Recently, rapid development in the field of fog-cloud technologies leads the development and spread of new computing paradigms. Fog-cloud computing is an internet-based technology and with its rapid development, there has been a significant increase in such information users all over the world. This rapid increase in users has also brought many problems. One of the most important of these problems is the availability of the load balancer. Therefore, in this study, the failure and repair behaviour of the load balancer and its effects on the quality of service (QoS) are discussed with a mathematical model in order to obtain better system performance. Mean queue length, throughput and mean response time results for QoS parameters are presented. In addition, the solution approach used in this study clearly shows the flexibility and effectiveness of the proposed solution for such systems.