Recently, there are so many researches on Autonomous Distributed Manufacturing Systems (ADMSs), where cooperation among agents is used to solve problems, such as the scheduling problem and the vehicle routing problem. We target ADMSs where an ADMS consists of two sub-systems: a Production System (PS) and an Autonomous Transportation System (ATS). This paper discusses an on-line Tasks Assignment and Routing Problem (TARP) for ATSs under conditions of given production schedule and finite buffer capacity. The TARP results in a constrained version of the Pickup and Delivery Problem with Time Windows (PDPTW), and this paper gives a mathematical formulation of the problem. This paper, also, proposes a cooperative algorithm to obtain suboptimal solutions in which no deadlocks and buffer overflows occur. By computational experiments, we will examine the effectiveness of the proposed algorithm. Computational experiments show that the proposed algorithm is able to obtain efficient and deadlock-free routes even though the buffer capacity is less.