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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. [ABSTRACT FROM AUTHOR]

This paper deals with an M/M/c balking retrial queue with vacation. Both single and multiple vacation policies are analysed. This system is investigated as a quasi-birth-and-death process. Using the matrix-geometric method, we derive the useful formulae for computing the rate matrix and stationary probabilities. Various system performance measures are further developed in the matrix-form expressions. We construct a cost function to determine the optimum value of servers and the optimum mean service rate subject to the stability condition at minimum cost. Quasi-Newton method, Nelder-Mead simplex method and simulated annealing method are employed to perform the optimization tasks. Under optimum operating conditions, we provide the numerical results for a comparison of vacation policies. An application example is given to illustrate the system's potential applicability. [ABSTRACT FROM AUTHOR]

We consider the distributions of operating characteristics of an M[x]/G/1 queue under vacation policies, where the first customer of each busy period receives an exceptional service. When all the customers are served in the system exhaustively, the server deactivates and operates one of two vacation policies: (1) multiple vacation policy and (2) single vacation policy. We develop the performance measures for both systems. Finally, some numerical illustrations are also given. These two vacation models have potential applications in day-to-day life, such as post offices, banks, hospitals, etc. [ABSTRACT FROM AUTHOR]

This paper considers the optimal management problem of a finite-capacity M/M/1/K queueing system with-policy in which the server may break down while working. When the number of customers reaches its capacityK, no further arriving customers are allowed to enter the system. Customers are allowed to system with probabilitypor the customers are still unable to enter the system with probability 1 − pas the queue length decreases to a certain threshold valueF. By applying the birth-and-death process, some important performance measures are derived. A cost model, developed to determine the optimal continuous and discrete control parameters for the-policy at a minimum cost, and sensitivity analysis are also studied. [ABSTRACT FROM PUBLISHER]

This paper deals with the ( p , N )-policy M/G/1 queue with an unreliable server and single vacation. Immediately after all of the customers in the system are served, the server takes single vacation. As soon as N customers are accumulated in the queue, the server is activated for services with probability p or deactivated with probability (1 − p ). When the server returns from vacation and the system size exceeds N , the server begins serving the waiting customers. If the number of customers waiting in the queue is less than N when the server returns from vacation, he waits in the system until the system size reaches or exceeds N . It is assumed that the server is subject to break down according to a Poisson process and the repair time obeys a general distribution. This paper derived the system size distribution for the system described above at a stationary point of time. Various system characteristics were also developed. We then constructed a total expected cost function per unit time and applied the Tabu search method to find the minimum cost. Some numerical results are also given for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we consider a single-server retrial queue with constant retrial rate and batch arrivals, in which the unreliable server has the option to take an additional vacation after the first essential vacation. Customers arriving at the system according to a compound Poisson process are served immediately as long as the server is available; otherwise, they enter a retrial orbit and form a single queue. When the orbit becomes empty, the server leaves for the first essential vacation, after which he may either remain idle within the system or take one of J optional vacations. When the server is busy, he is subject to random breakdowns and repairs. It is assumed that the service times, repair times and customer retrial times are arbitrarily distributed. The implementation of the supplementary variable technique makes it possible to derive the probability generating functions of the system size distribution at a random epoch. We also develop a variety of system performance measures as well as two reliability indices. Finally, we deal with the problem of cost optimization and provide a number of numerical examples. [ABSTRACT FROM AUTHOR]