###### Abstract
In Reference [12], the authors study the visiting time in a cultural space by considering various factors such as being first-time visitors, traveling with children, using a guidebook, being with a guided-tour, etc. The authors have used data that were collected via a global positioning system (GPS) as well as questionnaires distributed to visitors and concluded that the attractions with no admission charge are visited more than those with an admission charge. However, the visiting time is longer when the visitor pays for the visit. Additionally, in References [13; 14], the authors considered a cost optimization formulation to solve the planning problem and to determine the optimal tour for each visitor given a set of visitor preferences and constraints. From a more quantitative point-of-view, an extensive research effort to quantify QoE was initiated in Reference [15] where the authors studied the effect of smart routing and intelligent recommendations on visitors' QoE. In Reference [16], a holistic approach to the formulation and optimization of QoE functions was introduced. This identifies the most influential parameters that affect the QoE notion. Based on this, a human-in-the-loop approach was proposed in Reference [17] towards determining a physical, personal, and interest-aware museum touring approach that maximizes visitors' QoE. In Reference [18], the authors present a self-organizing mechanism for forming museum visitor communities, which exploits visitors' personal characteristics and social interactions and aims to enhance a visiting experience based on a participatory action research process. A location-aware recommender system is presented in Reference [19] where the authors make personalized recommendations to museum visitors based on classical observations, e.g., geo-localization over time as well as psychological and social aspects of visitors in relation to a museum's physical parameters. In addition, the proposed recommender system is characterized by its centralized operation where a central entity (i.e., the recommender system) takes decisions regarding the recommendation that should be proposed to the visitors without providing any intelligence or autonomicity to them. However, all the previously mentioned research efforts have focused on quantifying and optimizing the perceived QoE of visitors mainly via physical context parameters (e.g., museum size, placement of exhibits, etc.). They do not typically consider the impact of recommendation services made available by a museum on visitors' choices or on their optimal visiting time. Furthermore, they provide centralized approaches in order to formulate and optimize visitors' QoE. These may not scale well or may not even be feasible at all especially in a large cyber-physical social system because the decision-making process would require too much time for a stable outcome to be reached. In this paper, we address this particular issue in a formal and unified manner. The main goal of this paper is to introduce and design an optimization framework, which captures visitors' QoE in a quantifiable yet simplistic and manageable manner and determines the optimal recommendation selection for the visitors as well as their optimal visiting time for maximizing their QoE. Specifically, we rely on the iterative design and adoption of (i) a reinforcement learning framework to treat the problem of intelligent recommendation selection, and (ii) a game theoretic approach to determine the optimal visiting time of museum visitors, which is driven by their QoE in the museum. The latter approach was adopted due to the distributed nature of the optimization problem under treatment and the selfish behavior of visitors when maximizing their own perceived QoE, on one hand, and, on the other hand, based on the fact that the decisions of the various visitors are interrelated. Specifically, an increased visiting time of one visitor affects the perceived satisfaction (i.e., QoE) of the rest of the visitors in the museum since it increases the congestion in the museum.