Model Parameters

Given that Service 1 is an existing service with a mature demand, we assume for sim- plicity that it operates at full capacity,i.e.,its provisioned capacity matches its realized

demand, X₁. The new service, Service 2, has uncertainty in its demand that is denoted

by a random variablex2with known distribution, fx2. We use the notationX2to indicate

a realization of this demand. The provisioned capacity (number of users the network can handle) for Service 2 is a decision variable denoted byKs2andKd2for shared and

dedicated networks, respectively4. If the demand for Service 2 exceeds the provisioned

level (X₂>K_i, i={s2,d2_}), network resources can be adjusted to accommodate a fractionα of the excess demand, i.e.,resources are increased toKi+α(X2−Ki). The

4_{A shared network is, therefore, provisioned to handleX}

parameterαorreprovisioning coefficient, represents the fraction of excess demand that

reprovisioning can capture. This fraction is assumed to be independent of the magni- tude of the reprovisioning effort. In other words, the feasibility of and latency in se- curing additional capacity are the same regardless of the amount of capacity requested (at least within some bounds), with the latter possibly affecting the network’s ability to retain all the excess demand that was present. This is consistent with the provisioning

process of most computing and communications facilities. Whenα=0,reprovisioning

is unable, e.g.,too slow, to capture any excess demand, while α=1 corresponds to a

scenario where reprovisioning succeeds in accommodating the entire excess demand.

In other words, when α=1, a “provisioning phase,” is unnecessary as resources can

be secured on-the-fly. Different levels of provisioning flexibility, e.g., as afforded by

different types of virtualization technology, can be accounted for by varying α. Of

interest, as discussed in Section 2.4, is the fact that changing α can also change the

outcome of the provider’s decision process,i.e.,which infrastructure yields the highest

profit. Note that α is not a decision variable for the provider; it is an exogenous sys-

tem parameter whose value depends on the reprovisioning technology available to the service provider.

An additional point which bears mention is that a linear adjustment toα can trans-

form our model to an alternative one in which a service provider can always accom- modate the entire excess demand, but pays a higher per unit capacity cost in doing so. This equivalence between the two models is shown in Appendix A.3.

Next, we describe and contrast revenue and cost components of shared and dedicated

networks. To facilitate comparisons, we follow the standard practice,e.g.,[25, 60], and

consider only the present value of all future revenues and costs.

Services generate revenues from subscription fees paid by users. These fees are as- sumed set based on exogeneous market factors. Offering a service also incurs a per user connection cost,e.g.,cost of enabling last-mile connectivity, installing end-user access

equipments, operational costs of billing, etc. We denote by p_s1 and ps2 the per user

contribution margins- price less the variable costs- for Services 1 and 2 respectively in

a shared network. Similarly, pd1and pd2denote contribution margins for the two ser-

vices in dedicated networks. We note that p_s1and p_d1can differ from each other. For

example, support for voice service in a FiOS network5(a shared network used to carry

voice, data and video) calls for network termination equipment that is significantly

more complex than that used in a traditional voice network, e.g.,the FiOS equipment

needs to come with a battery pack to handle power outages. This then translates into

ps1>pd1. We also note that implicit in the definition of individual contribution margins

for each service is the assumption that they are incurred independently for each service,

i.e.,there are no economies of scope associated with users subscribing tobothservices. This assumes that there is no bundling discount for subscribing to both services, and that per user connection costs are additive across services. This is reasonable in settings such as the FiOS example, where the bulk of the connection costs are in termination equipment specific to each service.

In addition to per-user connection costs, offering network services also involves

fixed andcapacitycosts. Upfront fixed costs are independent of demand and capacity levels, e.g., they include facility rent, research & development expenses. These costs

are denoted by c_s for a shared network, and by c_d1 andc_d2 when each service is de-

ployed on a dedicated network. Capacity costs grow with network resources; they are incurred upfront because of provisioning and may also be incurred subsequently during reprovisioning. Unit capacity costs for Service 1 are denoted byas1 andad1 in shared

and dedicated networks, respectively, and by a_s2 and a_d2 for Service 2. We use the

term return on capacity to refer to the ratio of contribution margin to capacity cost,

pi

ai, i={s2,d2}for Service 2,with a parallel definition for Service 1.

The values that the above parameters take in shared and dedicated networks are obvi- ously related to each other. These relationships can exhibit different levels of economies and diseconomies of scope. We illustrate this through the example of overlay and inte- grated networks, which represent two possible options for realizing a shared network.

An overlay involves limited use of an existing infrastructure to deploy a new network service. For example, early versions of the Internet were deployed as an overlay on the existing phone network. End-systems connected using modems to transmit data over existing phone lines, and early routers were interconnected using available telephony transmission facilities such as T1 and T3 links. Control functions of the nascent Internet

were, however, kept separate from those of the phone network,e.g.,the Internet relied

In general, when a new service is deployed by way of an overlay, the networks of the two services share a common infrastructure (that of Service 1), but remain largely decoupled from each other. This limits the diseconomies of scope that could arise from complex interactions between them, but it also precludes significant economies of scope.

In contrast, an integrated network solution will operate both services on a truly com- mon network infrastructure. For example, many cable providers with “triple-play” of- ferings, have upgraded their infrastructure (backbone network and cable access net- work) so that it can carry the voice, data, and video traffic from those three services. This required upgrading backbone and access routers to allow differentiation (and pri- oritization) of different traffic types, but allowed reuse of the same router platforms and transmission facilities for all three services. In other words, an integrated network solution offers opportunities for greater economies of scope, but often mandates more expensive equipment to handle the individual requirements of each service. This in turn can translate into higher diseconomies of scope. The model of Section 2.3.2 can be configured to reflect any combination of economies and diseconomies of scope be- tween shared and dedicated networks.