Network and processing overhead associated with web services is a significant challenge to its performance. As a result, web service providers often announce a service level agreement. This ensures that consumers, who pay for the service, can get the service at a given quality level. In this paper, we study the competition between two providers offering functionally the same web services, where there is a monopoly service provider who offers a service that is complementary to their services. Each provider needs to decide a servicelevel (L or H) he/she would offer and a corresponding price for the selected service level to meet the QoS guarantee. We combine modeling constructs from game theory and queuing theory to propose a model that can provide useful insights to service providers about pricing and general competitive strategies.

Graham Higman published two important papers in 1960. In the first of these papers he proved that for any positive integer n the number of groups of order pn is bounded by a polynomial in p, and he formulated his famous PORC conjecture about the form of the function f(pn) giving the number of groups of order pn. In the second of these two papers he proved that the function giving the number of p-class two groups of order pn is PORC. He established this result as a corollary to a very general result about vector spaces acted on by the general linear group. This theorem takes over a page to state, and is so general that it is hard to see what is going on. Higman's proof of this general theorem contains several new ideas and is quite hard to follow. However in the last few years several authors have developed and implemented algorithms for computing Higman's PORC formulae in special cases of his general theorem. These algorithms give perspective on what are the key points in Higman's proof, and also simplify parts of the proof.