A stochastic model of the provision of guided tours to tourists

In this paper, we analyze a discrete-time Markov chain theoretic model of the provision of guided tours to tourists by a private firm. Specifically, we first determine the equilibrium probability distribution of the number of tourists in the guided tour providing firm's waiting room just before this firm begins to match tour guides with tourists. Second, we compute the long run expected number of tourists in this firm's waiting room. Finally, we ascertain the long run expected delay per tourist in the firm's waiting room.