## 1 Introduction
Such systems with repairable servers have been extensively studied. However, in actual situations, to cope with a possible main server failure, the system may be equipped with a standby server. [PERSON] and [PERSON] [31] first introduced the concept of working breakdowns. When the main server is repaired, a standby server will replace the main server and serve new customers at a slower speed. Once the repair is complete, the main server is immediately back in the system and available. By allowing standby servers to provide services, the system can handle emergencies that may arise during the repair process and optimize system utilization. In addition, a working breakdown service can reduce customer complaints accruing that need to wait for the main server to be repaired and reduce the waiting cost for customers or work. Thus, working breakdown services may be a more reasonable repair strategy for unreliable retrial queues. In most retrial queues with two-way communication, the number of servers is almost assumed to be one. But such an assumption seems unrealistic in real life. The goal of this article is to carry out an extensive analysis of a multi-server retrial queue, subject to a synchronous working vacation with two-way communication and a disaster. This model has potential applications in telephone consultation health hotline service systems. A detailed application example is provided in Section 5. The main contributions and innovations of this paper include  
1. Most two-way communication retrial queues in the existing literature consider a single server. This paper proposes a multi-server, two-way communication retrial queue subject to a synchronous working vacation and a disaster. 2. When the supplementary variable technique for deriving the closed form of the steady-state probabilities is no longer useful, we use the matrix geometric method to perform the steady-state analysis. 3. We derive explicit mathematical expressions for each major performance index. Through a numerical analysis, this research provides critical managerial insights for system architects or executives to evaluate system performance indices. 4. We conduct a multi-objective optimization study on a two-way communication retrial queue, considering a synchronous working vacation and a server failure caused by catastrophic events. This is very useful and helpful for system architects or executives to design management policies. 5. We compare the retrial queue without two-way communication to the retrial queue with two-way communication in terms of the average time spent in the buffer. For both discussed retrial queues, we study the impact of the outgoing generation rate on the average time spent in the buffer. By adjusting the outgoing generation rate to analyze the average time spent in the buffer, we provide actionable insights that can help system architects or executives make a more informed decision regarding the challenge of whether a server should make an outgoing call. 6. We also compare the server idle rate of the two-way communication retrial queue without a disaster and the two-way communication retrial queue with a disaster. For both retrial queues discussed, we study the impact of disaster rate on server idle rates. By analyzing a server's idle rate by adjusting the disaster rate, we provide actionable insights that can help system architects or administrators make more informed decisions. We organized this article as follows. In Section 2, we describe the retrial queue under consideration. Section 3 is devoted to the mathematical model of the steady-state analysis. The system performance indices are discussed in Section 4. Section 5 describes an application example. Section 6 contains the numerical results in the form of tables and graphs. We conclude the work in Section 7.