In this work, we present our first simulation results on the start-up, functioning and stopping (dry-out) of the multi-branch pulsating heat pipe (PHP) accounting for the fluid-tube thermal interaction and bubble generation (boiling). A theoretical model that generalizes an earlier proposed approach is described. It is shown that the account of tube heat conduction changes substantially the simulated PHP behavior. In particular, in the presence of tube heat conduction, the simulated PHP cannot provide stable oscillations without bubble generation. While the bubble generation may not be directly involved in the development of first oscillations, its role is crucial in preventing the oscillations halt. The mechanism of the oscillation sustainment by bubble generation is discussed. The PHP simulation shows basic phenomena of bubble interaction and regimes observed experimentally in transparent PHPs. The PHP ceases functioning when the evaporator power is larger than a threshold. The liquid films are evaporated so the evaporator dries out completely and the oscillations stop; the evaporator temperature rises steeply.