A differentiated service scheme to optimize website revenues

Abstract

We consider a website host server with web quality of service (QoS) capabilities to offer differentiated services. A quantitative modelling framework is set up to analyse the economic benefits of differentiated services and to build optimization models for managing the website host's connection bandwidth to the Internet (which is assumed to be the bottleneck factor determining the QoS). Three models are formulated corresponding to three operational scenarios to provide differentiated services. The first is for the marketing manager to classify visit requests as premium or basic when the information technology (IT) manager has already reserved bandwidths for the two classes, and the second is for the IT manager to allocate the total available bandwidth to each class when the marketing manager has already designated which visit requests are premium and which are basic. The third is for the joint optimization of request classification and bandwidth allocation when centralized coordination is possible. Analytic results are obtained for a special case that corresponds to very impatient customers requesting large amounts of data. Qualitative insights gained and numerical results obtained strongly support the implementation of differentiated services. More interestingly, the decentralized models that use simple and rough-cut rules yield solutions almost as good as the joint optimization model.

Appendices

Appendix A. Proof that expected speed G(λ) is decreasing in λ

Since z=λ/D₀, it is sufficient to prove that G(z) is decreasing in z. We can write the expected speed in a slightly different form as

Differentiating we find

where

Since the denominator of (A1) is always positive, we attempt to show that the numerator ν(z) is always negative in order to prove that G(z) is decreasing in z. We write

Taking m+n−1=k, this can be re-written as

Now, if

then . However,

From this, it now follows that if k is even, then grouping terms as above, we obtain and hence v(z)<0 which implies G′(z)<0.

If k is odd, let k=2s+1. Then, except the middle term in all other terms sum to a negative number. Since the middle term is

the lemma is proven. □

Appendix B. Proof that expected speed G(b) is increasing in b

First, we note that

Since

differentiating G(b) with respect to b, we find

where the numerator ν(b) is

with

It is easy to re-write the numerator as, . It is now possible to simplify the coefficient of z^u by grouping terms as follows:

Without loss of generality, we can assume m⩽u/2. Note that m=u/2 is possible only when u is even. Now, when m<u/2 we note that

So, C_m,u−m+C_u−m,m>0

Now, when u is even, we also need to consider the middle term in its coefficient, which is,

Thus, all the terms in the coefficient of z^u are positive, which proves the lemma. □