Two Modest Proposals
for Improving the Economic
Efficiency of Colocation Facilities

Version 0.1
November, 2000
Bill Woodcock
Packet Clearing House

Today, the colocation industry finds itself amidst a wide range of adolescent growing-pains, and is devoting very little introspection to the task of understanding their causes.  Fortunately, the problems are typically those of scaling, sizing, pricing, and apportionment; in short, problems of success, rather than problems of failure, like crises of quality or lack of demand.  In a sense, these are problems which we are happy to be encountering.  Nonetheless, they must be understood and resolved if the industry is to progress forward into a state of maturity and stable long-term economic competitiveness.

Colocation and exchange facilities may tout the quality of their air-conditioning, the snazziness of their lobbies, the reliability of their power, or the intelligence of their remote hands, but all of those are incidental of the true business of the facilities: allowing extensions of as many different networks as possible to come together in such convenient proximity that they can make and shift physical, logical, and economic interconnection in a nearly frictionless environment.  Only within an environment where many competing vendors are present and the friction of change is low can a competitive market for network services exist.  Colocation and exchange facilities attempt to provide such environments.  Again, two conditions must be present to create value: first, many competing vendors must be present, and second, the cost both in dollars and in difficulty of creating and changing interconnections with those vendors must be very low.

There are many methods of decreasing the disincentives to change in interconnections; primary among them is the creation of a high-speed packet switching fabric over which participants may create logical interconnections without physically visiting the premises and interconnecting the two parties with a new cable.  Free access by all participants to switch fabric connections and decreasing the cost of physical interconnections are the most obvious and most commonly applied solutions to the friction-of-change problem.  This paper, however, addresses the other half of the equation: maximizing the number of participants at each facility.

Meta-Discussion of the Problem Area

Any discussion of maximizing the size of individual colocation facilities must begin by addressing the macroscopic issue of density and distribution of the facilities themselves.  Since demand is growing but finite, there are a fixed number of traffic-exchange participants within any geographic region at any time.  The number of colocation facilities they're divided among governs the average number of participants at each facility, and thus the value of the facilities.  The distance which each participant must carry traffic to reach a facility, however, governs their cost of participation.  So the two extreme cases are these: if only one traffic-exchange facility existed in the world, it would be extremely distant from most potential participants.  Thus although its value would be maximized, the barriers to entry would be prohibitively high for most potential participants.  On the other hand, if there were a potential exchange facility already colocated with each potential participant, the cost for each participant to reach a facility would be zero, but the value would also be zero, since there would be no one else there with whom to exchange traffic.

The natural consequence is that wherever there's a small region bounded by a step-function in the distance-sensitivity of data circuit pricing, for instance a LATA, there is likely to be an optimal number of exactly one exchange facility within that region.  If additional unconnected exchange facilities are placed in the same region, they cannibalize each other to detrimental effect, since any customers they take from other exchange facilities reduce the value of the other exchange facility more than they increase the value of the new one, thus reducing the overall value of all the exchange facilities in the region.  For example, if there are ten participants in one facility in a region, and each pays ten dollars to participate, the value each derives is 0.9, or nine peers divided by ten dollars.  Alternatively, you can invert the fraction to find the cost per peer.  If a second exchange facility is added, and two peers move to it, and two peers choose to participate at both facilities, the cost for eight of the peers is ten dollars, and the cost for two of the peers is twenty dollars, for an average cost of twelve dollars.  However now two of the participants have three peers, six of the participants have seven peers, and only two of the participants still have nine peers, for an average of only 6.6 peers each.  The average value of peering in the region, then, has plummeted from 0.9 to 0.55.  If we add a third peering point, the value drops still further, both by increasing the cost to anyone who tries to retain peers, and by decreasing the number of peers any participant can expect to reach at whichever exchange facilities they're at.  Obviously if the number of peers is growing faster than the number of exchange facilities, this effect is mitigated as only potential value is unrealized, rather than current value being destroyed.

So, having established that we want to pack as many participants into as few facilities as possible, how do we accomplish the efficient packing-in? 

Optimizing the Price of Space

Exchange facility operators have a number of cost components: space, cooling system, battery and generator power, staff overhead and specific labor, switch-fabric equipment, and a myriad of others.  All of these costs and a profit must be extracted from the customer/participant, however the pricing scheme must also be structured so as to encourage behaviors which enhance the value of the facility, and discourage behaviors which limit or degrade it.  Simultaneously, the pricing scheme must not be so complex as to confuse the customer, or so arbitrarily volatile as to scare the customer.  My first proposal pushes both of these boundaries a little bit.

For reasons which I won't address within this paper, it's economically disadvantageous for colocation facility operators to expand individual facilities within one region beyond contiguous or directly adjacent spaces.  Thus any particular operator should maintain exactly one facility within a region, and that facility is of finite capacity, which is measured in "U" or "rack units" of space, each 1.75" high, 19" wide, and approximately 30" deep.  The equipment which participants use to interconnect is engineered to fit within either 1U or a multiple of that. 

Each participant brings an extension of their network to the facility, and efficient use of the limited space in the facility suggests that the only equipment which the participant should place at the exchange facility itself is that which facilitates connection of the rest of their network to the other networks represented at the exchange facility.  That is, if they chose to leave a management workstation in the exchange facility, that would be relatively wasted space, since the management workstation could more easily be located in the participant's office, where it wouldn't pose a sacrificed alternative use of the space.  One may argue that if the participant has to pay for the space, it's not waste from the point of view of the facility operator, but that's fallacious: if that space were rented at the same price to a different customer, it would allow the presence of a new network at the facility, which would increase the value of the facility to all participants.  That's what's at the heart of this proposal: encouraging the efficient space-use by all participants, so as to maximize the remaining space and allow as many additional participants to come to the facility as possible.

Some structure is necessary to prevent a tragedy of the commons.  Since for any individual participant, the value of using additional space at the same price may be higher than the value of one additional peer at the facility, individual participants have no incentive under current pricing schemes to further the collective good, and thus can't reap their share of a collective benefit which far outweighs the benefit that they might derive from the additional space.  What's needed is a transparent and equitable scheme which ensures for all participants that not only they, but all the other participants, will forego wasting space in favor of allocating it to additional peers.

Specifically, we need a pricing formula which encourages each participant to occupy the minimum space necessary to connect their network to the switch-fabric, yet which allows the facility operator to avoid penalizing early adopters or failing to derive revenue from available space early in the process.

For the variables:

F = percentage of the facility which is already full, including this customer's allocation

N = number of rack-units of space allocated to this customer

O = per-customer overhead costs

P = price seed

Q = scaling factor

Y= price paid by this customer

The following equation allows us to set a per-customer overhead which must be recovered, adjust price seed and scaling factors, and derive a per-rack-unit price for customers of any size, dependent upon the amount of remaining space in the facility:

To see how this plays out, let's take a facility which has an overhead cost of $250/month to deal with a customer, chooses a price seed of $20, and looks at scaling factors of 1.15, 1.6, and 1.75 in (for the sake of simplicity) the degenerate case of an empty facility.  Note that the empty facility (1+(0/100)) produces a multiplier of one for Q, the scaling factor, allowing us to more easily see the effect of changes in the combined value of (Q(1+(F/100))).

     Reference                     Q=1.15                       Q=1.6                       Q=1.75         

       N   Cost                     N   Cost                     N   Cost                     N   Cost

                                        2   $294                     2   $310                     2   $317

                                        3   $321                     3   $366                     3   $387

                                        4   $348                     4   $434                     4   $476

                                        6   $407                     6   $602                     6   $710

      11   $495                    11   $565                    11   $1177                  11   $1579

      22   $990                    22   $950                    22   $3269                  22   $4720

      44   $1980                  44   $1802                  44   $8772                  44   $15284

      88   $3960                  88   $3695                  88   $26084                88   $50818

    132   $5940                132   $5741                132   $49675              132   $103060

    176   $7920                176   $7895                176   $78566              176   $170339

I also included for reference output from the following model, which is commonly used in the industry today, constrained to multiples of 11U, as is also currently an unfortunate common practice:

This reference model is a specific case of the model I suggest, using values of 1 for scaling factor, 0 for overhead and percentage-already-full, and $45 for the price seed.  1(1+0/100) evaluates to 1, so all non-linear price-scaling is absent from this scheme.  Because there's no base charge to account for overhead, operators utilizing this current scheme must enforce a minimum rental volume of 11U, which often far exceeds the needs of participants, guaranteeing a wasteage of space which could otherwise be allocated to a new participant.

Further Optimizing the Utility of Facilities Which are at Full Capacity

Approval voting for last available space, either anonymously self-categorizing, or for specific candidates.

Auctioning of last available space should theoretically produce the same result, since it’s of relatively little value to a potential participant to join an exchange dominated by their competitors, rather than potential customers and suppliers.  However, in a facility with 100 spaces and 99 participants, it seems more sensible to address the problem by optimizing the value to the 99 rather than to the one.

Acknowledgments:

Thanks to Pindar Wong for critical contributions to this document.