Efficiency of Dynamic Pricing in Priority-based Contents Delivery Networks

Efficiency of Dynamic Pricing in Priority-based Contents Delivery Networks Noriyuki YAGI, Eiji TAKAHASHI, Kyoko YAMORI, and Yoshiaki TANAKA, Global Information and Telecommunication Institute, Waseda Unviersity 1 3 10 Nishi-Waseda, Shinjuku-ku, Tokyo, 169 0051 Japan Tel: +81 3 5286 3831 Fax: +81 3 5286 3832 Advanced Research Institute for Science and Engineering, Waseda University 17 Kikuicho, Shinjuku-ku, Tokyo, 162 0044 Japan E-mail: Abstract A large amount of content is frequently delivered to users in contents delivery networks. The traffic for this content causes heavy congestion, especially during peak-usage hours. If the content is delivered on a best effort basis during peak-usage hours in a transport network, users cannot estimate the download completion time when they start using a service. This problem can be solved by providing a guaranteed bandwidth service. However, to provide this in content delivery networks, the transport network requires a large capacity to deal with peak traffic even if many of the resources are not used in off-peak hours. To avoid the need to build additional capacity to meet peak usage demands, price incentives can be used to shift traffic from peak hours to off-peak hours efficiently. In a price based content delivery system, the tariff of several service classes is shown to each user in response to the user s request for content. Each user chooses one of the service classes according to his own need. By setting the tariff adaptively, a guaranteed bandwidth service can be provided without using extra capacity, and users who selected the guaranteed class can estimate the download completion time. In this paper, two pricing methods are proposed. One is a time functional method and the other is a waiting-time dependent method. These proposed methods are compared with a conventional fixed pricing method. We show that by using the proposed pricing algorithms, a traffic is balanced between peak hours and off-peak hours, and the sum total of users utility is increased. Key Words Contents Delivery, Quality of Service, Waiting Time, Pricing, Utility 1. Introduction Content delivery will become more popular in the near future and it is thought the traffic will become dominant in the network. There are many kinds of content that are delivered in services, such as HTML documents, pictures, softwares, movies, etc. In contents delivery networks, large-size content is frequently delivered. This traffic causes heavy congestion, especially during peak-usage hours. If the content is delivered on a best effort basis in a transport network, users cannot estimate the download completion time. This problem can be solved by providing a guaranteed bandwidth service. However, to provide this in a content delivery network, the transport network requires a large capacity to deal with peak traffic. However, many of the resources are not used in off-peak hours. Consequently, we propose a market-based approach which tries to shift the traffic from peak hours to off-peak hours efficiently. Using this method, a guaranteed bandwidth service can be provided without extra capacity and users can estimate the download completion time. This paper proposes two pricing methods: a time functional approach and a waiting-time dependent approach. Time functional pricing is a kind of spot pricing and waiting-time dependent pricing is a kind of dynamic pricing. In time functional pricing, the prices of off-peak hours and peak hours are set up separately. Users have to pay a high price if they need content delivered instantly during peak hours. On the other hand, the price is low in off-peak hours. Therefore, user s demand will be stimulated. It is thus necessary to predict accurate

traffic. If traffic prediction is wrong, the effect of this pricing method decreases. In waiting-time dependent pricing the prices are set up based on the current state of the network. Compared with time functional pricing, there is no need to predict traffic accurately. Since the price is set up according to the network state, the effect of pricing does not decrease in any particular situation. We compare these proposed methods with a simple fixed pricing method. In that system, a table of service levels and corresponding prices (tariff) is shown to each user at the start of each service and the user chooses one of the service classes. The effectiveness of these systems is evaluated from the viewpoint of the users utility. 2. Market-based Priority Control in Contents Delivery Network 2.1 Framework We consider the market-based content delivery system, which is shown in Figure 1. Let s look at the case of two service classes to simplify the problem. The priority class is the class that waiting time is guaranteed and non-priority class is the best effort class. First, a user request is sent to the server. Then, the server shows the waiting time, which is calculated from the congestion state of the network, and the price of a priority class. Each user then chooses one of the service classes shown in the tariff. The content is delivered so as to keep the waiting time that is promised at the start of each service. The price of the non-priority class is fixed to 0. On the other hand, the charge for a priority class is determined adaptively according to the congestion state of the network. The requests of the same class is delivered on the basis of a FIFO system. 2.2 Time Functional Pricing SERVER Figure 1 set tariff (1) request (4) content (3) selected class In the case of fixed pricing method, the congestion is controlled by setting prices higher. However, the users demands at off-peak hours also decrease. Time functional pricing does not have this problem and thus is often successfully used in telephone services by telecommunication common carriers. There is a day periodicity in a users demand pat- select service class (2) tariff USER Market-based Content delivery system. tern. Although time, day, week and month periodicity is also considered in spot pricing, we consider only time periodicity because this influences efficiency a lot for networks. Therefore, we consider time functional pricing. We define off-peak and peak hours, as shown in Figure 2. Let C 0 denote minimum price, ie. the price when the network is on off-peak hours. Let t denote the arrival time of the request. Then, price C of the priority class is defined as follows: C 0 0 t t 1, C = C 0 + a 1 (t t 1 ) t 1 <t t peak, (1) C 0 + a 2 (t t 2 ) t peak <t t 2, where a 1, a 2 is a constant value set up for the priority class. Let C max denote the maximum price, ie. the price when the network is congested. Then a 1, a 2 is decided as: a 1 = C max C 0 t peak t 1, a 2 = C 0 C max t 2 t peak. (2) 2.3 Waiting-Time Dependent Pricing In this method the price is set up to reflect the queue length in the buffer of the priority class. For time functional pricing it is necessary to predict users demand pattern accurately to achieve effective transmission of content. However, it is not efficient when the accuracy of the predictions deteriorates. On the other hand, waiting-time dependent pricing performs well without predicting the users demand pattern. To manage transmission of content, the number of each request and size of content are stored in the buffer.

Arrival Rate 3. Simulation Models 3.1 Network Model To simplify the problem, a single link with a total capacity of B as shown in Figure 4 is considered in the simulation. Off-Peak Time Peak Time Off-Peak Time USER 1 t 1 t peak t 2 Hours of the day SERVER B USER 2 Figure 2 Distribution of arrival rate. USER N 1.0 Figure 4 Network model. Price 0.8 0.6 0.4 0.2 0.0 0 W 1 W 2 W 3 W 4 W 5 W 6 Queue Length (Waiting Time) Figure 3 Price setting function for waiting-time dependent pricing. These requests are sorted in order of arrival. Requests for the priority class is delivered preferentially. The request for a non-priority class is delivered when there is no request in the buffer for a priority class. Then the queue length of the priority class data is given as: N Q priority = S j /B, (3) j=1 where B denotes the bandwidth of a bottleneck link in the content delivery network, where j = {1, 2,,N} and S j denotes the number of each requests of the priority class and the data size for each content. Prices are set up by calculating the waiting time and refering to Figure 3. 3.2 Traffic Model To simplify the calculation it is assumed that the arriving packets follow a Poisson distribution. Let us assume that the standardized mean arrival rate of requests for content is given as shown in Figure 5, where λ and λ 0 are the mean arrival rate and the mean arrival rate during the off-peak hours, respectively [2]. Demand Pattern 1 of the call arrival rate, shown in Figure 5, was given by two test services of VoD [3], [4]. Moreover, Demand Pattern 2 used in the simulation to examine the case when the accuracy of the demand prediction deteriorates. Then, λ 0 is decided as: λ 0 [1/sec] = R[1/day]/(36 3600), (4) where R is the number of average demands during the day. 3.3 User Model User s Utility The utility function is used to measure how a user evaluates the priority service class shown in the tariff. Let W denote the waiting time shown in the tariff. Let us define the user s utility function U(W )as[5]: U(W )=Dexp( kw), (5) where parameter k (k > 0) expresses the sensitivity of each user against the waiting time. When the value of

Arrival Rate λ/λ0 6 5 4 3 2 1 0 Demand Pattern 1 Demand Pattern 2 t 1 t peak t 2 0 6 12 18 24 Hours of the day The values of parameters a 1, a 2 of Equation (1) are given by substituting the values of C 0 and C max for Equation (2). 3.5 Waiting-Time Dependent Pricing The waiting time is partitioned off by 5 [min] and the price is set up for each section. Let l = {1, 2,,n} denote the ID of sections for waiting-time and C l the price of section l. The price of each section is set so as to fulfill the following conditions. Figure 5 rate. Distribution of standardized mean arrival 3.6 Parameters 0 C l 1, C l C l+1. (8) k is larger, the user s utility decreases rapidly when the delivery time becomes longer. On the other hand, if the value of k is close to 0, a user s utility has only a small influence on the waiting time. Parameter k can be statistically estimated by opinion tests [5]. In the simulation, however, we assume that there are many kind of users and we investigate the total utility when the value of k changes. Moreover, the parameter D expresses the user s utility at the time W = 0. Since each user has his own valuation on the service, the value of D is given randomly on (0,1]. User s Behavior Let us suppose each user behaves like the following as determined by prices. Let us define payoff H s to user s as [6]: H s = U(W ) C, (6) where W and C denote the waiting time and charge for the priority class shown in the tariff. When the payoff for priority class is positive he will select the priority class. And when the payoff is zero or less he will select the non-priority class. 3.4 Time Functional Pricing The parameters of Equation (1) are set as following. The parameters are t 1 = 18, t 2 = 24 and t peak = 21, as shown in Figure 5. Moreover, the parameters C 0, C max of Equation (2) are set up to fullfill the following conditions. 0 C 0,C max 1, C 0 C max. (7) Individual parameters used in the simulation are shown in Table 1. Table 1 Parameters. Parameter Value k [0.1,0.9] R 747 number of service classes 2 size of each content 650 MB capacity of bottleneck link 50 Mbps 4. Simulation Results 4.1 Optimal Price Set Time functional pricing Table 2 shows the set of optimal prices for Demand Pattern 1. The sum of users utility is maximized when we set the price according to Table 2. Parameter k is changed by 0.1 on[0.1, 0.9], and the optimal price set is calculated for each value of parameter k. The optimal price set is not so dependant on the value of k, as shown in Table 2. Waiting-time dependent pricing We calculated the optimal price set for waiting-time dependent pricing for Demand Pattern 1 for each value of k. Next, we derived the approximated curve of the optimal price, shown in Equation (9). The ratio of total users utility when using the optimal price set and when using the approximated curve is 1.00 : 0.99 at any value of parameter k. Therefore, Equation (9) can be used to get the approximation of the optimal price whatever the value of parameter k.

C(W )=0.2542Ln(W )+0.8937. (9) Table 2 Optimal Price Set for Time Functional Pricing. k Off-peak price C 0 Peak Price C max 0.1 0.15 0.60 0.2 0.15 0.60 0.3 0.15 0.60 0.4 0.10 0.70 0.5 0.10 0.70 0.6 0.10 0.70 0.7 0.10 0.70 0.8 0.10 0.70 0.9 0.10 0.70 Standardized total utility 1.10 1.08 1.06 1.04 1.02 1.00 0.98 Standardized total utility for Demand Pat- Figure 6 tern 1. Fixed Pricing Time Functional Pricing Waiting-Time Dependent Pricing 0 0.2 0.4 0.6 0.8 1 Parameter k 4.2 Comparison of Pricing Methods With Users Utility Figure 6 shows the relationship between the standardized total users utility and parameter k for Demand Pattern 1. Comparing fixed pricing with the two proposed methods, we can increase the sum of a users utility by using proposed methods. This is because the proposed methods can balance traffic load by setting prices adaptively while fixed pricing cannot. The proposed methods are more effective when the value of k is larger. This result suggests that when each user s utility is greatly influenced by the waiting time the proposed methods become more effective. Comparing the time functional and waiting-time dependent pricing systems, the values of the sum of users utility are almost the same. This result suggest that spot pricing performs as well as dynamic pricing when we can predict the demand pattern accurately. 4.3 Robustness Against Variations in Demand Pattern To analyze the robustness of the pricing methods againt deterioration of demand prediction, Demand Pattern 1 is used for the first 15 days and Demand Pattern 2 is used for the latter 15 days. However prices are optimized for Demand Pattern 1 in this simulation. Figure 7 shows the relationship between the standardized total users utility and parameter k. Comparing fixed pricing with the two proposed methods, we can increase the sum of a users utility using proposed methods similar to the results shown in 4.2. Waiting-time dependent pricing performs better than time functional pricing. This result suggests that dynamic pricing performs better than spot pricing when the accuracy of the demand prediction is lower. Standardized total utility 1.06 1.05 1.04 1.03 1.02 1.01 1.00 0.99 Standardized total utility for Demand Pat- Figure 7 tern 2. Fixed Priceing Time Functional Pricing Waiting-Time Dependent Pricing 0 0.2 0.4 0.6 0.8 1 Parameter k 5. Conclusion We focused on market-based content delivery systems and proposed two adaptive pricing methods: a time functional pricing method and a waiting-time dependent pricing method. First, we compared these two methods with fixed pricing from the view point of the user s utility. Using the proposed systems each user selects one of the service classes in accordance with his own valuation of the content and traffic load can be balanced in an efficient manner. On the other hand, since the prices are fixed in fixed pricing, the traffic load cannot be balanced efficiently. Therefore, the

sum of a users utility increases by the proposed methods. Second, we compared time functional pricing with waiting-time dependent pricing for when the users demand can be predicted correctly. The values of the sum of a users utility were same for time functional pricing and waiting-time dependent pricing. This result shows that same effect occurs for spot and dynamic pricing when traffic is predicted accurately. Third, we examined what happens when the accuracy of prediction deteriorates. In this case waiting-time dependent pricing performs better than time functional pricing, as the sum of a users utility of the time function pricing depends on the accuracy of the prediction. From the simulation results when the price is set statically, exact predictions are required to achieve an efficient transmission. Moreover, when the users demand is unpredictable, efficient transmission can be achieved by dynamic pricing by setting prices according to the state of the queue length in the buffer. The easy model was used in this examination to simplify the calculation. It is left for further study to use more realistic models. We have to take into account background traffic, however. It is difficult to keep the service level agreements completely because we would have to predict background traffic exactly. The assumptions of users behaviors in corresponding to the prices should be verified statistically. and Y. Tanaka, Waiting time versus utility to download images, 2001 Asia Pacific Symposium on Information and Telecommunication Technologies (APSITT2001), pp. 128-132, November 2001. [6] R. Gibbons, Game theory for applied economists (in Japanese), Sobunsha, July 1995. References [1] J. K. MacKie-Mason and H. R. Varian, Pricing the Internet, Public Access to the Internet, The MIT Press, 1995. [2] N. Kamiyama, An efficient transmission protocol for multicast video-on-demand system (in Japanese), IEICE Technical Report, SSE2000-252, IN2000-208, March 2001. [3] Haar P.G. de, et al., DIAMOND Project: Video-on-demand system, and trials, Eur. Trans. Telecommun., vol. 8, no. 4, pp. 337-344, 1997. [4] Bell Atlantic, Fact sheet: Results of Bell Atlantic video services video-on-demand market trial, Trial Results, 1996. [5] K. Nomura, K. Yamori, E. Takahashi, T. Miyoshi,