The appropriate control of maintenance effort in the edge computing based on open-source software (OSS) relates to stable and reliable operation, because the fault detection phenomenon depends on the effort expenditure. Actually, several software reliability growth models with testing-effort have been proposed in the past. In this paper, we propose cyclic Wiener process models to consider the network environment under the edge OSS operation. Then, we assume that the sawtooth wave and square one as the cyclic noises. Thereby, the proposed models will be able to comprehend two characteristics of OSS and network environment. Then, it will be useful to assess the operation effort expenditures with network environment of edge OSS service. Moreover, actual effort data sets are analyzed to show numerical examples of the proposed model considering the network environment under the edge OSS operation.