Auctioning Vertically Integrated Online Services: Computational Approaches for Real-Time Allocation

We develop three auction-based pricing and allocation solution methods for the case where a capacity-constrained online service provider offers multiple classes of unique, one-time services with differentiated quality. Consumers desire exactly one of the many service classes offered. We call such a setting a vertically integrated online services market. Examples of these services are webcasting of special events over the Internet, provision of video-on-demand, and allocation of grid computing resources. We model the pricing and allocation decision faced by firms in such a setting as a knapsack problem with an added preference elicitation dimension. We present a variety of computational solution approaches based on adaptations of the traditional greedy heuristic for knapsack problems. the solution approaches vary in efficacy depending on whether bidders are restricted to bid in one service class or allowed to bid in multiple service classes, as well as on the overall variability of the demand. In the case bidders can bid in multiple classes but are interested in consuming only one service class, a direct application of the heuristics developed for the single service case results in a nonfair allocation. We develop a novel data structure to eliminate the unfair allocation while maintaining the original computation complexity of the simpler setting. the paper contributes by presenting a menu of auction clearing mechanisms for selling vertically integrated online services. key woRds and phRases: auction-based pricing, online services, service classes, service computing, service pricing. we consideR the pRoBlem of pRicinG and providing vertically integrated online services delivered through the Internet. a vertically integrated service setting arises when consumers may have interest in several similar services, differing perhaps only in their quality levels, but are interested in consuming only one service. an example of vertically integrated services is the interactive webcasts of concerts, high-profile interviews, and sporting events such as international soccer and cricket matches, offered in text, audio, or full audio/video in a variety of bit rates, or even interactive format. typically, vertically integrated products are offered to differentiate and capture a wider market base by creating different quality versions of the same product [10, 20]. For such multimedia content-type services, we assume that the capacity provider is also the content owner and distributor. If that is not the case, we can maintain the structure of our results by simply assuming that the capacity provider factors in the appropriate licensing fees in his or her reserve price. auCtIONING VERtICally INtEGRatED ONlINE SERVICES 67 While immense strides have been made in developing and utilizing technical advancements of such technology, the analysis and understanding of dynamic pricing and allocation approaches required to facilitate emerging markets for vertically integrated digital services are still in nascent stages. We consider the case where a consumer would like to purchase only one of multiple quality differentiated services that are offered based on his or her preferences and budget. Despite recent technological advances, the lack of proper mercantile processes and associated preference elicitation mechanisms still precludes multiple quality differentiated services being widely offered. typically, a single (best-effort) level of service is the only option available for consumers even when the desired quality of service could potentially be delivered in a given service class. Further, the wide uncertainty in demand for unique one-time services coupled with the lack of economic incentives at the provider’s end makes it difficult to justify procuring server capacity to serve all customers at the desired service level. We propose an auction mechanism and develop a series of solution methodologies that allows a service provider to price and allocate multiple services, each at multiple quality levels, in a way that allocates the computational resources fairly to its customers. We expect our approach to be applicable to a variety of other digital service markets. these include: 1. Computational Grids and Peer-to-Peer (P2P) networks—Consider the case of a commercial storage grid operated by kontiki.com. the grid operator utilizes hard drive storage on networked pCs owned by consumers. the total capacity available to sell is variable over time and the consumers may have “hard needs” for immediate storage as well as some “soft needs” based on anticipated usage. the flexibility in consumers’ needs creates a vertically integrated market where total storage capacity available is constrained and the total demand at a given time establishes an appropriate clearing price. Similarly, consider a p2p bandwidth sharing market that can be facilitated by technologies such as Bittorrent (www.bittorrent.com). the Bittorrent framework uses a part of a consumer’s upstream bandwidth in exchange for downloading shared content. an auction-based vertically integrated market may be facilitated in this environment when a consumer might be willing to share variable amount of upstream bandwidth depending on the price [3, 13]. Bapna et al. [1] discuss how the bids can be specified in such a setting. the downloaders can bid for different bundles of data rates or, in the case of kontiki.com, different amounts of fixed and variable storage they are renting. the capacity constraint corresponds to the total amount of storage and bandwidth a sharer is willing to provide to the p2p network. 2. Business-to-Business (B2B) Video-on-Demand (VoD) Content Shelf Space— the issue of optimally managing the server capacity, or the “content shelf space” as it is referred to in the VOD industry, is also very important for firms that develop and deploy VOD servers in digital cable markets. Firms in these 68 BapNa, GOES, aND Gupta markets serve as intermediaries between content providers, such as ESpN and Disney, and consumers in specialized, high-bandwidth digital cable markets. In today’s environment, such firms have to consider what shows to carry in HDtV, with its variety of resolution levels and what to carry in SDtV format, and what to carry in both formats. this creates the vertically integrated service structure in this B2B market. the VOD server’s capacity is the critical link in maintaining the desirable service quality level with broadband broadcast technologies. 3. Asynchronous Transfer Mode (ATM) networks—In an atM network, quality of service refers to specific traffic-handling parameters that are adhered to for a given circuit. Essentially, it allows each individual circuit and traffic type to receive the support it needs, hence allowing voice, video, and data traffic integration over a single network. Because of the inherent flexibility provided by the virtual circuit concept, managing an atM network efficiently is a challenge because of the enormous number of choices available for setting the various operational parameters. although timeand service-sensitive accounting and billing are more appealing to customers, carriers and service providers tend to provide “flat rate” atM services, which typically lead to an inefficient allocation. Our work can be used to derive an “optimal” bandwidth allocation plan together with a pricing system, for real-time delivery of services such as videoconferencing and other digital streams. table 1 summarizes the two key components of the problem structure for the abovementioned examples. Entries in this table exemplify vertically integrated services where a service provider offers multiple service quality choices. users select one of these. Each row also specifies the corresponding resource constraint. We develop a series of computational methods that can be used by providers offering vertically integrated service to achieve the following: 1. a demand collection mechanism that allows the customers (consumers or other firms) to bid for the services, 2. a pricing mechanism that determines the final prices at each service level, 3. a capacity allocation mechanism that allocates the necessary server resources to customers in each service level, 4. the determination of the service mix to be provided with guaranteed quality levels at the server side, and 5. an optimization mechanism to maximize the total revenue from the available service mix for a given server capacity. We designate (1)–(5) as a real-time computational infrastructure for revenuemaximizing content providers. For analytical tractability, we assume that there are no network delays and last mile problems. For instance, content providers may have caching arrangements with companies such as akamai to push their content to the edge of the network. Our pricing scheme allocates the available server capacity among various competing services requiring different quality metrics. Note that in an environment where quality of service is not important, a best-effort model suffices and pricing of auCtIONING VERtICally INtEGRatED ONlINE SERVICES 69 services is not an important consideration. We also do not consider a time dimension to the demand. these will serve as natural extensions in the future. We formulate such a resource allocation problem as a knapsack problem with two additional constraints. users have values for the services offered and desire to be assigned a single service that consumes an exogenously specified amount of capacity. the total number of services, and the service mix, offered is constrained by the server’s overall capacity. the first additional constraint imposes the structure of an auction-based pricing mechanism, while the second is an assignment constraint that ensures that a consumer is at most allocated one quality level for a given service. the structural impact of the auction constraint is that the contribution of an individual item to the knapsack is no longer static and independent of the other items. While knapsack problems have been applied to a wide variety of scenarios such as capital budgeting, cargo loading, and cutting stock, and a variety of efficient heuristics that perform well in practice are well known (see, e.g., [5, 15]), the two additional constraints of our problem restrict the straightforward application of these techniques. Besides developing a novel market model for vertically integrated services, our computational infrastructure makes the following three major contributions. First, we modify the well-known greedy heuristics for the knapsack problem to account for the auction constraint for a nonvertically integrated service setting (where consumers are restricted to bidding in only one of the many quality-differentiated service classes). Second, we demonstrate that under different marginal valuation conditions, different knapsack heuristics perform better. Finally, we observe in the case of vertically integrated services (where consumers are allowed to bid in multiple quality–differentiated service classes, but have an interest in consuming no more than a single class) that a direct application of the aforementioned heuristics results in a nonfair allocation (e.g., an allocation where a bidder may be served in a less preferred class even when he or table 1. Resource-Constrained Vertically Integrated Services arise in a Variety of Settings Nature of vertically Setting integrated services Resource constraint Webcasting of Different bit rate video Streaming server’s capacity live events streams, audio streams, to serve simultaneous or textual commentary connections P2P file sharing Variable upstream P2P user’s storage and bandwidth a user is bandwidth willing to share Video-on-demand Distribution of HDTV, Video-on-demand server content shelf space SDTV shows to be streaming capacity carried by syndicators for resale ATM networks Voice, video, and data Circuit capacity traffic services 70 BapNa, GOES, aND Gupta she has a bid higher than a successful bidder in his or her preferred class). Moreover, ensuring that the assignment constraint is binding (i.e., consumer gets service in at most one quality) is computationally expensive. to overcome these challenges we construct a novel data structure that allows us to adapt the techniques we develop for the simpler nonvertically integrated case.