Internet Service Providers (ISPs) nowadays deal with high demand to promote good quality information. However, the knowledge to develop new pricing scheme that serve both customers and supplier is known, but only a few pricing plans involve QoS networks. This study will seek new proposed pricing plans are offered with QoS networks involved. The single link multi QoS Networks scheme is solved as an optimization model by comparing two models in multi QoS networks. The decisions whether to set up base price to be fixed to recover the cost or to be varied to compete in the market are considered. Also, the options of quality premium to be fixed to enable user to choose classes according to their preferences and budget or to be varied to enable ISP to promote certain service are set up. � 2013 Asian Network for Scientific Information.

This article will analyze new improved charging scheme with base price, quality premium and QoS networks involved. Sain and Herpers [5] already attempted to obtain revenue maximization by creating charging scheme of internet. The plan is attempted to solve multi service networks scheme as an optimization model to obtain revenue maximization using our improved model based on Byun and Chatterjee [2] and Sain and Herpers [5]. The results show that improved model can be solved optimally using optimization tool LINGO to achieve better revenue maximization. Better results are obtained in all cases rather than in [5]. The advantage of our new model is that ISP also can set up their base price and quality premium based on ISP preferences. For some cases for getting revenue maximization, we do not offer one service and just utilize some of the services.

The research on cardinality of polynomials was started by Mohd Atan [1] when he considered a set, V(f-;p?)={umodp?:f-(u)?0modp?}, where ? > 0 and f-=(f1,f2,?fn). The term f-(u)?0-modp? means that we are considering all congruence equations of modulo p? and we are looking for u that makes the congruence equation equals zero. This is called the zeros of polynomials. The total numbers of such zeros is termed as N(f-;p?). The above p is a prime number and Zp is the ring of p-adic integers, and x-=(x1,x2, ?xn). He later let N(f-;p?)=card V(f-;p?). The notation N(f-;p?) means the number of zeros for that the polynomials f-. For a polynomial f (x) defined over the ring of integers Z, Sandor [2] showed that N(f;p?)? mp12ordpD, where D ? 0, ? > ordpD and D is the discriminant of f. In this paper we will try to introduce the concept of symbolic manipulation to ease the process of transformation from two-variables polynomials to one-variable polynomials. � 2016 Author(s).

Internet Service Providers (ISPs) nowadays deal with high demand to promote good quality information. However, the knowledge to develop new pricing scheme that serve both customers and supplier is known, but only a few pricing plans involve QoS networks. This study will seek new proposed pricing plans are offered with multi service multi link networks involved. The multi service multi link Networks scheme is solved as an optimization model by comparing two models in multi QoS networks. The results showed that by fixing the base price and varying the quality premium or varying the base price and quality and setting up the equal capacity link values, ISP achieved the goal to maximize the profit. � Springer International Publishing Switzerland 2015.