Introduction
In the previous section of this essay a negative congestion externality was shown to exist where the quantity of data/traffic demanded exceeded the capacity of the network. In this section of the essay the concept of an Application Data Unit (ADU) will be used to explain the determination of the size of the congestion externality. This will then be used to develop a relationship between congestion and the demand for internet usage.
The Application Data Unit (ADU)
In estimating the size of the congestion externality it is necessary to determine the best measure of the impact of congestion on internet users. One method used to measure the impact of delay is to measure the time delay for sending a 'packet'1 of data to a destination. This was the method used by MacKie-Mason and Varian (1994a:13-18), who measured the round trip time delay of single packets to several major cities. This approach however has been criticised on the grounds that because of the operation of TCP/IP,2 single packet delay does not accurately capture the impact of congestion on internet users. (Clark (1997:218)
Since " a communications network is as good, or as bad, as its users perceive it."(MacKie-Mason, Murphy & Murphy (1997:279)), a measure which takes in to account the users evaluation of network performance is thus necessary. This essay supports the view that "the criterion a user has for evaluating network performance is the total elapsed time to transfer the typical data unit of the current application, rather than the delay for each packet." (Clark (1997:218)) An ADU is simply the typical size of a data element for an application.(Clark (1997:218)). Thus the ADU for someone using a web browser is the size of a typical web page whilst for someone using email it is the size of a typical email message.3
This means that the impact of delay will be related to the size of the ADU for the application. Applications with larger ADU's will be more adversely affected by any reduction in data throughput.4 Furthermore, some applications such as real-time video and audio applications experience significant degradations in quality as congestion increases. (Clark 1997:219). Users' assessment of congestion will therefore be related to the type of application they are using as well as the ADU transfer time. Table 1 provides a suggested ranking5 of the relationship between application type and the impact of congestion.
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Table 1: Application Type and Impact of Congestion |
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____________________________________________________ |
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Likely Impact of Congestion |
Application |
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____________________________________________________ |
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Very Severe |
Real time audio and video |
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Severe |
Web Browsers - Graphics On |
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Large FTP transfers |
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Moderate |
Web Browsers - Graphics Off |
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Slight |
IRC |
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Telnet |
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Minor |
Email, Usenet |
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____________________________________________________ |
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Now, consider Figure 4 below. In order to simplify our analysis let us assume that a users evaluation of the cost of delay is related to the type of application they are using.6 In Figure 4, three different MPC curves have been drawn representing the cost of delay for different application types. The impact of the congestion at Q0 will be different depending on the application being used. For example MPC0 could represent email, MPC1 no-graphics web browsing and MPC2 web browsing with graphics on. These have corresponding marginal costs at Q0 of P1, P2 and P3. This illustrates the point that an application with a large ADU or poor tolerance of delay will be more adversely effected by congestion.
What then determines the MSC of congestion? The impact of congestion on internet users as a whole will depend on the mix of applications in use at the time the congestion occurs. For example, if there is a large number of individuals utlising web browsers with graphics switched on, then the impact of congestion, and hence the MSC, will be larger than if the dominant use of the internet at that time is for email. The size of the MSC thus depends on the application mix at the time the congestion occurs.
A similar diagram to Figure 4 can thus be constructed to show the difference in MSC for different application mixes. Figure 5 shows the MSC for two different application mixes. Firstly, MSC1 illustrates the marginal social cost where the application mix is predominantly applications with small ADU's. MSC2 illustrates the marginal social cost where the application mix is predominantly applications with large ADU's. It can be seen from this that as with the MPC in Figure 4, for any given congestion level such as Q0, the MSC is higher where the application mix is dominated by applications with larger ADU's and poor tolerance of delay.
Since the congestion externality is equal to the gap between the MPC and MSC, the size of the congestion externality will thus depend on the application mix of internet users when the congestion occurs. Where the application mix is dominated by larger ADU applications, the congestion externality is greater.7
The Congestion Externality and the Marginal Benefit of Network Size
Earlier in this essay a diagram representing the relationship between marginal benefit and network size was presented. The Marginal Benefit (MB) curve eventually showed diminishing returns from increased network size due to the influence of negative factors, including congestion. It is now possible to incorporate our analysis of congestion in to this earlier diagram to illustrate the impact of congestion on marginal benefit.
Starting at Figure 6b. At network size N+, the MPB in the presence of congestion is given by the lower portion of the blue MPB line. A demand curve for this network size is then constructed in Figure6a.. Where the price paid is equal to the MPC then quantity Q+ is demanded. However as explained earlier , because of congestion a negative externality (C ) exists, equal to the gap between the MPC and MSC. As network size increases outward to N*, the quantity of traffic demanded and the congestion externality both increase. However once network size passes N* demand shifts backward to the left. This is represented in Figure 6a by demand curve DN- .As demand decreases so does the quantity of traffic demanded and the congestion externality also falls. If the network grows to size N#, the congestion externality is zero.8
The individuals MPB without the congestion externality is found by adding the portion of the externality borne by the individual onto their MPB curve. This produces a curve such as the upper portion of the blue MPB curve. This higher MPB would then produce a demand curve which would sit further to the right for any given network size. For example, at network size N+, the demand curve with lower congestion would be to the right of the original demand curve. The important implication of this is that a reduction in congestion will therefore lead to an increase in the demand for usage.
Two features need to be highlighted here. Firstly, the congestion free MPB would produce a different network elasticity. This comes about because the increase in the MB of size means that demand, and hence the quantity demanded will, ceteris paribus, increase by a greater amount. Thus a given percentage change in network size will produce a greater change in the quantity of traffic demanded than in the presence of congestion. Secondly, the network size at which total benefit is maximised is greater in the absence of congestion. Hence a higher level of usage is demanded in the absence of congestion.
The effect on MSB is similar to that on MPB except that the increase in MSB is greater than increase in MPB.9
Figure 7 illustrates the effect of congestion on the MSB of network size. As with MPB, the MSB in the absence of the congestion externality can be found by adding back the congestion externality to the MSB curve. Thus the MSB curve without the congestion externality will be given by the upper portion of the green MSB curve. As with MPB, in the absence of the congestion externality the total social benefit is now maximised at a larger network size.
Also, if MSB was to be plotted in the demand/quantity space such as Figure 6a, the original MSB curves would lie slightly above (to the right) of the demand curves. In the absence of the congestion externality the demand would increase, however because the MSB increases by a greater amount, the MSB curves would shift outward by a greater amount.
Conclusion
In this essay we started out by constructing a relationship between marginal benefit (both private and social) and network size, in the presence of congestion. The concept of the ADU was then used to find the size of the congestion externality for different network sizes and a given application mix. This externality was then added back to the marginal benefit of network size. What this then gives is the marginal benefit of network size, in the absence of the congestion externality. This is the maximum marginal benefit of network size possible ceteris paribus. This is significant since it allows for the impact of factors which reduce congestion to be analysed. The next section of this essay will draw on the model developed so far to explore the possible policy implications of this model.
Endnotes
1.Raw data on the internet is usually sent as a series of small data 'packets', not as a stream of data. For more information see (
Hahn & Stout (1994:29-31)).2. Recall the earlier discussion on the 'Slow Start/Congestion Avoidance/Fast Retransmit' methods implemented by TCP to addresses congestion of internet traffic. Under TCP, congestion will lead to a slow down in the rate at which packets are sent in to the network. The impact of congestion on users will therefore by a slow down in the throughput of transfers, rather than constant increases in the delay experienced by individual packets. (
Clark (1997:218) Delays for individual packets may therefore not be the best measure of delay.3. Although it does not alter the validity of the ADU in the context which it is used in this model, it should be noted that other factors may lengthen the time taken to transfer an ADU besides congestion. For example some email programs and indeed some internet access providers may have a policy of only transmitting email at certain time intervals (e.g. hourly, two hourly).
4. This can be explained by a simple numerical example. Let us assume the ADU for a web browser with graphics switched on is 20k and with graphics off the ADU is 5k. If the rate of transfer falls from 2k per second to 1k per second the time taken to transfer the ADU for a browser with graphics on will increase from 10 seconds to 20 seconds. For a browser with graphics switched off the ADU will go from taking 5 seconds to 10 seconds to complete. The number of seconds taken to transfer the larger ADU has thus increased by a greater amount.
5. This ranking is suggested based on the authors personal experience with the listed application types. It should be noted that altering the rankings does not change the validity of the transfer time for an ADU as the appropriate measure of the impact of congestion.
6. It should be remembered however that this assumption has been criticised for ignoring the heterogeneity across users and across time. (
MacKie-Mason, Murphy & Murphy (1997:279) However for the purpose of the simple model being constructed in this essay the assumption will be allowed to stand.7. For example in Figure 5, with MSC1, at Q0 the congestion externality is equal to P2-P1, whilst with MSC2, the congestion externality is larger, P3-P1.
8. It should be noted that the congestion externality is also zero at a smaller network size in the region N<N*.
9. The increase in MSB is greater because it captures the aggregated benefits of reduced congestion rather than the increased benefits to an individual user.
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