The amount of international trade is rapidly increasing as a result of globalization. It is well known that as the size of a vessel becomes larger, the transportation cost per container decreases. That is, the economy-of-scale holds even in maritime container transportation. As a result, the sizes of containerships have been steadily increased for reducing transportation costs. In addition, various handling technologies and handling equipment have been introduced to increase the throughput capacities of container terminals. Quay crane (QC) that carries out load/unload operations plays the most important role among various handling equipment in terminals. Two typical examples of advanced QC concepts proposed so far are double trolley QC and supertainer QC. This paper suggests a method of estimating the expected value and the standard deviation of the container handling cycle time of the advanced QCs that involve several handling components which move at the same time. Numerical results obtained by the proposed estimation procedure are compared with those obtained by simulation studies. In order to demonstrate the advantage of advanced QCs, we compared their expected cycle times with those of a conventional QC.