This work considers a preemptive priority queueing system with vacation, where the single server may break down with imperfect coverage. Various combinations of server vacation priority queueing models have been studied by many scholars. A common assumption in these models is that the server will only resume its normal service rate after the vacation is over. However, such speculation is more limited in real-world situations. Hence, in this study, the vacation will be interrupted if a customer waits for service in the system at the moment of completion of service during vacation. The stationary probability distribution is derived by using the probability generating function approach. We also develop varieties of performance measures and provide a simple numerical example to illustrate these measures. Optimization analysis is finally carried out, including cost optimization and tri-object optimization.

The purpose of this study is to investigate an M/M/R retrial queue with geometric loss and Bernoulli feedback, in which all servers are subject to breakdowns and starting failures. After the completion of service, unsatisfied customers can join the retrial group with probability p or depart from the system with probability 1 − p . All servers may breakdown at any time, and the failed server undergoes repair immediately when a breakdown occurs. An arriving customer finding all servers unavailable (busy or down), will either join the orbit with probability b or leave the system with probability 1 − b . For such a queuing model, the authors apply the matrix‐geometric method to compute the stationary probabilities and develop system performance measures in the steady state. Moreover, they construct a cost model and formulate an optimisation problem of minimising the expected cost per unit time. Finally, numerical results are given for illustrative purposes.

In many industries and plants, a stable power supply system with acceptable cost/benefit is essential. This paper investigates the cost-effectiveness of an unreliable retrial system that includes standby generators and experiences the switchover failures of standby generators. Four different standby retrial configurations are included, and each configuration includes various numbers of primary and standby generators. Upon arrival, a failed generator is repaired immediately if the server is available; otherwise, the failed generator will enter into orbit. The server is subject to breakdown even when the server is idle. The explicit expressions of the mean time-to-failure and steady-state availability for each configuration are derived and compared. We also compare the cost/benefit ratio among four configurations. The developed results can provide managers with decision reference for stable power supply system and cost reduction.

The purpose of this paper is to explore the multiple-server machine interference problem with standby unsuccessful switchover and Bernoulli vacation schedule. Failure times of operating and standby machines are assumed to have exponential distributions and repair times of the failed machines and vacation times of servers are also assumed to have exponential distributions. After the completion of service, the server either goes for a vacation or may continue serving for the next machine. The vacation policy we considered is a single vacation policy. In practice, the switchover may experience a significant failure. The matrix analytical method and recursive method are employed to obtain the steady-state probability vectors, and closed-form expressions of some important system characteristics are obtained. The problem of cost optimization dealt with a number of numerical examples is provided by the Quasi-Newton method, the pattern search method, and the Nelder-Mead simplex direct search method. Expressions of various system characteristics are derived. Sensitivity analysis is performed numerically for system parameters. This paper presents the first time that machine interference problem with unsuccessful switchover for a group of repairable servers with vacations has been obtained, which is quite useful for the decision makers.

We study the multi-server machine interference problem with repair pressure coefficient and a modified Bernoulli vacation. The repair rate depends on the number of failed machines waiting in the system. In congestion, the server may increase the repair rate with pressure coefficient $\theta$ to reduce the queue length. At each repair completion of a server, the server may go for a vacation of random length with probability $p$ or may continue to repair the next failed machine, if any, with probability $1-p$. The entire system is modeled as a finite-state Markov chain and its steady state distribution is obtained by a recursive matrix approach. The major performance measures are evaluated based on this distribution. Under a cost structure, we propose to use the Quasi-Newton method and probabilistic global search Lausanne method to search for the global optimal system parameters. Numerical examples are presented to demonstrate the application of our approach.