Receiver Buffer Requirement for Video Streaming over TCP Taehyun Kim a and Mostafa H. Ammar b a Wireless and Mobile Systems Grou, Freescale Semiconductor, Austin, TX 7735, USA E-mail: taehyun.kim@freescale.com b Networking and Telecommunications Grou, College of Comuting, Georgia Institute of Technology, Atlanta, GA 333, USA E-mail: ammar@cc.gatech.edu ABSTRACT TCP is one of the most widely used transort rotocols for video streaming. However, the rate variability of TCP makes it difficult to rovide good video quality. To accommodate the variability, video streaming alications require receiver-side buffering. In current ractice, however, there are no systematic guidelines for the rovisioning of the receiver buffer, and smooth layout is insured through over-rovisioning. In this work, we are interested in memory-constrained alications where it is imortant to determine the right size of receiver buffer in order to insure a rescribed video quality. To that end, we characterize video streaming over TCP in a systematic and quantitative manner. We first model a video streaming system analytically and derive an exression of receiver buffer requirement based on the model. Our analysis shows that the receiver buffer requirement is determined by the network characteristics and desired video quality. Exerimental results validate our model and demonstrate that the receiver buffer requirement achieves desired video quality. Keywords Media over Networks, Video Streaming, Streaming Video Protocols 1. INTRODUCTION A video streaming alication has to emloy a transort layer rotocol to transmit acketized video. Since TCP is the dominant rotocol in the Internet, it is reasonable to emloy TCP for video streaming: recent measurement study has reorted that % of video streaming flows are actually delivered over TCP. 11 Esecially, there are many situations in which video streaming servers are located behind firewalls that ermit only re-secified ort numbers. In this scenario, video streaming over TCP is the only choice to get around the firewalls over the well-known ort numbers (e.g., HTTP or RTSP). Also, the reliable acket delivery of TCP is imortant, when error resilience is not imlemented in a video codec. While the use of TCP rovides reliable video stream delivery, it is difficult to rovide good quality of streaming video over TCP: 1) the sawtooth behavior of additive increase and multilicative decrease (AIMD) incurs significant data rate variability, and ) the use of retransmission timeouts may introduce unaccetable end-to-end delay, and the retransmitted data may be delivered too late for dislay. 3, 5, 9 These drawbacks of TCP can be mitigated to some extent through the use of receiver-side buffering. The buffer size has to be large enough to insure that desired video quality can be achieved. In current ractice, however, there are no systematic guidelines for the rovisioning of the receiver buffer, and smooth layout is insured through over-rovisioning. We are interested in memory-constrained alications where it is desirable to determine the right receiver buffer size. This aer, therefore, considers the question of how large the receiver buffer should be in order to achieve desired erformances for streaming video over TCP. To this end, we characterize video streaming over TCP in a systematic and quantitative manner. Our starting oint is an analytic model of a streaming system of CBR video. Based on this model, we quantify the receiver buffer requirement. Exerimental results validate our model and demonstrate that the minimum buffering delay can achieve desired video quality. The remainder of the aer is organized as follows. In Section, we resent a video streaming model and derive the receiver buffer requirement. Section 3 shows exerimental results to validate our model. This aer is concluded in Section.
. MODEL AND ANALYSIS.1. Video Streaming Model over TCP Figure 1 shows a video streaming model which consists of a sender and a receiver. We assume that the sender transmits re-recorded CBR video over a unicast TCP connection, and the receiver is equied with a receiver buffer in front of a video decoder. The decoder waits to fill the buffer before dislaying video. There are two tyes of buffering delay caused by the receiver buffer. Initial buffering: to accommodate initial throughut variability or inter-acket jitters, it is needed to emloy initial buffering. While a streaming alication achieves more tolerance with larger initial buffering, it increases the startu latency and resonse time. Rebuffering: the decrease of throughut within a TCP streaming session might cause the receiver buffer starvation. When this haens, a decoder stos dislaying video until it receives enough video ackets. Note that rebufferings take lace in the middle of video streaming, and therefore the rebuffering delay requirement for a long video stream is determined by the congestion avoidance algorithm of TCP. In this aer, we assume that the amount of the initial buffering delay and the rebuffering delay is identical, so that the receiver buffer size for initial buffering and rebuffering is the same. Network k Sender Receiver Figure 1. A video streaming model over TCP Let λ k be the arrival rate of video ackets at round k, and λ be the video encoding rate, where a round is defined by a duration between the transmission of ackets and the recetion of the first acknowledgment (ACK) in a congestion window. It is assumed that a round is equal to the round-tri time (RTT) and indeendent of the congestion window size. Figure (a) shows a tyical behavior of a TCP flow. We consider the TCP Reno model in this aer, since it is one of the most oular imlementations in the current Internet. 7 In this model, the steady state throughut is determined by the congestion window size which is adjusted based on acket losses. A acket loss can be detected by either trile-dulicate ACKs or timeouts, where we denote the former events by TD and the latter by TO. Consider a TD eriod (TDP) in Figure (a). Each TDP starts immediately after trile-dulicate ACKs and increases the congestion window size by 1/b until trile-dulicate ACKs are encountered again. However, when multile ackets are lost and less than three dulicated ACKs are received, a TO eriod (TOP) begins. In each TOP, a sender stos transmitting data ackets for a timeout interval and retransmits non-acknowledged ackets. Note that the timeout interval in a TOP increases exonentially until it reaches T. On the other hand, Figure (b) shows the layout characteristic at a receiver, where it is assumed that the video layout rate is two ackets worth of data er RTT. We can observe that, if a right size of receiver buffering is emloyed, a consistent CBR layout can be achieved without any interrution. In this aer, the erformance of a video streaming alication is evaluated by the buffer underrun robability and the disrution frequency: Note that λ k is a function of time secified by round k, whereas there is no subscrit on λ, since the data rate fed into a video decoder is assumed to be CBR. Note that b =if delayed acknowledgment is imlemented at the receiver. Otherwise b =1.
TDP i TDP i+1 T T T TDP 1 3 k 1 1 35 3 3 5 9 13 1 33 39...... 3 3 1 7 11 15 31 37 Z TD Z TO (a) Packet arrival characteristic at a receiver 1 3 5 7 1 9 1 11 1 13... 3 15 31 37 33 39 3... buffering delay (b) Playout characteristic at a decoder Figure. An illustration of receiver buffering time The buffer underrun robability is defined by n/n, where n is the number of buffer underrun events, and N is the number of eochs in a video stream. An eoch is defined by E[Z TD + Z TO ], where Z TO is the duration of a TOP, and Z TD is the duration between two TOPs. Note that a Z TD consists of one or more TDPs. The disrution frequency 1 is defined by n/t, where n is the number of buffer underrun events, and T is the duration of a video streaming session. Since T consists of N eochs, a disrution frequency can be exressed by the ratio of the buffer underrun robability to the duration of an eoch... Receiver Buffer Requirement We investigate the erformance when average TCP throughut matches video encoding rate. This is the case when the video encoding rate is determined by the access link bandwidth, and the available bandwidth is limited by the access link caacity. For examle, many video streaming websites rovide multile coies with identical content, generated at different data rates. A receiver selects an aroriate stream that matches with the access link caacity. We assume that the video encoding rate is equal to the average TCP throughut and does not change over time. Hence, the encoding rate is modeled by 7 1 λ = ackets/rtt, b 3 + T R min(1, 3 3b )(1 + 3 ) where is the acket loss rate of a TCP streaming flow, R is the round-tri time, and T is the retransmission timeout. Let q k be the receiver buffer size at round k. Since λ k ackets are received and λ ackets are drained in a TDP, the buffer size is given by q k = q k 1 + λ k λ, (1) where k =1,,...,X i ; and X i is the number of round where a TD loss is detected. On the other hand, since no acket is delivered to a receiver, the receiver buffer size in a TOP is given by where k =1,,..., Z TO /R. Notations in the aer are summarized in Table 1. q k = q k 1 λ, ()
Table 1. Notations q receiver buffer size at round q k receiver buffer size at round k q min minimum buffer size acket loss rate R round-tri time λ k arrival { rate of video ackets at round k: Wi 1 λ k = + k b 1 ackets/rtt, in TDP i, otherwise. λ video encoding rate b number of ackets that are acknowledged by an ACK W i congestion window size at the end of TDP i X i number of round where a TD loss is detected Y i number of ackets sent in TDP i α i the first acket lost in TDP i β i number of ackets sent in the last round T retransmission timeout desired buffer underrun robability P u We define the buffer underrun robability by the robability of the minimum buffer size to be non-ositive. Since a receiver is either in a TDP or in a TOP, the buffer underrun robability at time t is decomosed into the sum of conditional robabilities, such that P {q min } = P {q min t Z TD }P {t Z TD } + P {q min t Z TO }P {t Z TO }. (3) From the conditional buffer requirements in (3), we can derive the buffer size requirement under which the robability that the unconditional minimum buffer size goes non-ositive. Theorem.1 below states that the minimum buffer requirement is determined by the network characteristics and desired buffer underrun robability. THEOREM.1. Given network model characterized by the acket loss rate (), RTT (R), and retransmission timeout (T ), the receiver buffer size (q ) that achieves desired buffer underrun robability (P u ) is given by q.1 [1 + 9. P u b (T 3b R ) min(1, 3 )(1 + 3 )]. Proof. See Aendix. Given receiver buffer size, required buffering delay is determined by d = q B(,R), where B(, R) is the steady state TCP throughut. 7 Therefore, d corresonds to the time delay for buffered ackets to be drained. The duration of an eoch can also be determined, 7 such that an eoch of a TCP flow is given by E[Z TD + Z TO ]= R( b 3 min(1,3 +1) f() 3b + T ) 1, where f() =1+ + + 3 + +1 5 +3. 3. EVALUATION In this section, we resent exerimental results by which layout disrution characteristics are evaluated. The exerimental results including simulation scrits are available in the comanion website.
3.1. Exerimental Setu TCP throughut dynamics are generated over a single bottleneck toology. The number of TCP streaming flows is set to 5. All access links have sufficient caacity so that any acket dro occurs at the bottleneck link: the access links have 1Mbs caacity and 1ms delay, whereas the bottleneck link has 1Mbs caacity and ms delay. We run ns- simulations over this toology. To model the TCP throughut dynamics, we use the throughut exerienced between streaming senders and receivers: the throughut is measured by counting the number of ackets delivered from a sender to a receiver. All data ackets are 1 bytes long. The queue management algorithm running on intermediate routers is the random early detection (RED). To construct dynamic network characteristics, cometing traffic (or cross traffic) is generated by triggering ersistent FTP flows 1 seconds rior to TCP streaming sessions. The number of cross traffic flows is varying to investigate the effect of the acket loss rate on the erformance of TCP streaming. Unless otherwise secified, following sets of configurations are examined, each of which generates 1 traces using different random seeds. In all configurations, the duration of simulation time is set to seconds. Configuration 1: the number of cometing FTP flows is assumed to be 3 that leads video streaming flows to have 1.3ms RTT, 179.ms T,.% acket loss rate, and 1.Mbs throughut. Configuration : the number of cometing flows is set to. Measured characteristics of video streaming flows are 11.3ms RTT, 1.3ms T,.79% acket loss rate, and 9.1kbs throughut. Configuration 3: the number of cometing flows is 9. Measurement results are 1.ms RTT, 11.ms T, 1.% acket loss rate, and 715.kbs throughut. It should be noted that measured round-tri delays are different in each configuration, because of the queuing delays in the intermediate routers as well as link delays. To estimate the acket loss rate in each configuration, we emloy the TCP throughut equation. 7 The equation rovides an analytic relationshi between the acket loss rate, RTT, T, and TCP throughut. However, as the relationshi is too comlicated to yield a closed form of a acket loss rate as a function of throughut and RTT, we develo an iterative algorithm in Figure 3 based on the bisection method. Since the TCP throughut equation is continuous and an estimated throughut must lie in the acket loss rate of [, 1], the existence of a root is guaranteed by the intermediate value theorem. Also the estimated acket loss rate is unique, since the estimated throughut is monotonically decreasing as the acket loss rate increases. 1: rocedure ComuteLossRate (R, B) : l =, h =1 3: while h l >ɛdo : =( l + h )/ 5: B = 1 : if B <B 7: h = : else 9: l = 1: enddo 11: endrocedure R b 3 +T min(1,3 3b )(1+3 ) Figure 3. Packet loss rate estimation algorithm The erformance of TCP streaming exeriments is evaluated by the buffer underrun robability and the disrution frequency as defined in Section.1. Note that the number of eochs is given by the simulation time ( seconds) divided by an eoch, and the disrution frequency is the buffer underrun robability divided by an eoch.
3.. Buffer Underrun Probability In the first exeriment, we measure the buffer underrun robability in each TCP streaming flow. We investigate 5 TCP streaming flows, since each configuration contains 1 traces, each of which contains 5 TCP streaming flows. Figure (a) shows the buffer underrun characteristics of configuration 1. The solid line secifies the minimum buffering delay requirements in Theorem.1 to achieve desired buffer underrun robability. Each error bar corresonds to the measured buffer underrun robability of 5 TCP streaming flows with 99% confidence interval. When RTT, T, and the acket loss rate are 1.3ms, 179.ms and.%, buffering delays targeting desired buffer underrun robabilities of %, %, and % are 3.53, 7., and 1.13 seconds resectively. Exerimental results show that measured buffer underrun robabilities are tightly bounded by the solid line of 99% confidence level. Observe that the range of the confidence interval is reduced as buffering delay is increased, since the variance of measured buffer underrun robabilities is decreased. 1 1 1 Underrun robability (%) Underrun robability (%) Underrun robability (%) 1 3 5 7 9 1 11 1 13 1 15 (a) Configuration 1 1 3 5 7 9 1 11 1 13 1 15 (b) Configuration 1 3 5 7 9 1 11 1 13 1 15 (c) Configuration 3 Figure. Buffer underrun robability characteristics Note that the buffering delay characteristic is a non-linear curve. For examle, when buffering delay is increased from 3 seconds to 9 seconds in Figure (a), desired buffer underrun robability is reduced by.31%. However, when buffering delay is increased from 9 seconds to 15 seconds, the robability is reduced by only 1.%. Therefore, a system designer can find a oint of marginal return using the non-linear characteristics. Figure (b) shows the buffer underrun robability of configuration. Required buffering delays targeting P u =%, %, and % are.7, 5.1, and 1. seconds resectively. Comared with Figure (a), the 99% confidence intervals are loosely bounded by the buffering delay requirement curve. This is because, as the acket loss rate is increased, the o(1/) term in (1) gets more significant, and the measured buffer underrun robability deviates more from the desired buffer underrun robability curve. Figure (c) shows the buffer underrun robability of configuration 3. Required buffering delays for P u =%, %, and % are.,.5, and 9.1 seconds resectively. Exerimental results demonstrate that desired buffer underrun robability becomes more conservative, as the acket loss rate is increased. 3.3. Disrution Frequency In this exeriment, we investigate disrution frequency characteristics which was defined in Section.1. Measured disrution frequency is defined by the number of buffer underrun events during the second simulation time. Figure 5 shows disrution frequency characteristics for configuration 1,, and 3. The error bar secifies the 99% confidence interval, and the solid line shows desired disrution frequency which is defined by the ratio of desired buffer underrun robability to the duration of an eoch. Hence, Figure 5 exhibits the same characteristics as Figure : 99% confidence interval of measured disrution frequencies is tightly bounded by desired disrution frequency when the acket loss rate is small. However, as the acket loss rate is increased, desired disrution frequency becomes a conservative bound.
.1.1.1 Disrution frequency (Hz).... Disrution frequency (Hz).... Disrution frequency (Hz).... 1 3 5 7 9 1 11 1 13 1 15 (a) Configuration 1 1 3 5 7 9 1 11 1 13 1 15 (b) Configuration Figure 5. Disrution frequency characteristics 1 3 5 7 9 1 11 1 13 1 15 (c) Configuration 3. CONCLUSION In this aer, we consider video streaming over TCP. While the use of TCP rovides the reliable video stream delivery, the bursty nature of TCP requires buffering at a receiver for smooth video layout. Since it is desirable to determine the right size of receiver buffer in memory-constrained alications, we quantify the buffering requirement to achieve desired buffer underrun robability by analytically modeling the CBR video streaming. Our analysis shows that the receiver buffer requirement is determined by the network characteristics and desired buffer underrun robability (or disrution frequency). Exerimental results validate our model and analysis. APPENDIX: Proof of Theorem.1 In a TDP, since the acket arrival rate is greater than zero, and it is increased linearly until it encounters trile dulicate ACKs, the receiver buffer size at round k in (1) is given by q k = q + k (λ j λ) j=1 = q + k b + (W i 1 λ 1)k. () On the other hand, the receiver buffer size in a TOP in () is given by To rove Theorem.1, the following relationshis 1 are used : q k = q k λ. (5) W i = W i 1 + X i b 1 () Y i = α i + W i 1 (7) Y i = X i (W i 1 + W i )+β i. () Note that the exressions in () and () are different from the original equations 7 by a constant term. However, for small values of, TCP throughut in a TDP can still be exressed by B TDP (, R) = 1 3 R b + o( 1 ). (9) We assume that a round in Z TO is equal to RTT, although no ACK acket is received during Z TO. Although three dulicated ackets are lost and not delivered to a receiver in a TDP, the data recetion rate can be aroximated by the data transmission rate for small. The relationshis can be verified from the ith TDP in Figure (a): the arameters given by W i 1 = W i =, X i =, Y i =39, α i =3, β i =3, and b =satisfy (), (7), and ().
To achieve a desired buffer underrun robability, we need to consider the minimum buffer size in () and (5). Using the Markovian inequality, the buffer underrun robability at time t in a TDP is given by P {q min t Z TD } = P {q b (W i 1 λ 1) } E{ b (W i 1 λ 1) } q = b (E{W } λe{w } + λ + λ E{W } +1), (1) q where E{W } stands for the average of Wi 1 and E{W } for the average of W i 1. Equation (1) can be solved using (), (7), and (). From (), it follows that E{X} = b E{W } + b. (11) Observe that squaring () leads to W i = W i 1 + Wi 1Xi b + X i b Xi b W i 1 +1. Hence, the average of X i is given by E{X } = 3b E{W } b E {W } + b E{W } + b. (1) Note that squaring () after maniulating the Wi 1 term yields W i W i W i 1 + W i 1 = X i b X i b +1. (13) From (11), (1), and (13), the correlation of congestion window sizes between adjacent TDPs is given by E{W i W i 1 } = 1 (E{W } + E {W }). (1) We consider (7) and () to derive E{W }. Since α i is the first acket lost in a TDP, α i can be assumed to have a geometric distribution with the robability. Hence, it follows that E{α i } = 1 and E{α i } =. With this assumtion, squaring (7) leads to E{Y } = + E{W } +1+ E{W } E{W }. (15) In the same way, E{Y } can also be obtained by () and (1). Since β i is the number of ackets in the last round, it can be assumed to have a uniform distribution in [1,W i ]. Therefore, squaring () yields E{Y } = E{X } ( 5E{W } + E{W i W i 1 })+E{β}E{X} 3E{W } + E{β } = b (3 E{W } 1 E {W } + E{W } + 1)( 7 E{W } + 1 E {W })+ 3b E {W }( 1 E{W } +1) + E{W } +3E{W } +1. (1) Since the average window size is given 7 by E{W } = 3b + o( 1 ), we assume E{W } = O( 1 ). By equating the relationshis in (15) and (1), we can derive a relationshi, such that Hence, 1b E {W } b 3 E{W } 9 = o( 1 ). E{W } = 3 + 7 3b + o( 1 ). (17)
Note that the long-term average of λ k is equal to λ. Therefore, TCP throughut in (9) can also be alied to λ, such that λ = 3 b + o( 1 ). From (17), the buffer underrun robability in a TDP in (1) is bounded by P {q min t Z TD } b [ 3 + 7 q 3b 3 3 b 3b +( b ) ]+o( 1 ) =.1 q + o(1 ). (1) To derive an exression of the buffer underrun robability in a TOP, we consider (5) and aly the Markovian inequality. Since the minimum buffer size in a TOP is given at k = Z TO /R, wehave P {q min t Z TO } = P {q ZTO R λ} E{ZTO } q R λ, (19) Since the average duration of a TOP is described by E{Z TO f() } = T 1, where f() =1+ + + 3 + +1 5 + 3, (19) leads to P {q min t Z TO } T 3 q R b + o( 1 ). () Now we derive the unconditional robability of buffer underrun from the conditional robabilities. Since W i is a regenerative rocess over the eriod of Z TD + Z TO,wehave P {t Z TD E{Z TD } }= E{Z TD } + E{Z TO }, P {t Z TO E{Z TO } }= E{Z TD } + E{Z TO }, where E{Z TD b } = E{n}(E{X} +1)R, E{X} = 3 + o( 1 ), and E{n} is the average number of TDPs in Z TD. Consider the robability of TO loss indication Q, which is given 7 by Q = 1 E{n} min(1, 3 3b ). From (1) and (), the buffer underrun robability is thus P {q min } = P {q min t Z TD }(E{X} +1)+QP {q min t Z TO }T f() 1 (E{X} +1)R + QT f() 1 3 b min(1, 3 3b )T f() 1.1 q R b 3 + T q R b R 3 + min(1, 3 3b.1 9. [1 + q b (T 3b R ) min(1, 3 )T f() 1 + o( 1 ) )(1 + 3 )] + o( 1 ). (1) Therefore, given desired buffer underrun robability, such that P {q min } P u, required buffer size is given by q.1 [1 + 9. P u b (T 3b R ) min(1, 3 )(1 + 3 )].
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