درباره الگوریتم های قیمت گذاری برای سیستم های تحویل محتوای بسته شده

Businesses offering video-on-demand (VoD) and downloadable-CD sales are growing in the Internet. Batching of requests coupled with a one-to-many delivery mechanism such as multicast can increase scalability and efficiency. There is very little insight into pricing such services in a manner that utilizes network and system resources efficiently while also maximizing the expectation of revenue. In this paper, we investigate simple, yet effective mechanisms to price content in a batching context. We observe that if customer behavior is well understood and temporally invariant, a fixed pricing scheme can maximize expectation of revenue if there are infinite resources. However, with constrained resources and potentially unknown customer behavior, only a dynamic pricing algorithm can maximize expectation of revenue. We formulate the problem of pricing as a constrained optimization problem and show that maximizing the expectation of revenue can be intractable even when the customer behavior is well known. Since customer behavior is unlikely to be well known in an Internet setting, we develop a model to understand customer behavior online and a pricing algorithm based on this model. Using simulations, we characterize the performance of this algorithm and other simple and deployable pricing schemes under different customer behavior and system load profiles. Based on our work, we propose a pricing scheme that combines the best features of the different pricing schemes and analyze its performance.

The Internet is seeing an explosive growth in commercial activities. Downloadable software and multimedia are especially popular. One can think of scenarios where customers can download music, movies, and even books after online transactions. Video-on-Demand (VoD) is one such service in the Internet. However, in spite of the immense research interest in VoD over the last decade [1], [2], [3], [4] and [5], commercial efforts have failed to materialize. One of the possible reasons why they have failed until now is the lack of a good business model. Given the renewed interest in such services, it is very important to develop a sound business model. When the content is popular, and user interactivity is not required, using multicast [6] and [7] or broadcast [8] mechanisms to serve many users simultaneously improves scalability of the system. This is accomplished by a technique known as batching. Requests for the same content are aggregated over a period of time and then served in one single transmission using a one-to-many delivery mechanism such as multicast or broadcast. This benefits the content provider greatly because fewer resources are utilized at the cost of a small waiting time for the customers. In this paper, using analysis and heuristics, we develop a business model for systems implementing batching for content distribution. In our earlier work [9], [10] and [11], we have developed pricing models for systems that do not implement batching. Pricing must take into account customer valuations as well as resource constraints. Let us consider an illustrative example. Consider a content provider selling downloadable CDs. The number of CDs that can be downloaded from the web site within a given time frame is limited by the bandwidth and server resources available. Furthermore, the resources available cannot be arbitrarily increased. This is because, the demand (or request arrival process) in an Internet setting may not be easily predictable. For instance, a very exclusive and popular music album available at the web-site may increase demand for a short period of time, say a fortnight. Once the initial popularity wanes, demand (and hence request arrival rate) will drop. Long-term investments in high capacity links and server resources to meet the demand may therefore not be a practical solution. At the same time, short-term acquisition of server resources and bandwidth may not be possible. In such a situation, two questions arise: (1) can the content provider increase revenues during the peak times by serving the same number of customers for a higher price? and (2) can the content provider reduce the number of customers denied service1 during peak times by charging a higher rate for the service? These are interesting questions that need to be answered for successful deployment and acceptance of content distribution networks by the commercial world. Our objective in this paper is to answer the above questions by constructing a formal model for pricing content in a system with dynamic load patterns. To develop a thorough understanding of the fundamental problem area, we limit our considerations in this paper to a rudimentary, yet practically relevant, content delivery architecture. Our work presents essential findings, which provide the foundation for future extensions towards more complex scenarios. Even so, there are various choices for pricing the content: subscription-based pricing, quoted-price, sealed-bid auctions, etc. In this work, we restrict ourselves to a quoted-price model, wherein the content provider quotes a price to the customer. The customer may accept or reject the service based on his/her valuation of the service. We observe that if customer behavior is time invariant and well known, then a strategy of charging a fixed price can maximize the expectation of revenue if there are infinite distribution resources. When resources are constrained, fixed pricing may not maximize expectation of revenue. Nevertheless, there is usually a strong case for a fixed price because it is simple to implement. In this work, our goal is to explore the benefits of a dynamic pricing structure. We believe that subscription-based pricing coupled with a dynamic pricing scheme can address most customers’ concerns. Risk-averse customers can opt for the subscription pricing while other customers can opt for the quoted-price model. Since requests are batched, subscribers’ requests will not compete for resources with the quoted-price model customers. We formulate the problem of pricing in a batching system as a constrained optimization problem. We show that for some kinds of customer behavior, even when that behavior is well known, the problem of maximizing the expectation of revenue is intractable. In reality, customer behavior cannot be accurately known.2 We propose a framework to understand customer behavior parameters in such a situation. Using this framework, we develop a pricing algorithm. We also study other simple, yet effective pricing schemes3 that can be adopted in a content delivery system. Our objective in this paper is not to proclaim that one pricing mechanism is superior to another. Our aims are: (1) to understand the choices available to a content provider in a dynamic environment, and (2) to characterize these pricing options under different customer behavior and system load profiles. To this end, we perform simulations under different scenarios and evaluate the pricing schemes using two metrics: revenue and customer satisfaction (as measured in the number of requests denied due to lack of resources). Finally, we propose a hybrid scheme that combines the best features of different pricing schemes to improve revenue and system performance. The problem of pricing would appear to be very similar to the pricing problem at say DVD rentals or movie theaters. However, there is one significant difference that may prevent us from applying pricing strategies from such systems to a content delivery service. The crucial difference is that, all products in a content delivery system compete for common server and bandwidth resources. To illustrate this point, consider the case where a content provider has only enough resources to accept one request. Suppose that there are two requests—one for content A, where the customer is willing to pay $5 and the other for content B, where the customer is willing to pay $10. By rejecting the request for A (by quoting a price greater than $5), and accepting the request for B (by quoting exactly $10), the content provider generates more revenue. Thus, the content provider must intentionally over-price content A in order to increase the returns per unit resource consumed. On the other hand, in a conventional market, it would be counter-productive to intentionally over-price any of the content. This problem is therefore specific to a system with the characteristics just described. The rest of the paper is organized as follows. Section 2 briefly reviews related work. Section 3 presents our system architecture and batching model. Section 4 presents our theoretical results about maximizing the expectation of revenue in a batching system. Section 5 develops a customer behavior model and a framework for estimating the parameters governing the customer behavior. Section 6 presents a class of simple and effective pricing schemes while Section 7 characterizes their behavior using simulations. In Section 8 we discuss our insights and suggest ways to extend our framework to a competitive market with multiple QoS classes. We conclude the paper in Section 9.

We examined the problem of pricing in a content delivery system implementing batching. We noted that pricing must consider customers’ valuations as well as resource constraints. We observed that in the absence of any resource constraints, a fixed pricing strategy can maximize the expectation of revenue. We showed that this may not hold true when resources are limited. We formulated the problem of revenue maximization as one of constrained optimization and showed its intractability under certain conditions. Since customer behavior may not be known, we propose a class of non-increasing functions to approximate customers’ expectation to purchase products and discuss how the parameters governing this function can be ascertained. We also describe a pricing algorithm (MSEP) based on this mechanism. To better understand the dynamics of pricing, we studied the performance of six different pricing algorithms under different customer behavior and system load profiles. We discovered that the class of fixed pricing algorithms can generate high revenues, if there is some prior knowledge about customer behavior. In the absence of such knowledge, the revenue earned can be arbitrarily low depending on the customer behavior. In such situations, the MSEP algorithm yields consistently high revenues, at the expense of a high service denial rate. In contrast, a system load-based pricing algorithm (SP) has minimal service denial rate. We therefore combined the MSEP algorithm and the SP algorithm in order to generate high revenues with minimal service denial rate. We found that though there is some loss in revenue when compared with MSEP, the gains in terms of reduced service denial rate far outweigh the loss.