Ternary optical computer(TOC) has become a research hotspot in the field because of the advantages such as inherent parallelism, numerous trits, low power consumption, extendibility, bitwise allocability and dynamical bitwise reconfigurability. Meanwhile, its performance evaluation attracts more and more attentions from potential users and researchers. To model its computing ecology more accurately, this paper first builds a three-staged TOC service model by introducing asynchronous multi-vacations and tandem queueing, and then proposes a task scheduling algorithm and an optical processor allocation algorithm with asynchronous vacations of some small optical processors after dividing equally the entire optical processor into several small optical processors which can be used independently. At the same time, the analytical model was established to obtain important performance indicators such as response time, the number of tasks and utilization of optical processor, based on M/M/1 and M/M/n queuing system with asynchronous multi-vacations. In addition, relevant numerical simulation experiments are conducted. The results illustrate that the number of small optical processors, vacation rate and the number of small optical processors allowed to be on vacation have important effects on the system performance. Compared with synchronous vacation, asynchronous vacation not only ensures the system to obtain better maintenance but also improves the system performance to some degree.