Search

Abstract In many actual issues, such as call center and cloud service computing center, retrial systems have been widely applied to derive the performance measures. This study takes up a multi-server retrial system with partial servers synchronous vacation and customer geometric loss. An arriving customer finding no servers available either enters a retrial group according to first-in-first-serve discipline or balks. In the retrial group, only the first customer can retry for his service. A customer from the retrial group finding all servers unavailable decides either balks or reenters the retrial group. Partial servers may be on vacation simultaneously when they become idle at the moment of service completion and system conditions satisfy the administrative policy. This retrial system is analyzed as a quasi-birth-death process, and some general descriptors are developed. Optimization problems, including single-objective and bi-objective, are constructed to help the manager’s decision-making. Numerical results are displayed tabularly and graphically. A potential application in which the proposed model can be applied is provided. [ABSTRACT FROM AUTHOR]

Motivated by some real stochastic service systems, we study a feedback retrial queue with customer balking and unreliable servers (servers subject to breakdowns). A customer will either join a retrial orbit or balk if all servers are busy upon his arrival. After a service completion, the customer either leave the system or enter the retrial group again for additional service. The customer who is interrupted by the server failure will be served by another server if available; otherwise, he will be contacted later and treated as leaving the system. We use a quasi-birth-and-death process to analyze this system with almost all possible uncertain factors and derive major performance measures of the system. We also develop a cost function determining the optimal parameter settings of the system under the stability condition. Probabilistic Global Search Lausanne approach is employed in solving the optimization issue. The effects of parameters on performance measures of the system are examined numerically. Finally, we discuss the application of the model in the telephone medical consulting service system. [ABSTRACT FROM AUTHOR]

• A multi-criteria replacement policy under cumulative damage models is discussed. • The mean cist rate is formulated. • The optimal replacement policy is presented theoretically. • Numerical examples are provided. This paper investigates an extended replacement policy for a two-unit system subject to shocks and cumulative damage. As a shock occurs, the system suffers two types of effects: type I shock-effect is rectified by a minimal repair and type II shock-effect is removed by a corrective replacement. The probability of type II shock depends on the number of shocks from the last replacement. Each type I shock causes a minor failure of unit 1 and some damage to unit 2. These damages to unit 2 are additive and the system fails when the total damage exceeds a critical level L. A replacement policy (T, m, l) is considered in which the system is preventively replaced at age T or at the m th type I shock or at the time which the total damage to unit 2 exceeds a pre-specified level l ; and is correctively replaced either at the first type II shock or when the total damage to unit 2 exceeds a failure level L , whichever occurs first. The optimal policy that minimizes the expected cost rate is determined analytically. The proposed model extends several existing results. Our replacement policy is more general, flexible, and applicable in the real situations. [ABSTRACT FROM AUTHOR]