The on-line problem of k delivery-carts on a real line is studied in this paper, which is a generalization of the well-known k-server problem. How k delivery-carts serve a sequence of requests must be determined in an online manner. With the help of Position Maintaining Strategy (PMS for short), a competitive algorithm in a ratio of k + 2 has been obtained. Furthermore, another deterministic on-line strategy is proposed, namely, the Local Double Coverage Strategy (LDCS for short), and a competitive algorithm with competitive ratio k is achieved. Finally, a particular case concerning an elevator is analyzed and some results have been obtained.
