Equilibrium strategies for overtaking free queueing networks under partial information

In this thesis, we are interested in finding equilibrium strategies for customers arriving at overtaking free queueing networks, only knowing partial information about the state of the system. The overtaking free condition does not allow customers to be overtaken by those behind them. We suppose that customers arrive at the system according to a Poisson process and that their service times at any queue are independent and exponentially distributed. Upon her arrival, the tagged customer is informed about the total number of customers in the system and chooses whether to join or not. Assuming that all customers follow the same strategy, the aim of the thesis is to find the equilibrium strategy that gives the maximum profit for any arriving customer. We show that such a strategy exists and is a pure or mixed threshold strategy. After analyzing the two-node tandem network and the multi-node tandem network, we focus on queueing networks with a branching structure, the so called tree networks. The work is extended with some numerical calculations, simulations and examples of non-overtaking free networks.