. Therefore, C = C 3 (T i ) def = i b L i + i ((L i? 2B) 2 + Ti 2 )=2 i T i + 1 Now, we derive T i that minimizes C. By minimizing C 1 (T i ), C 2 (T i ), and C 3 (T i ) respectively, we have the optimal threshold T i. T i = 8 >< >: ( p 2L i i + 1? 1)= i if i 1 or B L i =2 B if 0 < i < 1 and B < L i =2 ( q 2 i L i + 2 i (L i? 2B) 2 + 1? 1)= i if i 0 and B < L i =2 (3) where 1 def = 2(L i? B)=B 2 and 0 def = 1=(L i? 3B=2). Note that the optimal threshold increases as the popularity of the video decreases. For popular videos (or when i is big), the optimal threshold is smaller than the buffer size. For cold videos (or when i is small), the optimal threshold is between L i? B and L i. For lukewarm videos (or when i is in between), the optimal threshold is B. 4.1 Effect of the Optimal Threshold To demonstrate the effect of the optimal threshold, we show that threshold-based multicast reduces the expected server bandwidth required for each video significantly. We compare threshold-based multicast with 13

14 FCFS batching and the basic CIWP scheme. FCFS batching is a batching scheme that schedules client requests in a First-Come-First-Serve (FCFS) order. See [10] for a detailed description of FCFS batching. It is easy to see that FCFS batching is a special case of threshold-based multicast obtained by setting the threshold to be 0. The basic CIWP uses the First-Come-First-Serve policy for scheduling the server channels and corresponds to threshold-based multicast with the threshold set to the length of the video. Now, we derive the average server bandwidth required for each of the three schemes. For ease of the exposition, we consider only popular videos in which the optimal threshold is less than buffer size. Threshold-based multicast: the average server bandwidth required for video i is given by (2). That is, p ( 2L i i + 1? 1)b: FCFS batching: the average server bandwidth required for video i is since every request requires a complete stream. L i i b Basic CIWP: the average server bandwidth required for video i (Case C from above) is i b L i + i ((L i? 2B) 2 + L 2 i )=2 i L i + 1 In Figure 7, we plot the average server bandwidth required for those three schemes when the video length is 90 minutes and the client buffer can hold 15 minutes of the video. We observe that the server bandwidth required by both FCFS batching and basic CIWP grows linearly as a function of the request rate. In contrast, the average server bandwidth required by threshold-based multicast grows linearly as a function of the square root of the request rate. Furthermore, there is a significant gap between threshold-based multicast and the basic CIWP even when the request rate is small. 5 Simulation Study So far, we have focused on one video. Typically, multiple videos of varying popularity are stored in a video server. In this section, we demonstrate the performance of threshold-based multicast via simulation. We simulate threshold-based multicast, FCFS batching, and the basic CIWP. We assume that there is a fixed 14

15 expected server bandwidth (in unit of b) sever bandwidth vs. request rate FCFS Batching basic CIWP threshold-based multicast request rate (per minutes) Figure 7: Server bandwidth vs. request rate. number of server channels and present the effect that multiplexing the channels among all videos has on the waiting time of requests. In our simulation, requests arrive according to a Poisson process with an expected interarrival time of 1=, where is the request rate. Video selection follows a Zipf-like distribution [18]. In other words, the probability of choosing the ith video is p i = f i PNj=1 f j : where f i = 1=i 1?, i = 1; : : : ; N and N is the number of videos in the system. Here is a parameter used added to specify the skew factor. A value of = 0:271 is known to closely match the popularities generally observed by video store rentals [4]. The request rate for video i is i = p i : Unless noted otherwise, the workload and system parameters chosen for the simulation are listed in Table 2. Each simulation run simulates 150 hours of client requests. 5.1 Effect of Number of Server Channels Figure 8 shows the effect of the number of server channels on the expected waiting time under the three schemes. In this simulation, the request arrival rate is 50 requests per minute, all videos are 90 minutes long, 15

16 Default Range Number of Videos 100 N/A Request Rate (requests/min) Video Length (minutes) Number of Channels Disk Size (minutes of data) Skew Factor N/A Table 2: Parameters chosen for the simulation. expected waiting time (Minutes) waiting time vs. server channels FCFS Batching basic CIWP Threshold-based Multicast number of server channels Figure 8: Expected waiting time vs. number of server channels. 16

17 prob. of waiting vs. server channels FCFS Batching basic CIWP Threshold-based Multicast prob. of waiting number of server channels Figure 9: Probability that a client has to wait. and the client buffer can store 15 minutes of video data. Note that 15 minutes of MPEG-1 video data is about 150 Mbytes. Such disk space costs less than $15 today. In the next section, we will see how the buffer size affects the expected waiting time. Our simulation results show that threshold-based multicast achieves an expected waiting time close to 0 with only 800 channels, while FCFS batching results in an expected waiting time of greater than one minute with 2000 channels! Threshold-based multicast reduces the expected waiting time under any number of server channels significantly. In fact, the performance of the basic CIWP is closer to FCFS batching than it is to threshold-based multicast. In Figure 9, we plot the probability that a client has to wait for service. We observe that, when there are 800 channels, only 7% of the clients have to wait for service under threshold-based multicast while almost all clients have to wait for service under the basic CIWP and FCFS batching! 5.2 Expected Waiting Time vs. Client Buffer Size Figure 10 shows the effect that the buffer size has on the expected waiting time. In this simulation, the request arrival rate is 50 requests per minute and there are 800 server channels available. Since FCFS batching does not take advantage of the client buffer, its performance does not improve when the client buffer size increases. On the other hand, both threshold-based multicast and basic CIWP dramatically decrease the expected waiting time as the buffer size increases. Furthermore, threshold-based multicast significantly reduces 17

18 expected waiting time expected waiting time vs. buffer size FCFS Batching basic CIWP Threshold-based Multicast buffer size (minutes of video data) Figure 10: Expected waiting time vs. buffer size. the expected waiting time as the buffer size increases. 5.3 Expected Waiting Time vs. Request Arrival Rate Figure 11 shows the effect of the request arrival rate on the performance of threshold-based multicast. We assume that the buffer can hold 15 minutes of video data and that there are 800 server channels. We plot the expected waiting time for the request arrival rate in the range of 40 and 100 requests per minute. We see that threshold-based multicast consistently reduces the expected waiting time by over 4.5 minutes compared to FCFS batching and over 3.3 minutes compared to the basic CIWP. Even when the request rate increases to 100 requests per minute, the expected waiting time is still less than 1 minute in threshold-based multicast. 6 A Hybrid of CIWP and SIWP Scheme It has been suggested in [8, 9, 10, 12] that videos should be divided into hot and cold sets, and that the hot set should be scheduled using a server-initiated scheme and the cold set should be scheduled using a clientinitiated scheme. In this section, we introduce a hybrid of a CIWP and SIWP scheme. We use the SIWP scheme, Greedy Disk-conserving Broadcast (GDB), studied in [11] for hot objects and threshold-based multicast for cold objects. Under this scheme, a video object is partitioned into segments and each segment is 18

19 expected waiting time (Minutes) expected waiting time vs. request arrival rate FCFS Batching basic CIWP Threshold-based Multicast request arrival rate Figure 11: Expected waiting time vs. request arrival rate. periodically broadcast via a dedicated channel. The sizes of these segments are carefully designed in such a manner that clients who wish to receive the video object can join the appropriate channels to receive various segments at scheduled times to ensure continuous playback of the video object. Figure 12 illustrates how the schemes work through a simple example. A video is partitioned into four segments: A, B, C, D of length d, 2d, 2d, and 5d respectively. Each segment is broadcast periodically via a dedicated channel. Clients prefetch video data according to a schedule that ensures continuous playback. Furthermore, clients are guaranteed a maximum service latency of d minutes with only 4 dedicated channels. The key issue in periodic broadcast schemes is to determine how to partition video objects into segments so as to enable continuous playback at clients. A method for partitioning video objects is referred to as a partition function, which determines the performance of a periodic broadcast scheme. Given K i dedicated multicast channels, a partition function f (n) divides a video object into K i segments, T 1 ; T 2 ; : : : ; T Ki, as follows. P K For n = 1; 2; : : : ; K i, segment T n contains f (n)l i = i m=1 f (m) minutes of video data, and its data starts P P P P n?1 at the f (m)l K m=1 i= i f m=1 (m) th minute of the video and ends at the n K m=1 f (m)l i = i m=1 f (m) th minute of the video. In [11], a set of constraints on partition functions are derived based on resource availability at the client side. For example, if the network bandwidth at the client side is only sufficient to support two channels (i.e., receiving from two channels simultaneously), the optimal partition function f (n) used in 19

20 Video: Channel 1: Channel 2: Channel 3: Channel 4: A B C D d 2d 2d 5d AAAAA AAAAAAAAAAAAAAA B B B B B B B B B B C C C C C C C C C C D D D D Client 1: arrive display A B C save D D Client 2: disk data d arrive display A save B save B C D C D disk data 4 d time Figure 12: An example of GDB scheme. GDB has the following form: f GDB (n) = 8 >< >: 1; if n = 1 2; if n = 2; 3 5; if n = 4; 5 12; if n = 6; 7 5f (n? 4); if n > 7 (4) P K The average service latency experienced by a client is L i =2 i m=1 f (m) minutes. We begin by proposing a video classification algorithm that divides videos into hot and cold sets. Following this, we show the potential and limitations of the hybrid scheme through simulation. The key idea of classifying a video is to identify the algorithm that minimizes the expected server bandwidth needed to serve requests for that video. That is, the ith video is classified as hot if GDB uses fewer channels for the video than threshold-based multicast does, and vice versa. For simplicity of exposition, we assume that there is sufficient disk storage in the client. Suppose that our goal is to achieve an expected latency of 0.35 minute. We need to dedicate 9 channels for each video in GDB (using partition sequence 1, 2, 4, 4, 10, 10, 24, 24, 50). 20

21 1.2 1 waiting time vs. server channels Hybrid Scheme Threshold-based Multicast expected waiting time number of server channels Figure 13: Performance of the hybrid scheme. Under threshold-based multicast, the average server bandwidth for video i is ((2) in Section 4) ( p 2L i i + 1? 1)b. Therefore, videos for which p 2L i i + 1? 1 > 9 are classified as cold and scheduled under thresholdbased multicast, and videos for which p 2L i i + 1? 1 9 are classified as hot and scheduled with GDB. We now show the potential and limitations of the hybrid scheme by simulation. We assume that the arrival rate is 80 requests per minute and that the client buffer can hold 34 minutes of video data, which is sufficient for GDB. All other parameters are the same as those given in Table 2. Figure 13 shows that the hybrid scheme significantly reduces the expected waiting time when the number of server channels is less than 890. As the number of server channels increases, the expected latency of the hybrid scheme becomes greater than threshold-based multicast. This is because when there are sufficient channels to permit threshold-based multicast to reduce the waiting time of hot objects, whereas GDB s expected latency for hot objects is fixed at 0.35 minute. Therefore the expected latency is at least 0.35 times the percentage of the hot object requests in the hybrid scheme, whereas the threshold-based multicast can reduce the latency further. From the figure, we can see that in order to achieve an expected waiting time of 0.35 minute (our design goal), the hybrid scheme needs only 760 channels whereas threshold-based multicast requires 860 channels. The hybrid scheme saves 100 channels! 21

22 7 Conclusions This paper presents a novel multicast technique that significantly reduces the demand on the server network- I/O bandwidth. Unlike existing CIWP schemes, threshold-based multicast uses a threshold to control the frequency that a complete video stream is multicasted. We derive an optimal threshold, given any client buffer size and client request arrival rate, that minimizes the server bandwidth required. We show both analytically and by simulation the significant performance gain over both batching and the basic CIWP. Furthermore, we systematically combine threshold-based multicast with a broadcasting scheme, GDB, to further improve the performance of the video delivery system. References [1] P.W. Agnew and A.S. Kellerman. Distributed Multimedia. Addison Wesley, ACM Press. [2] T. S. Perry, The Trials and Travails of Interactive TV, IEEE Spectrum, April [3] C.C. Aggarwal and J.L. Wolf and P.S. Yu. A Permutation-Based Pyramid Broadcasting Scheme for Video-on-Demand Systems. Proc. of the IEEE Int l Conf. on Multimedia Systems. June [4] C.C. Aggarwal and J.L. Wolf and P.S. Yu. On Optimal Batching Policies for Video-on-Demand Storage Server. Proc. of the IEEE Int l Conf. on Multimedia Systems. June [5] S. Viswanathan and T. Imielinski. Metopolitan Area Video-On-Demand Service Using Pyramid Broadcasting. IEEE Multimedia Systems. 4: , [6] K.A. Hua and S. Sheu. Skyscraper Broadcasting: A New Broadcasting Scheme for Metropolitan Video-on-Demand Systems. ACM SIGCOMM. Sept [7] K.A. Hua and Y. Cai and S. Sheu. Patching: A Multicast Technique for True Video-on-Demand Services. ACM Multimedia. Sept [8] A. Dan and P. Shahabuddin and Dinkar Sitaram and D. Towsley. Channel Allocation Under Batching and VCR Control in Movie-On-Demand Servers, Journal of Parallel and Distributed Computing, 30, 2 (November 1995), pp [9] A. Dan and P. Shahabuddin and D. Sitaram, Scheduling policies for an on-demand video server with batching. In Proc. of ACM Multimedia, October 1994, pp [10] A. Dan and D. Sitaram and P. Shahabuddin, Dynamic Batching Policies for an On-Demand Video Server. In Multimedia Systems, 4: ,

23 [11] L. Gao, J. Kurose, D. Towsley, Efficient Schemes for Broadcasting Popular Videos, Proceedings of NOSSDAV, Cambridge, UK, July [12] D.L. Eager and M. K. Vernon, Dynamic Skyscraper Broadcasts for Video-on-Demand, Technical Report #1375, Computer Science Department, UW-Madison, May [13] P.J. Shenoy, P. Goyal and H.M. Vin, Issues in Multimedia Server Design, ACM Computing Surveys, December, [14] K. Almeroth and M. Ammar, On the Performance of a Multicast Delivery Video-On-Demand Service with Discontinuous VCR Actions, International Conference on Communications, Seattle, Washington, USA, June [15] K. Almeroth and M. Ammar, The Role of Multicast Communication in the Provision of Scalable and Interactive Video-On-Demand Service, In Proc. of Network and Operating System Support for Digital Audio and Video, Durham, New Hampshire, USA, April [16] A. Dan, Y. Heights and D. Sitaram, Generalized Interval Caching Policy for Mixed Interactive and Long Video Workloads, In Proc. of SPIE s Conf. on Multimedia Computing and Networking, pages , San Jose, California, January [17] K. Almeroth and M. Ammar, A Scalable, Interactive Video-On-Demand Service Using Multicast Communication, Proc of International Conference on Computer Communication and Networks, San Francisco, California, USA, September, [18] G. Zipf, Human Behavour and the Principle of Least Effort, Addison-Wesley, [19] S. W. Carter and D. D. E. Long. Improving Video-on-Demand Server Efficiency Through Stream Tapping, Proceedings of the International Conference on Computer Communication and Networks (IC- CCN 97), Las Vegas: IEEE, September 1997, pp

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