Information station for customer navigation with escorting guides

Various service systems, such as hospitals, central train stations and libraries, operate an information station to guide incoming customers to their desired destinations. Classically, the guides installed at information stations only describe the route to the desired destination, while the customers are then required to look for the destination by themselves. However, the disadvantage of this regular guidance system is that customers can experience difficulties in following the navigational instructions, and as a result, might spend unnecessary time in looking for the destination. Thus, we investigate a different approach toward guidance, which has been implemented recently in some hospitals, according to which the guides, instead of just providing navigational instructions, escort the customers to the desired destination. We model such a service station as a three-dimensional quasi-birth-and-death process and derive its steady-state probabilities and performance measures using matrix geometric methods. By means of economic analysis, we consider three possible options for the system manager: (i) operating only a regular station; (ii) operating only an escorting station; and (iii) operating both types of station. We provide a scheme to choose the optimal option and to determine the optimal number of servers at each operational station, while considering customer preferences and strategic behavior.