In many real-world systems, the vague information leads to inappropriate analysis. Generally, lack of sufficient knowledge of a process in random environment and vagueness of the whole system are two important challenges for modeling a system. Therefore, this chapter considers parallel queues systems with encouraged arrivals shared server. The various arrival rates, service rates, and processing times of jobs/tasks usually assumed to be uncertain. Hence, we describe the theory of queuing in a possible vague environment where encouraged arrival rates and service rates are considered to be uncertain numbers. Then, novel measures to handle vague information are employed. A bi-serial and two parallel servers linked in series are considered having vague parameters. Modeling such a system using specific techniques with respect to industrial application is purposed. In implementation, system characteristics are modeled using vague numbers and sensitivity analysis indicates the validity and effectiveness of the result. The proposed vague queue model is employed for a healthcare system to improve decision-making.