7.4 Equivalent Bandwidth
7.4.4 Numerical Validation
In this section we evaluate the analytical approach of equivalent bandwidth estimation on three types of flows: VoIP, Video and Data. VoIP and Data sessions are modelled as ON-OFF processes with UDP as transport protocol for VoIP and Video, and TCP as transport protocol for Data sessions. Recall that TCP automata reacts to packet losses. Hence, we evaluate the equivalent bandwidth of TCP flows under the hypothesis of loss free transmission. This is justified by the final goal of bandwidth estimation which is allocating resources according to application needs.
Refer to Tables 5.3 , 5.8 and 5.10 (Chapter 5) for the definition of G711C, MPEG4 and W1 traffic source models that we will use in this evaluation.
7.4.4.1 Equivalent Bandwidth for G711C VoIP Application
VoIP applications have a common characteristic which is the constant packet size and constant packet inter-arrival time during ON periods. All results concerning the estima- tion of the equivalent bandwidth of G711C application model hold for other VoIP codec types.
The squared coefficient of variation of service time process in a deterministic service queue for VoIP packets is null (c2
s = 0) because packet sizes are constant, while the
squared coefficient of variation of packet arrival process for N ON-OFF processes is given by [SW86]:
c2a = wc21+ 1 − w (7.24) c2
1 is the squared coefficient of variation of single ON-OFF connection and it is calculated
as function of the packet transmission probability p during period ON, constant packet inter-arrival T , TOF F duration: c21 = 1 − p 2 (T /TOF F + 1 − p)2 (7.25) w = 1 1 + 4(1 − ρ)2(N − 1) (7.26)
The average rate is RM = PON ∗ RON and the maximum rate is RON = T1.
Using the previous formulas we estimate the equivalent bandwidth of constant number of G711C applications with two variable parameters: the buffer size K and the target packet loss probability E. Results are depicted on Figures 7.6 and 7.7.
We note that the estimated value of the equivalent bandwidth decreases with large buffer size as traffic bursts are more easily absorbed. Besides higher packet loss rate results in lower value of the equivalent bandwidth. The estimated values will be checked in a performance test later.
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Figure 7.6: G711C Equivalent Bandwidth Estimation (Variable Buffer Size)
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7.4.4.2 Equivalent Bandwidth for Web Sessions
The packet arrival process in Web sessions is complicated as it depends on the TCP algorithm. As a consequence, the squared coefficient of variation of packet arrival process can not be estimated analytically. Two solutions to this problem may be proposed: first, we can measure the value of c2
a directly on the generated trace. This requires having the
generated traffic before evaluating the equivalent bandwidth, which may not be useful when used in a QoS management server (the SIP proxy server). That is why we suggest a second heuristic based on the approximation of packet arrival process during ON periods by a constant process of the same average. Thus, we need to estimate the average rate during the ON period when only the file size is known.
Authors in [SKV01] present a formula to calculate the transfer time when TCP is used on short-lived connections (one ACK per two packets b = 2).
T (Nb) = RT T (log1.57(Nb) + (f (p, RT T )Nb + 4p log1.57(Nb) + 20p))+ (10 + 3RT T )Nb 4(1 − p)Wmax√Wmax
(7.27) The parameters are:
• Nb: The file size in packets.
• Wmax: The maximum reception window.
• p: The packet loss probability. • f(p, RT T ) = 2.32(2p+4p(1+RT T )2+16p3 3)+
1+p 103RT T
As we are concerned with the ON periods of Web sessions, the file transfer activity is very short compared to the idle period. Thus, this formula is appropriate to our study case. Meanwhile, a major simplification can be done when estimating the equivalent bandwidth with small loss probabilities. Indeed, the contribution of the first term RT T log1.57(Nb) is dominant, and the equation can be used in its simpler form:
T (Nb) = RT T log1.57(Nb) (7.28) Using the estimated transmission time during the ON period we can estimate the average transmission rate: λON = Nb T (Nb), Nb = QON P s (7.29)
Having the average λON we can use the same formulas as for VoIP while considering
constant packet inter-arrivals during the ON period (which is only an approximation). However, the packet service time process is not constant as packet sizes are not con- stant. However, by using the maximum segment size in the TCP algorithm we generate packets of (MSS+Header= 984+40 =1024 Bytes). As a result we generate 1024 bytes for all packets except the last one (the residual value). Consequently, the squared coeffi- cient of variation of packets service time for Web session can be supposed null (c2
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Figure 7.8: HTTP Equivalent Bandwidth Estimation (Variable Buffer Size)
The equivalent bandwidth estimation procedure is similar to the VoIP case, and similar results were obtained (See Figures 7.8, 7.9).
The same observation can be made on the equivalent bandwidth for Web sessions as for VoIP applications.
7.4.4.3 Equivalent Bandwidth for MPEG4 Video Application
The MPEG4 Video application traffic has different characteristics from VoIP and Web applications. Indeed, the squared coefficient of variation of packet arrival process can not be estimated analytically, and can not be assimilated to constant packet inter-arrivals as for VoIP applications. In order to estimate the equivalent bandwidth we need to evaluate the MPEG4 traffic c2
a value offline on the generated traffic. However, as we use MPEG4
traffic models with constant (1000 bytes) packet sizes (refer to Chapter 5 ), the squared coefficient of variation of service time in a deterministic service queue for Video packets is null (c2
s = 0).
The equivalent bandwidth estimation procedure is similar to previous cases. We show results only as function of Buffer size (see Figure 7.10).
7.4.4.4 Performance Validation
We validate the estimated equivalent bandwidth values for VoIP, Video and Web Sessions in network environment. For this purpose, we inject the traffic generated by the three
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Figure 7.9: HTTP Equivalent Bandwidth Estimation (Variable Packet Loss Rate)
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types of sessions into a queuing system of deterministic service. The service rate is chosen as a function of equivalent bandwidth. In this test, we evaluate the equivalent bandwidth for 30 packet size buffer at 1% packet loss rate with a variable number of connections. Results for VoIP sessions are listed in Table 7.1.
Table 7.1: Validation of the Equivalent Bandwidth for G711C Application N EB (GI/D/I/K) Kbps Loss Rate %
100 3164 1.45
200 6330 1.37
300 9494 1.24
500 15824 1.11
1000 31648 1.03
We note that the GI/D/1/K queue system model underestimates the equivalent bandwidth when the number of connections is small. The observed loss rate is higher than the target value (1.45% instead of 1% for N = 100).
Table 7.2: Validation of the Equivalent Bandwidth for Web Sessions N EB (GI/D/I/K) Kbps Loss Rate %
100 9494 1.9
200 11531 1.5
300 16142 1.38
500 25490 1.09
1000 50980 1.07
In Table 7.2 we show the results for Web sessions traffic. They are similar to VoIP case. Notice that constant packet inter-arrivals approximation during ON periods for Web sessions lead to acceptable results. Although this is not the real behaviour of inter- arrivals, we obtain acceptable loss rate. This approximation allows analytical estimation of the equivalent bandwidth for Web sessions directly.
Similar results where obtained for video traffic. Meanwhile, the squared coefficient of variation of packet arrival process was estimated on the generated video traffic trace.