## 3 Models and Preliminaries
### Recommendation Models and Policies  
As mentioned before, we assume that a museum offers different recommendations to the museum visitors that correspond to different levels of perceived QoE as well as different times allocated to a museum visit. We assume that more visitors will ask for an enhanced type of recommendation, which will increase the demand for the specific recommendation and create a longer waiting queue to obtain that service. Therefore, the recommendations can be characterized by a congestion control parameter \(c_{x},x=A,B,C\), which, among others, represents the potential waiting time for the specific recommendation type. In such a way, the visitor should consider the tradeoff of selecting an enhanced type of recommendation, which may increase his/her perceived satisfaction in a shorter invested visiting time [12]. However, the corresponding usage-based congestion of this recommendation may be further translated to the waiting time. In this paper, we consider and study for demonstration purposes and without loss of generality, three different indicative types of recommendations, which are generic enough and, in the following, are presented with an increasing level of QoE. * Recommendation A (\(R_{A}\)): The museum provides a map of the museum at its entrance without visitors waiting in long queues for this service. However, visitors may have to spend a lot of time in order to navigate themselves without guidance in the museum. Moreover, visitors perceived  
Figure 2: Visiting efficiency function for different visiting styles of the museum visitors. QoE, i.e., \(Q_{A}\), is limited because the information received about exhibits is based only on the corresponding text-tags attached to each exhibit, which provides relevant information about it. * Recommendation B (\(R_{B}\)): A facilitator is provided by the museum to navigate the visitors in the museum and provide additional useful information about exhibits. Visitors create groups when they arrive at the museum and a facilitator starts the museum tour with the group at specific timeslots. Therefore, museum visitors on average should wait a longer time than in the previous case in order for the group to be created and the touring to start. However, their perceived QoE, i.e., \(Q_{B}\) is increased when compared to Q\({}_{A}\) because they gain more information about exhibits and their visit is shorter and more efficient due to its structured and guided nature. * Recommendation C (\(R_{C}\)): Besides the previously described characteristics of the recommendation \(R_{B}\), the facilitator offers headphones to the museum visitors so that the information is provided in their native languages. Such groups are typically scheduled to start tours in sparse timeslots and, thus, their waiting time increases. However, the perceived QoE of a visitor, i.e., \(Q_{C}\), increases due to the enhanced obtained service. Based on the above description and without loss of generality, it is expected that \(Q_{A}<Q_{B}<Q_{C}\) in our proposed framework. Moreover, it should be noted that additional types of recommendations can be considered without violating the principles and application of the proposed framework. It is also highlighted that this ordering is not binding or restrictive for our framework and a different ordering could have been obtained. Thus, the (three) different recommendations considered in this paper are not restrictive at all neither in nature (what do they actually represent) nor in size (number of recommendation types) and a larger number of recommendations with different characteristics could have been assumed. For fairness purposes and in order to support the concept of the \"open museum to everybody\", we assume that all the above-described recommendations have the same cost (price) for museum visitors. Though actual pricing is out of the scope of our current study, the cost of each recommendation could be easily accommodated by our proposed framework if combined within the congestion control parameter \(c_{x},x=A,B,C\).