The single unreliable server double orbit Markovian retrial queue with customers’ balking behavior has been investigated. The arriving customers may not wish to proceed for the service when the system seems overcrowded. On joining the system, if the server is busy then customers are forced to join ordinary orbit or executive orbit as per their demand. It is assumed that the server is unreliable and subject to breakdown and repair. For the steady-state analysis of the system, Chapman–Kolmogorov steady-state equations are framed and then solved by using probability generating function. Furthermore, various performance metrics are derived explicitly. An illustration is taken to analyze the effects of the system parameters on the performance metrics. ANFIS technique is implemented to authenticate the steady-state results. Further, a nonlinear cost function is also formulated which is then minimized by using the quasi-Newton method.

研究了具有不言而喻行为的单一不可靠服务器双轨道马尔可夫重试队列。当系统似乎人满为患时，到达的客户可能不希望继续进行该服务。在加入系统时，如果服务器繁忙，那么客户将根据其需求被迫加入普通轨道或执行轨道。假定服务器不可靠，并且可能会发生故障和维修。对于系统的稳态分析，将Chapman–Kolmogorov稳态方程组框起来，然后使用概率生成函数进行求解。此外，显式导出了各种性能指标。举例说明了系统参数对性能指标的影响。实现了ANFIS技术以验证稳态结果。进一步，