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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]

Natural ventilation of all the floors of a multi-story building may require a tall stack. To provide satisfactory ventilation flow rates for a multi-story building and to restrict the height of the ventilation stack, this paper proposes a hybrid ventilation scheme of mechanical ventilation in the upper-level floors and natural ventilation of lower-level floors with the stack pressure induced by the warm discharge flows from all of the floors. This scheme is achieved by connecting the lower-level naturally ventilated floors to the upper-level mechanically ventilated floors via a common stack. A model is developed to optimize the quantity of mechanically ventilated floors required to provide satisfactory ventilation rates for the lower naturally ventilated floors and also minimize the energy consumption. The applicable conditions associated with the ventilation scheme are expressed explicitly. The model predictions are validated against a computational fluid dynamics (CFD) simulation. The results indicate that the proposed scheme is effective at energy savings if the key engineering parameters are appropriately designed. A larger exhaust opening of the stack and an optimized vent area of the ventilated rooms are helpful to both the increase in the quantity of naturally ventilated floors and the decrease in the energy consumption. [ABSTRACT FROM AUTHOR]

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]

Abstract: The problem addressed in this paper is to compare the minimum cost of the two randomized control policies in the M/G/1 queueing system with an unreliable server, a second optional service, and general startup times. All arrived customers demand the first required service, and only some of the arrived customers demand a second optional service. The server needs a startup time before providing the first required service until the system becomes empty. After all customers are served in the queue, the server immediately takes a vacation and the system operates the (, )-policy or (, )-policy. For those two policies, the expected cost functions are established to determine the joint optimal threshold values of (, ) and (, ), respectively. In addition, we obtain the explicit closed form of the joint optimal solutions for those two policies. Based on the minimal cost, we show that the optimal (, )-policy indeed outperforms the optimal (, )-policy. Numerical examples are also presented for illustrative purposes. [Copyright &y& Elsevier]

Abstract: This paper analyzes the -policy M/M/1/K queueing system with working vacation and an exponential startup time. The -policy deals with the issue of controlling arrivals to a queueing system, and the server requires a startup time before allowing customers to enter the system. For the queueing systems with working vacation, the server can still provide service to customers rather than completely stop the service during a vacation period. The matrix-analytic method is applied to develop the steady-state probabilities, and then obtain several system characteristics. We construct the expected cost function and formulate an optimization problem to find the minimum cost. The direct search method and Quasi-Newton method are implemented to determine the optimal system capacity , the optimal threshold and the optimal service rates at the minimum cost. A sensitivity analysis is conducted to investigate the effect of changes in the system parameters on the expected cost function. Finally, numerical examples are provided for illustration purpose. [Copyright &y& Elsevier]

Abstract: Optimal values of the design parameters for a fin-tube heat exchanger of a household refrigerator under frosting conditions are proposed to improve its thermal performance and extend its operating time. In the optimization procedure, fin spacings of the heat exchanger are selected as the design parameters, and the average heat transfer rate, frost mass, and operating time are considered to be objective functions. The response surface and Taguchi methods are employed to optimize the design parameters. As a result, the average heat transfer rate and operating time of the optimum models increases by up to 6.3% and 12.9% compared to that of the reference model, respectively. [Copyright &y& Elsevier]

Abstract: This paper studies the M/M/1 machine repair problem with working vacation in which the server works with different repair rates rather than completely terminating the repair during a vacation period. We assume that the server begins the working vacation when the system is empty. The failure times, repair times, and vacation times are all assumed to be exponentially distributed. We use the MAPLE software to compute steady-state probabilities and several system performance measures. A cost model is derived to determine the optimal values of the number of operating machines and two different repair rates simultaneously, and maintain the system availability at a certain level. We use the direct search method and Newton’s method for unconstrained optimization to repeatedly find the global minimum value until the system availability constraint is satisfied. Some numerical examples are provided to illustrate Newton’s method. [Copyright &y& Elsevier]