Allocation Rules

As discussed in subsection 2.4.2.2, the allocation rule has two main components: the objective function and the set of allocation constraints. In the current literature on auction- based approaches for composite service selection, there are two dominant formulations of the objective function:

1) Utility maximization:

This formulation includes all quality attributes and the price in the objective function. The aim is to maximize the utility (of the composite service execution) for the requester as in proposals by (Esmaeilsabzali and Larson 2005; Mohabey et al. 2007a; Watanabe et al. 2012) or maximize the utility across all participants including the requester and providers, as in the proposal by Blau et al. (2010). 2) Cost minimization (profit maximization):

This approach formulates the objective function only based on the price. Some proposals aim to minimize the cost for requester, such as works by Mohabey et al. (2007b), while some others maximize the profit for providers (more specifically, the willingness-to-pay of the service requesters) such as the proposal by Lamparter (2007).

The proposals following the first formulation mostly specify an objective function similar to the ILP-based global optimization approaches: maximizing the sum of the utilities of the end-to-end quality attributes (including the price) while taking into account the importance of each quality attribute for the requester through assigning a weight to the attributes, as discussed in subsection 3.5.2.

There are exceptions to this approach, such as the works by Watanabe et al. (2012) and Blau et al. (2010). Watanabe et al. (2012) has proposed a two-step approach. At the first step, a set of quality maximizing providers are selected for each task. As this selection is performed locally for each task, the second step aims to check and resolve the potential end-to-end quality constraint violations, through a round of negotiation with the set of selected service providers.

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Blau et al. (2010) has proposed an objective function that maximizes the utility across all participants, bidders and the bid-taker. The objective function is defined as:

𝑎𝑟𝑔𝑚𝑎𝑥_𝑓∈𝐹 (𝛼. 𝜑(𝒜_𝑓) − 𝒫_𝑓)

where 𝑓 ∈ 𝐹 is the set of services to be selected for a composite service request; 𝒜_𝑓 is the aggregated quality profile of the set of services 𝑓 that includes all quality attributes except for price; 𝜑 is a function that maps quality profile of 𝑓 to a score; 𝛼 is the requester’s maximum willingness to pay for the composite service; and 𝒫_𝑓 is the total price asked for the set of services in 𝑓.

To be selected, the set 𝑓 needs to maximize the difference between the price the requester is willing to pay for a composite service based on its quality profile and the price asked by providers to provision the composite service. The proposed objective function is different from other proposals in two aspects:

1. The objective function considers both sides; maximizes the willingness to pay of the requester for providers and minimizes the procurement cost for the requester;

2. The utility function is Simple Additive with respect to all quality attributes, except for price. This gives a score for the quality profile of the set of services which is multiplied by the requester’s maximum willing to pay.

As discussed in subsection 3.3, the main challenge for the utility maximizing formulation is elicitation of the weights for different quality attributes from the service requester. To address this problem, some researchers have formulated the objective function only based on price.

The price-based formulation excludes the need to specify the weights for quality attributes, and at the same time, provides enough support for service requester to specify their end-to-end quality requirements through adding extra constraints to the allocation rule. The price-based formulation assumes that service requesters generally have a clear understanding of what level of quality is acceptable for them, for example what should be the maximum response time of the composite service or its minimum availability. This assumption is less restrictive than the assumption about the weights for quality attributes, especially when more than two or three quality attributes are involved.

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Nevertheless, each formulation is suitable for a different group of service requesters. If a requester is interested in maximizing the quality of the requested service and they have clear understanding of the trade-off between quality attributes, the utility maximization formulation can be adopted. Whereas if the requester’s main concern is the cost of the procurement or they do not have specific preferences toward the priority of different quality attributes, the cost minimization formulation is suggested. Adopting such a perspective, He et al. (2014) has discussed both formulations, although the experiments only cover the utility maximization formulation.

As the set of allocation constraints to be included in the auction’s set of allocation rules, researchers have generally considered the requester’s constraints regarding the end-to- end quality of the composite service; for example constraints over the response time, availability or budget of the composition.

In addition to this set, Mohabey et al. (2007b) has proposed a constraint over the interface of the sequential services in a composition to ensure interface matching. However, their model assumes that providers have specified the interface of each service (with all its complexity regarding the data structures) by a global identifier which allows the model to match the interfaces against one another. There is no discussion on if such an assumption can be supported by the existing web service specification standards such as WSDL.