_{1}

This paper examines the effect of allowing prioritization of traffic on a congestible network under three demand scenarios. First, it is shown that when prioritization does not affect usage, average congestion on the network increases. Second, this result is shown to hold when there is demand shifting toward the prioritized network service but no impact on total network traffic. Finally, it is proven that for prioritization to reduce average congestion on a network it must reduce the total traffic on the network.

On February 26, 2015, the US Federal Communications Commission (FCC) revised their Open Internet rules. These rules outline three main sets of regulations. First, Internet service providers (ISPs) cannot block access to legal content. Second, they cannot throttle access on the basis of content. Finally, and subject to much debate, the FCC disallows paid prioritization. Paid prioritization would allow ISPs to divert capacity to some content over non-prioritized content in exchange for compensation from the content provider.

A number of recent papers debate that network neutrality and paid prioritization would have an effect on consumer welfare and capacity investment. Some argue that allowing service providers to monetize capacity though paid prioritization will cause them to invest in additional capacity and use their capacity more efficiently. Proponents of allowing paid prioritization include Chen and Nalebu [

In this note, I examine how network congestion would be affected by prioritized traffic for a given level of capacity. Three cases are compared. First, it is shown that when consumer usage of all network services is perfectly inelastic, prioritization of some traffic increases average network congestion. Second, this result is expanded to the case where total network traffic is inelastic but traffic shifts toward the prioritized service. Finally, it is proven that for prioritization to reduce average congestion on a network it must reduce the total traffic on the network. In other words, less congestion for the prioritized traffic is insufficient to reduce average congestion unless the corresponding increase in congestion on the non-prioritized traffic reduces demand for the network overall.

To model network congestion, I expand upon the seminal MacKie-Mason and Varian [

consumption vector

To include prioritization into the model, let there be one content provider,

Thus, to maintain congestion

From this equation come two key observations. First, the capacity is separable and constant-sum. Solving (1) for

Unsurprisingly, capacity diverted to the prioritized traffic as

The effect of increasing traffic for a non-prioritized service,

Theorem 1. Given average congestion without prioritization

This result presumes that demand for each of the services

Now, to simplify the notation, let a negative index on demand denote demand for all services except the magnitude of the index, e.g.

Theorem 2. For a given level of capacity

for all

While Theorem 2 states that when total demand is inelastic, prioritizing traffic increases the average level of congestion, the proof does not require that the guaranteed level of congestion for prioritized traffic be less than before prioritization (see Appendix). In fact even deprioritized traffic will increase the average level of congestion as long as it does not eliminate usage of the deprioritized service. As such, Theorem 2 states that to minimize the average congestion traffic on a network faces, Net Neutrality is the required policy.

When total demand for the congestible resource is not perfectly inelastic with regard to prioritized traffic, demand can either increase or decrease as prioritized congestion is reduced. Total demand may increase if prioritization of a given service attracts new users to the network. On the other hand, total demand may be reduced by prioritization if the corresponding increase in congestion for non-prioritized traffic sufficiently discourages network usage. Theorem 3 states that average congestion can be reduced only in the case where prioritization of some traffic causes total demand for the network to decline.

Theorem 3. Defining the average network congestion as

if and only if

^{1}

While this paper is agnostic on the efficiency of paid prioritization and network neutrality, it is strongly suggestive that any prioritization scheme will lead to higher network congestion. When the cost of changing network capacity is large, firms will alter their capacity infrequently. As such, capacity can be taken as a sunk investment and congestion will depend primarily on usage. As firms are unlikely to use prioritization to reduce demand for their network, the above results can be taken to show that in the absence of a net neutrality rule average congestion on the network will increase.

I would like to thank the participants at the 2015 Western Economic Association International session 27 for their invaluable suggestions.

SamuelRaisanen, (2015) A Note Regarding Prioritization on Congestible Networks. Theoretical Economics Letters,05,606-615. doi: 10.4236/tel.2015.55071

We want to show that combining all traffic to use capacity

mined by the remaining capacity. Formally stated this says, given

Proof. For temporary simplification of notation, let

Since

and because

Algebraic manipulation verifies that

As

Substituting for

Rearranging the definitions of

Proof. Given that

Additionally, this is a strict inequality whenever

Multiplying through by

From here adding terms

Proof. Each of the following implications is bidirectional and follows from

Given that

Dividing by