Analysis of a pricing method for elastic services with guaranteed GoS

Journal of Service Science and Management, 2012, 5, 386-402 doi:10.4236/jssm.2012.54045 Published Online December 2012 (http://www.SciRP.org/journal/jssm) Analysis of a Pricing Method for Elastic Services with Guaranteed GoS Marcos Postigo-Boix, José L. Melús-Moreno Department of Telematics Engineering, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain. Email: marcos.p[email protected], [email protected] Received September 24th, 2012; revised October 26th, 2012; accepted November 10th, 2012 ABSTRACT Service Providers (SPs), which offer services based on elastic reservations with a guaranteed Grade of Service (GoS), should know how to price these services and how to quantify the benefits in different scenarios. This paper analyzes a method for evaluating the price of a service based on elastic reservations with a guaranteed Grade of Service. The method works as follows: First, the SP determines the requirements of the service that wants to offer; Second, the SP evaluates the average rate of the accepted elastic reservations of the service with a guaranteed GoS; Third, the SP calculates the price that guarantees the GoS with an aggregate demand function that depends on a demand modulation factor of the elastic reservations that is the mean reserved bandwidth, Bres; and Finally, the SP obtains the optimum value of the elasticity of the reservations that gives the maximum revenue, and the required access bandwidth in this case. The paper not only applies the method to a class i of elastic reservations when a linear-based demand and a revenue function are selected, but it also analyzes the influence of each one of the considered parameters. This method could be extended to the case of multiple classes of independent and guaranteed elastic services, applying the method to each service with its estimated demand and revenue functions. Keywords: Elastic Reservations; Streaming; GoS; Mean Reserved Bandwidth per Accepted Request; Aggregate Demand Function; Pricing; Revenue 1. Introduction Service Providers (SPs) want to estimate the revenue of the services that they provide that usually depends on the applied price to the offered services. Currently, the services that the SPs present treat to cover a wide spectrum of profiles in the aim to adjust them to the preferences of their different users. In that sense there exist users that request elastic services that could be delivered with variable bandwidth, that is, they assume that not always they could receive the same bandwidth for the requested service (the bandwidth reservation for the service is elastic and it fluctuates between a minimum and a maximum values). One example of this type of elastic service is the delivery of streaming video flows with different compression levels. Users want to get high-quality for their reservations, but also they could accept some tolerable degradation in the quality of their reservations if the reduction of the price for this service is significant. Elastic reservations require the support of new signaling mechanisms other than the most commonly used today, the resource ReSerVation Protocol (RSVP) [1]. As an alternative, the Next Steps in Signaling (NSIS) [2] protocol family allows to reserve bandwidth in a specific range. The Internet Engineering Task Force (IETF) created the NSIS Working Group in 2001 to solve new signaling needs for reservations. Since then, several Internet RFCs and papers have been published [3,4], including the QoS NSIS Signaling Layer Protocol (QoS-NSLP) that describes the procedures to signal QoS reservations between a Desired QoS and a Minimum QoS. In our scenario each one of them will respectively represent the bandwidth that the user wants to reserve and the minimum bandwidth that the user needs to work properly. Figure 1 shows the proposed scenario for the reservation of elastic services using the QoS-NSLP-based signaling mechanism. According to Figure 1, when the user wants to watch a video he access to the website where the SP lists their offered SLAs. In Figure 1, the SLA is defined by the Grade of Service (GoS) and other parameters such as the Desired and the Minimum QoS, which are respectively the highest (H) and lowest (L) bandwidth reservations for the service, and the elasticity of the reservations (  ). In this paper this parameter, for a class i, is defined according to (1). Thus, if the elasticity of the reservations is 0 the Desired and the Minimum QoS have the same bandwidth and the elasticity is 1 if Copyright © 2012 SciRes. JSSM Analysis of a Pricing Method for Elastic Services with Guaranteed GoS 387 Figure 1. Scenario of the reservation of elastic services based on the QoS-NSLP signaling mechanism. the Minimum QoS bandwidth is 0. In the scenario of video content distribution of Figure 1 the SP determines both values, the highest-quality (H) and the lowest-quality (L). Thus the elasticity for the reservations of class i would be: 1 ii LH i   (1) In this scenario, another important parameter that helps users to qualify and to differentiate among SPs is the reserved bandwidth per accepted request Bres,i. It represents the effectively reserved bandwidth of class i for each user within its specified range, that is, between the Hi and Li. In addition, the metric ,res i B defines the mean reserved bandwidth per accepted request, which establishes the mean size of the reservations of class i in the requested range. This metric represents a demand modulation factor of the accepted reservations in the sense that users would desire that the SP offered the value of this metric closer to Hi. According to Figure 1, the SP allows their clients to request elastic reservations with the same GoSi in an established bandwidth range for each reservation of class i. In this paper, some previous considerations should be done from the scenario described in Figure 1: First, the parameters GoS and ,res i B are related to the reservations of the class of service i. The reservations are represented by their length and their reserved bandwidth of the generated session. Thus, each established session is characterized by the time since the user asks for the reservation until the session ends up, and does not take into account the features of the packets transmitted during the session; Second, although many definitions have been used to evaluate the GoSi for a class i of service, the evaluation of this parameter here is based on the probability of obtaining an accepted reservation within the requested range; And third, all the reservations of class i, have the same priority. Figure 2 shows the entities involved in the scenario described in Figure 1. Thus the SPs, which may also act as Content Providers (CPs), offer for each class of service, class i, a guaranteed GoSi. In that sense the SPs should establish the appropriated agreements with the Network Providers (NPs) to buy the necessary access bandwidth that allow them to have the appropriated access bandwidth (Bi) in order to guarantee the offered GoSi. Therefore, in this paper, it is proposed and analyzed a method that evaluates the price of a class i of guaranteed elastic reservations related to some of the described parameters such as: its elasticity, its guaranteed Grade of Service, its mean reserved bandwidth and the available access bandwidth for the reservations. Qualitatively speaking it works as follows: First, the SP establish the characteristics of the service that wants to offer; second, the SP obtains the average rate of the accepted elastic reservations of this class, class i, with a guaranteed GoSi; third, the SP calculates the price of these reservations that guarantee the GoSi with a demand function that also depends on a demand modulation factor, ,res i B. This last parameter could be justified by the desire of users of paying more for the reservation when the value of ,res i B, is closer to Hi. And finally, the SP obtains the value of the elasticity of the reservations that gives the maximum revenue and the optimal bandwidth that maximizes the revenue for this elasticity. The pricing method for a class of guaranteed elastic service also could be extended to the evaluation of multiple classes of independent and guaranteed elastic services, applying the obtained expressions in this paper to each considered class. However Copyright © 2012 SciRes. JSSM Analysis of a Pricing Method for Elastic Services with Guaranteed GoS 388 Figure 2. Entities considered. this method is unable to evaluate and to analyze the case of dependent services, since to deduce the appropriate demand functions or to establish the relations between the variables that are involved in is very difficult task with the analytical tools used here. It is straight to deduce qualitatively speaking some conclusions, such as, the value of the established GoS for the reservations determines the accepted demand of the requested services. So, qualitatively speaking, if the guaranteed GoS is high the accepted requests will be less than if the guaranteed GoS is low and consequentially, the price of the service would increase for the considered access bandwidth. However, the SPs not only want to get qualitative results, but they also need to establish procedures to know how to quantify the price of these services and to create the appropriated scenario to offer them. Many questions could appear about the utility of this method for the SPs. Thus, the first one could be for them to try to identify the convenience of its implementation, that is, when this method could be appropriated to implement for elastic services? Other, without any specific order, maybe when the SPs don’t have enough resources (limited access bandwidth) and also, their users could accept some changes in the type of service they have requested. In this case, does the obtained revenue allow them to get what they want? Or even, will be the obtained revenue for the elastic reservations not far away or even better than for inelastic ones? Or, the same question could be formulated in other words, what should be the size of the resources (access bandwidth) that prioritizes the use of the elastic against inelastic reservations? How many users could access to the service using elastic reservations in comparison to the case of using inelastic reservations? What is the value of the elasticity of the reservations that gets the maximum revenue? etc. The method must allow answering these questions to the SPs with the aim of getting the solutions that best fit their requirements to price elastic reservations. In essence, this paper presents four main contributions:  An evaluation of the proposed pricing method that allows to assign price to multiple classes of independent and guaranteed elastic streaming services with the same priority and, according to some parameters such as the elasticity of their reservations, the available resources (access bandwidth), as well as, other parameters that define and establish the offered services and their demand functions. Each one of the independent classes could be evaluated following the same procedure as for a class i.  The analysis highlights the importance of the elasticity when the access bandwidth is limited, as well as the importance of its appropriated dimensioning, in order to maximize the revenue of the SP.  The analytical evaluation of the price assignation for a single class of elastic reservations, class i, is based on a closed-form expression that reduces the computational complexity of the Markov models.  The demand function for each service will depend not only on its price (€/reservation), pi, as usually is considered, but also on a demand modulation factor, ,res i B that also depends on the access bandwidth. Although the selected demand function in the paper is a linear-based function that depends on the price and the access bandwidth, it could be considered another Copyright © 2012 SciRes. JSSM Analysis of a Pricing Method for Elastic Services with Guaranteed GoS 389 one. In any case, the price will be finally obtained inverting this demand function. The remainder of the paper is organized as follows. Section 2 presents some research in this field and it is labeled as related work. Section 3 describes the proposed pricing method for services based on elastic reservations. Section 4 analyzes and applies the proposed method to evaluate the price assignation for a single class of elastic reservations, class i, when a linear-based demand function Di and a revenue function are selected, quantifying and highlighting the importance of the elasticity of the reservations and the available resources (access bandwidth) in the evaluation of the SPs revenue. Section 5 summarizes the main conclusions. Also this paper includes two appendices. In Appendix A, the GoSi and the mean reserved bandwidth per accepted request ,res i B are deduced by means a Markov-chain based model (based on quadratic computational complexity) and an approximate model (based on constant complexity). As the approximate model is very close to the Markov-chain based, the analysis of the method is done based on that because it allows understanding more clearly the relations among the parameters that use this method in the process of assigning prices in Section 4. In Appendix B, the price for a class i of elastic reservations is analytically deduced, taking into account the selected linear-based demand function Di. 2. Related Work This paper describes and analyzes a method that helps SPs to price elastic services with guaranteed GoS, selecting an aggregate demand function, D, that establishes the relation between the number of users that are willing to get the service and the price they pay for it. The price of each class of these services is based on: the average rate of the accepted class of elastic reservations with guaranteed GoS and their mean reserved bandwidth per accepted request, ,res i B. In [5] the parameters Bres,i and ,res i B were introduced and was also analyzed how is the influence of the value of the GoSi in their evaluation In that sense, the parameter ,res i Bis considered as a demand modulation factor for the price of the elastic reservations. This paper introduces the parameter ,res i B as a new component in the determination of the price of the elastic reservations and also carries out the analysis and calculation of the elasticity of the reservations that maximizes a chosen revenue function. Although many methods to price services have been proposed only a few are focused on elastic reservations but neither of them has jointly tackled the issues treated in this paper. For example, no papers assume the GoS as a constraint that affects the price of the services based on elastic reservations. Thus, in this section some papers that share part of the issues related in this paper have been revised. Reference [6] analyses the quantitative influence of the guaranteed GoSi in the evaluation of the mean reserved bandwidth for each reservation ,res i B. Additionally the paper proposes a method to establish the prices of two classes of elastic services, but differs from the paper presented here since the calculated price there didn’t have into account the influence of the user’s demand, that is, the price of the service always depend on the considered aggregate demand function. The proposal presented in this paper is totally different from the presented there, since here there is selected an estimated (linear-based) demand function for the service that establishes a relation with the price of the service and the ,res i B. Further, is also analyzed how the elasticity and the bandwidth affect the SP’s revenue. In [7] the same authors of this paper described a method to price substitute guaranteed services. There, it was selected an exponential aggregate demand function. The prices were found inverting their demand functions and knowing that in equilibrium it is accomplished that the value of the average rate of accepted reservations for each class of service, that maximizes the chosen revenue function, is equal to its aggregate demand function Di. Besides, the considered method, N classes of substitute services, was only graphically analyzed for the case of two substitute services, the access bandwidth and the elasticity of the reservations were fixed, the determination of the demand functions of the two substitute services, each one depending on the price of the other service, and the attainment of the pairs of the accepted demand (which were obtained by trial and error until they match an expression) that accomplished for both services the guaranteed GoS and maximized the revenue. Although in this paper the used method to deduce the price of the elastic services seems to be the proposed in [7], there are many substantial differences in its application. Thus, in [7] wasn’t presented any kind of analysis of the obtained results, due to the difficulty of getting them from the use of a Markov-chain based model. However, in this paper, the approximate analytical solution (closed form solution) allows to establish in a clear way the relationships between the parameters that intervene in the method in the process of pricing elastic services. This paper differs from the presented in [7] at least in three aspects: First, it only treats with one class of service, although the considered dependencies are more complex than there. In fact, the graphical results depend among other parameters on the access bandwidth and the elasticity of the reservations, what allows getting the elasticity and the access bandwidth that optimize the selected revenue function. Second, the demand function of the services depends not only on the price, but on a demand modulation factor, ,res i B . Third, the utilization of the method is based on an approximate analytical model (very close to the simulation model) used in the evaluaCopyright © 2012 SciRes. JSSM Analysis of a Pricing Method for Elastic Services with Guaranteed GoS 390 tion of the GoS and ,res i B , and different from the model used in [7]. Some papers present different methods to price elastic services but the proposed solutions that are described there are clearly separated to what is presented in this paper. Thus in [8], the authors present a combined study of price competition and traffic control in a congested network where the SPs set the prices in the aim to maximize their profits. In [9] the authors present a State Estimation based Internet traffic flow control system where the objective is maximize the aggregate bandwidth utility of network sources over their transmission rates. In [10], the paper focuses on the provider competition aspect, in a game theoretic setting, the traffic considered is elastic and there are multiple types of it and each type of traffic is sensitive to a different degree to Quality of Service (QoS). In [11] the authors design a framework that is composed of feedback signals and the corresponding source adaptation scheme to provide differentiated bandwidth service for elastic and inelastic applications. In [12], authors propose an appropriate prioritization pricing structure where users are provided with incentives and are able to choose between two service classes. In [13], authors present an integrated solution (integrating pricing into QoS routing) for enabling the next generation Internet to achieve the differentiated service and availability guarantee. Reference [14] describes in a wireless scenario an admission control algorithm that optimizes the revenue when the QoS is guaranteed. The price depends on the holding prices (bandwidth reserve), the usage price (average usage, the elasticity of the traffic) and the congestion price. References [15-17] present the issue of pricing related to different scenarios and further features for the offered services. Thus in [15] the authors briefly review the state of the art and technological growth of congestion control for integrated service networks since pricing is a proper tool to manage congestion, encourage network growth, and allocate resource to users in a fair manner. Reference [16] is one of the first books that treat conjunctly technology and pricing and, in reference [17] the authors present a recent classification of the proposed pricing methods in wireless networks. In references [18-20] different methods are presented to determine the user utilization function. Thus in [18], the authors propose a solution for bridging the gap between the existing theoretical work on optimal pricing and the unavailability of precise user utility information in real networks. In [19] users specify the utility or value they attach to different quantities of resource using a utility function, so the resource allocator knows the utility function of users at the time of resource allocation and then allocates resources based on the objective of maximizing the aggregate average utility obtained by unit time. In [20] each user is assumed to have a utility function which is a concave increasing function of the rate at which she sends data through the network. The problem is to find the vector of users’ rates such that the sum of all users’ utility functions is maximized, subject to resource capacity constraints. Other references evaluate how admission control affects the obtained GoS (considered as a technical constraint) of the services. These papers analyze not only the case of a class of service, but for multiple service classes. Thus in [21] authors pay their attention to the interrelation between pricing and admission control in QoS-enabled networks and propose a tariff-based architecture framework that flexibly integrates pricing and admission control for multi-domain Diffserv networks. In [22] a comprehensive survey about Call admission control in wireless networks is shown. In [23] authors say that traditional CAC schemes mainly focus on the tradeoffs between new call blocking probability and handoff call blocking probability. Therefore, they introduce the pricing as an additional dimension of call admission control process in order to efficiently and effectively control the use of wireless network resources. In [24] authors investigate the conditions where both BE traffic and traffic explicitly requiring QoS (Guaranteed Performance, GP) are present and they propose three CAC rules for the GP traffic. In [25] authors utilize admission control algorithms designed for revenue optimization with QoS guarantees to derive optimal pricing of multiple service classes in wireless cellular networks. Other authors analyze price assignation and propose solutions that work in different behavior. Thus in [26], it is described a scalable connection management strategy for QoS-enabled networks to tackle the problem of appropriately provisioning and allocating connections. In [27] is introduced a service model that provides per-flow bandwidth guarantees, where users subscribe for a guaranteed rate. In [28] authors consider the problem of pricing for bandwidth provisioning over a single link. The network administrator controls the resource allocation by setting a price at every epoch, and each user’s response to the price governed by a demand function. In [29] authors investigate the sensitivity of resource allocation and the resulting QoS to resource prices in a reservation-based QoS architecture that provides guaranteed bounds on packet loss and end-to-end delay for real applications. In [30] is considered the pricing and allocation issues of distributing digital contents via Web and P2P channels. Utilizing a game theoretic model, the allocation equilibrium with respect to various business goals is examined. In [31] is established a method to assign prices based on-packet queues sizes in the networks. 3. A Pricing Method for Services Based on Elastic Reservations This section describes the pricing method for multiple classes of independent and guaranteed elastic reservations. However, before going on with the method, it is Copyright © 2012 SciRes. JSSM Analysis of a Pricing Method for Elastic Services with Guaranteed GoS 391 convenient to take into account the difficulty of determining the aggregate demand function D i, which is a similar problem in many proposals of pricing services. The knowledge of this function in advance is always, as many researchers have pointed out, a very difficult task that the SP needs to solve. As it is known, the aggregate demand function usually represents the sum of individual demands of each user that have different willingness to pay for the service. It is hard to identify this behavior and therefore, the curve that shows the desire of the users to pay a price for the requested services. Thus, the SP has to estimate by whatever means it deems adequate (analytically, by simulation, heuristically, etc.) the demand function for each service. For simplicity, this paper assumes that in the evaluation of a service class of elastic reservations, class i in Section 4, the chosen aggregate demand function is linear-based. Of course, if the demand function changes, the quantitative results that the method obtains should be different. The outcomes of this method are the price pi and the value of the elasticity of each service ξi and the optimal bandwidth that maximize the SP’s revenue. The method consists of the following steps: The SP determines the service requirements that limit its feasibility. Figures 1 and 2 illustrate the first requirement: the SP wants to offer guaranteed and independent services based on elastic reservations. This implies that each service has to guarantee a particular GoSi, for the service of each elastic reservation with elasticity ξi that is determined by the SP in order to optimize its revenue. Also, the service requires a Desired QoS equal to Hi Mb/s and therefore, from (1), the Minimum QoS will be equal to i  1 i H    . Other requirement could appear from the available resources of the SP, that is, the access bandwidth for each independent service (Bi Mb/s). As each service allocates Bi, the sum of the reservations of all classes should be below this access bandwidth Bi. Bi may be limited due to several circumstances, such as the network access technology used by the SP to offer the service. The SP evaluates the maximum demand (in terms of requests per unit time) that can be allowed for the service in order to guarantee the requirements of step 1, the value of the GoSi for every offered class of independent elastic reservations. In this paper, we present in Appendix A.2 an analytical expression that roughly approximates the GoSi for the elastic services that are offered using an access bandwidth Bi. This expression has been validated by simulation and using the loss system model also included in Appendix A.2. The SP obtains the price of the service i that guarantees the GoSi. In order to obtain the price for the service, the SP needs to estimate the demand function Di by whatever means it deems adequate. This paper assumes a linear-based demand function, explained in Appendix B, that depends on the price and the mean reserved bandwidth ,res i B, (a demand modulation factor that is calculated in Appendix A.3). Since ,res i B is also dependent on Bi, the demand function is also defined in terms of the price of the service and Bi. The SP evaluates the revenue Ri using the obtained price in step 3 and finds out the elasticity of the reservations that maximizes the revenue. In addition, if bandwidth was not limited, the SP could obtain the bandwidth that optimally determines the service access bandwidth Bi. The revenue function, used in this paper, assumes for simplicity that only depends on the price, the rate of accepted requests and the cost of the access bandwidth. However, it is well known that more complex expressions, which may express part of the SP’s business model, could also be used. 4. Analysis of the Method: The Importance of the Elasticity of the Reservations and the Bandwidth on the SP’s Revenue In this section we apply the pricing method, described in Section 3, to analyze quantitatively how the price of a class i of elastic reservations and the revenue change depending on the elasticity of the reservations and the access bandwidth of the service. 4.1. Step 1: Determining the Requirements for the Service Before the SP applies this method, it should define the suitable parameters for each class of elastic service. Thus, in this paper it is assumed a guaranteed GoSi = gi, for all reservations, the same elasticity, and the highest bandwidth of the requested reservation range is Hi that is equal to the maximum required bandwidth to deliver the content (Btop,i). Specifically, it is supposed a guaranteed GoSi of 0.95, Hi = 1 Mb/s, and 3 minutes for the mean reservation holding time. Also, other parameters for the linear-based demand function as it is presented in Appendix B are: Dmax,i = 120 reservations/minute, Btop,i = Hi = 1 Mb/s and Pmax,i = 10€ . Step 2: Evaluating the maximum demand that guarantees the GoS. The SP calculates the average rate of the accepted reservations,  i, that guarantees the GoSi. Using the approximation (12) in Appendix A.2, the expression for the maximum accepted demand (2) is obtained.   1 GoS 11 ii iiii g i BH g   i        (2) Figure 3 shows graphically how the maximum accepted demand that guarantees a GoSi = 0.95 changes for different values of elasticity and bandwidth. If the elasCopyright © 2012 SciRes. JSSM Analysis of a Pricing Method for Elastic Services with Guaranteed GoS Copyright © 2012 SciRes. JSSM 392 ticity tends to 1, the demand tends to +∞, since the reservation requests always are accepted. On the other hand, if the elasticity is zero, the demand tends to a minimum value if bandwidth is fixed, since a reservation with elasticity 0 requires no less than Hi Mb/s. For the rest of combinations of bandwidth and elasticity,  i increases slightly for low-medium elasticity values and for high elasticity values  i increases sharply approaching to a vertical asymptote to +∞ for elasticity equal to 1. As Bi increases, the maximum accepted demand also increases in a linear way with a higher slope as elasticity approaches to 1. Also it is worth to mention that the values of the guaranteed GoSi, Hi and the holding time 1 i  have an impact on the maximum accepted demand. Thus, the lower they are, the higher can be the maximum accepted demand. with the maximum accepted demand. Regarding the guaranteed GoSi and according to (3) the price tends to be 0 as lower is gi. This is because the SP can guarantee a GoSi that tends to 0, even if the maximum accepted demand is considered. The Desired QoS,Hi, and the mean holding time of the reservations, 1 i  , make the price to increase if bandwidth is limited, since the required resources (bandwidth) also increases. Finally, the increasing of the maximum accepted demand Dmax,i, implies that the price augments in the aim toguarantee the GoSi and therefore, the average rate of accepted reservations decreases. On the other hand, an augment of the maximum price Pmax,i implies that the price increases since the willingness to pay of users also increases. 4.3. Step 4: Establishing the Elasticity of Reservations and the Bandwidth in Order to Maximize the Revenue 4.2. Step 3: Calculating the Price Appendix B describes the demand function for the analyzed service that depends on the users’ willingness to pay and a demand modulation factor (i.e., the mean reserved bandwidth per accepted request that is described in Appendix A). In this step, the SP obtains the price of the accepted elastic reservations that guarantee a GoSi = gi. This price can be obtained using expressions (2) and (19) when Btop,I = Hi. The SP calculates the revenue from the deduced price of the service that guarantees the GoS for this class of service, class i. In this paper, an intuitive revenue function Ri(4) is considered that have three terms: the accepted service’s demand DiGoSi, the price paid for the service pi and the cost of the allocated resources, which is supposed proportional to the access bandwidth. Alternatively, other more complex revenue functions [32] could be applied in order to include other special characteristics of each SP. Figure 4 shows graphically how the price pi changes for different values of elasticity and bandwidth. The price decreases to 0€ when the elasticity i  approaches to   GoS Cost λGoS € minute ii ii i iiiii RD p B pB      (4)  max, 1 1 342 Mb/s ii i i i BDHg B  , or similarly, when Bi approaches to The SP evaluates the revenue substituting in expression (4) the value of the price that guarantees the GoSi (3), the value of  i for ,top i i B   22 max, 113421 ii i i i i DH g    Mb/s . H(32), and the value of the GoSi (12), as it is shown in expression (5). A price of 0€ means that the GoSi is guaranteed even    2 max, max, 2 max, GoS 2 max, 1 1 11 11 1 01 ii i ii ii ii g i iiii i B PBD g HD p BDH g                    iiii i Hg  (3)     2 max, max, 2 max, 2 max, 1 1 11 11 11 11 ii iiii i ii i i i ii ii i i i i i BB PBBD g HHD R BBD                   iii Hg Hg   (5) Analysis of a Pricing Method for Elastic Services with Guaranteed GoS 393 0 200 400 0 0.5 1 0 1000 2000 3000  i B i (Mb/s)  i (req/min) Figure 3. Maximum demand for a guaranteed GoSi = 0.95 and Hi = 1 Mb/s. 0 200 400 0 0.5 1 0 5 10  i B i (Mb/s) p i (€) Figure 4. Price for a Guaranteed GoSi = 0.95 and Hi = 1 Mb/s. In the case that the SP has a limited bandwidth the elasticity of the reservations that maximizes the revenue, * i  is: max, max, max, 31 13 1 03 ii ii ii i i ii i BBDH HD g R BDH           i i g g  (6) Figure 5 shows graphically how the revenue Ri(5) changes for different values of elasticity and bandwidth and Figure 6 shows how the elasticity that maximizes the revenue for a Guaranteed GoSi depends on bandwidth. Analyzing expressions (5) and (6), it can be deduced that the revenue increases until the value of elasticity given by 1114 Mb ii B   0 200 400 0 0.5 1 0 100 200 300  i B i (Mb/s) R i (€/min) Figure 5. Revenue for a Guaranteed GoSi = 0.95 and Hi = 1 Mb/s. 0100 200 300 400 0 0.2 0.4 0.6 0.8 1 B i (Mb/s)  i * Figure 6. Values of the elasticity of the reservations that maximize the revenue for a Guaranteed GoSi = 0.95 and Hi = 1 Mb/s. demand Dmax,i, makes the revenue and the elasticity that maximize the revenue to increase and an increment of the maximum price Pmax,i, forces the revenue to increase, since the willingness to pay of the users also increases, but this effect has no impact on the optimum elasticity. The revenue for the optimum elasticity of the reservations is the following: max, max, max, max, max, max, max, max, 3 2 9 1 when 3 1 1 11 11 when 3 1 when . 3 ii ii ii ii iiiii i iii i ii ii ii ii ii i ii ii iii iii i B RP DgB H BDHg BB RP g HHD DHgB DHg RB BDHg                              s, if 114 Mb s i B. If bandwidth is higher than this value, the elasticity of the reservations will not provide any significant benefit in comparison with an inelastic reservation. The optimum value of the elasticity is different for each considered Bi and decreases as Bi increases. This behavior is due to the fact that an increment of Bi implies more resources that allow accepting more users with less elasticity in their reservations. On the other hand, if the SP is forced to use a pre-established price, the use of a lower gi can increase its revenue. The increase of Hi, and 1i  implies that the optimum elasticity augments. Finally, an increase of the maximum accepted ii B  (7) In the case that the SP has not limited bandwidth the value of the bandwidth that gives the best revenue, when Copyright © 2012 SciRes. JSSM Analysis of a Pricing Method for Elastic Services with Guaranteed GoS 394 is applied the elasticity of the reservations that maximizes the revenue. It further allows an optimal dimensioning of the access bandwidth Bi, is * i B and is expressed according to (8). * max, 2 max, max, max, * 2 max, max, max, 0 13 27 11 2 ii ii i i ii i ii i i ii ii ii i iiii P H PDg P BH H P H Dg PH    3 i i i                        (8) Figure 7 shows how the revenue * ii i R    (7) changes for different values of bandwidth. As it can be seen, the revenue has a maximum equal to 268.16€/min for i= 165.87 Mb/s that corresponds to B0 i    . The value of the optimum bandwidth i decreases with the increment of the price of the access bandwidth ( B i  ). 5. Conclusions This paper proposes a pricing method that helps SPs to assign suitable prices to multiple classes of independent streaming elastic services with guaranteed GoS. The paper determines the price of one class i of elastic streaming services taking into account the accepted average rate of reservations λi, with a guaranteed GoSi and, assuming a linear-based function as aggregate demand function Di. The SPs that want to offer elastic services should have to calculate their prices. In this process this method could help them in calculating them by means of defining or estimating in advance for these services some of the parameters that best could match their needs for the available resources. Some of them are: the value of the offered elasticity of the reservations ξi (it could be what offers the maximum revenue), the highest value of the reserva0100 200 300 400 -100 0 100 200 300 B i (Mb/s) R i   i =  i * (€/min) Figure 7. Optimum bandwidth for the elasticity of the reservations that maximizes the revenue for a Guaranteed GoSi = 0.95 and Hi = 1 Mb/s. tion Hi, this parameter is related to the maximum quality of the delivered content that the SP expects to give their users, the value of the guaranteed GoSi (this value could be set according to the value offered by other SPs or totally different) and the available resources (i.e., the access bandwidth, Bi). On the other hand an issue that could be difficult to determine is the aggregate demand function. However, it is known that the SPs have the appropriate tools to approximately estimate this function and to overcome this situation. The accuracy of this estimation is crucial to evaluate the price using this method. Currently we are developing simulation tools for estimating and establishing the profile of the users that could access to this type of services what would make possible to deduce appropriated aggregate demand functions in scenarios where the SPs could offer these elastic services. Also, we are also working on extending this method to the case of substitute services and to include different priorities to the reservations based on their elasticity. Finally it is our challenge to analyze the case of multiple classes of elastic services that are not independent, in this sense simulation tools are under investigation since analytic models to deduce the derived aggregated demand functions in this case and the relations between the parameters that intervene are really hard to find out. Future work should also include a deep revision and proposal of new revenue functions and consequently in the their evaluation, the value of the elasticity that maximizes their revenues and what should be the relation in each case among the elasticity, the access bandwidth and other parameters involved in the aim to get the maximum revenue. 6. Acknowledgements This work was supported by the Spanish Research Council under projects TEC2009-14598-C02-02, and the consolidated research group 2009 SGR 1242 funded by the Generalitat de Catalunya. REFERENCES [1] B. Braden, et al., “Resource ReSerVation Protocol (RSVP), Version 1, Functional Specification,” RFC 2205, 1997. http://www.rfc-editor.org/rfc/pdfrfc/rfc2205.txt.pdf [2] R. Hancock, G. Karagiannis, J. Loughney and S. Van den Bosch, “Next Steps in Signaling (NSIS): Framework,” RFC 4080, 2005. http://www.rfc-editor.org/rfc/pdfrfc/rfc4080.txt.pdf [3] J. Manner, G. Karagiannis and A. MacDonald, “NSIS Signaling Layer Protocol (NLSP) for Quality-of-Service Signaling,” RFC 5974, 2010. http://www.rfc-editor.org/rfc/pdfrfc/rfc5974.txt.pdf [4] J. Ash, A. Bader and C. Kappler, “QoS-NSLP QSPEC Copyright © 2012 SciRes. JSSM Analysis of a Pricing Method for Elastic Services with Guaranteed GoS 401 0 5 10 0200 400 0 50 100 B i (Mb/s) p i (€)  i (req/min) Figure 16. Particularized demand function for i  = 0, Dmax = 120 requests/minute, Pmax = 10 € and Btop = 1 Mb/s. 0 5 10 0200 400 0 50 100 B i (Mb/s) p i (€)  i (req/min) Figure 17. Particularized demand function for i  = 0.8, Dmax = 120 requests/minute, Pmax = 10€ and Btop = 1 Mb/s.      max, ,max, 2 max, 2 max, ,max, max, ,max, max, 2 max, 2 ,max, ,11 1 when , 1 1 , ,1 when , 11 ii iiii i i top i i ii iii ii itopi i ii iii ii top i i ii ii iii itopi i Dp DpB H BP Dp pP B H BP Dp DpB B BP pP DpHB BP                           max, , max, 1, ii top i ii DpB P        max, max, max, max, , max, max, ,1 1 when , 1 , ,0 when . i iii i i i iii i to ii iii ii p DpB D P p pP B D B P DpB pP             If : ,top i i BH      max, ,max, 2 max, 2 max, ,max, max, ,max, max, 2 max, 2 ,max, ,11 1 when , 1 1 , ,1 when , 11 ii iiii i i top i i ii iii ii itopi i ii iii ii top i i ii ii iii itopi i Dp DpB H BP Dp pP B H BP Dp DpB B BP pP DpHB BP                             max, 2 max, max, ,max, max, 2 max, ,max, max, 1, ,1 1 when , 1 , ,0 when . ii i ii ii iii i top i i ii iii i itopi i iii ii Dp H P Dp DpB H BP Dp pP B H BP DpB pP                  (32) Also, we can express the value of price as following. If   ,1 top i i i BH  :  max, max, max, max, 1 , 0 i ii i iii ii PD D pB D            i (33) If   , 1 iitopii H BH   :        max, , max, max, , 2 , max, max, max, , , max, max ,1 1 when 1, 1, 1 ,1 when , 1 , ,1 i iii i topi ii i ii iiiiii top i i top i i iii i iii iii iiiiii top i i i i iii i pBP B DH DHBH B B pBP DB DBH B B B pBP D                            topi   , max, , when , , ,0 otherwise. i i iiitopi i iii DB B pB         (34) pi (31) If : ,top i i BH Copyright © 2012 SciRes. JSSM Analysis of a Pricing Method for Elastic Services with Guaranteed GoS Copyright © 2012 SciRes. JSSM 402        max, , max, max, , 2 , max, max, max, , max, max, ,1 1 when 1, 1, 1 ,1 when , 1 , ,1 i iii i topi ii i ii iiiiii top i i top i i iii i iii iii iiiiii top i i i t i iii i i pBP B DH DHBH B B pBP DB DBH B H B B pBP D                            i   , max, , when , , ,0otherwise. op i i ii iiii top i i iii H DHB H B pB         (35)