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This investigation presents a Markov model for the performance analysis of the fault tolerant machining system with failure-prone server and supported by warm standbys. To utilize the server's idle time, provision of server's working vacation has been done which make the system cost effective. The online and warm standby machines may fail and can be repaired by a single skilled repairman. Due to capacity constraint, when the system reaches its full capacity, no more jobs for repairing of failed machines are allowed until the workload of repair jobs reduces to a threshold level 'F'. Before initiating the repair of the failed machines in case of coming back from the vacation state, the server requires the setup time. To make system fault tolerable, apart from standby provisioning and repairing of failed machines, the concepts of reboot and recovery are included for the formulation of Markov model. The various performance measures including the reliability indices are derived by using the transient probabilities which are computed using Runge–Kutta method. By taking a suitable numerical illustration, various system indices are examined with respect to different parameters. The computational tractability and sensitivity analysis carried out for the established metrics will provides valuable insights for the maintainability and up-gradation of the existing machining systems. [ABSTRACT FROM AUTHOR]

Due to rapid growth of today's technology in fast speeding digital networks and industrial organizations, there is a need to develop a model which proves to be useful in handling designing issues of computer and telecommunication systems and many other related digital systems. To accomplish this, we have made an attempt to provide a remedy for modeling some discrete-time (digital) systems of day-to-day life viz. Broadband Integrated Services Digital Network (BISDN), Asynchronous Transfer Mode (ATM) and related computer communication technologies, wherein the models for continuous-time queues fail. This is due to the fact that the discrete-time systems are more appropriate than their continuous-time equivalents to model digital systems. In these systems, time is treated as discrete random variable and is measured in fixed size data units such as machine cycle time, bits, bytes, packets, etc. In this study, we analyze a Geo/Geo/1 retrial queue wherein the service facility may leave for more economical type of vacation schedule, called as working vacation. The inter-arrival-time, retrial time, service time and working vacation time are assumed to be geometric distributed in discrete environment. We have used matrix geometric method to compute various useful performance measures of interest. Further, we obtain joint optimal values of most sensitive parameters such as vacation returning rate (η) and service rate of the server during working vacation (μ) via direct search method based on heuristic approach. Numerical results are also facilitated to depict the performance of the developed model. [ABSTRACT FROM AUTHOR]

In this paper, we model a discrete-time renewal input queue with change over times and Bernoulli schedule vacation interruption under batch service ( a, c, b) policy. The service, working vacation and change over times are geometrically distributed. At the instants of a service completion, the vacation is interrupted and the server is resumed to a regular busy period with probability 1 − q if there are c or more customers in the system, or continues the vacation with probability q. Employing the supplementary variable and recursive techniques, we have derived the steady state queue length distributions at various epochs. Some performance measures and a cost model have been presented and an optimum service rate has been obtained using geneticalgorithm. Numerical results showing the effect of the parameters of the modelon the key performance measures are presented. [ABSTRACT FROM AUTHOR]

This paper deals with a single server retrial queueing system with working vacation in which the server works with different service rates rather than completely terminating the service during its vacation period. We assume that both service times in a regular service period and in a working vacation period are generally distributed. The steady state distributions of the server state and the number of jobs in the orbit were obtained along with other performance measures. The general decomposition law for this retrial queueing system is established. The effects of various parameters on the system performance are also analyzed numerically. [ABSTRACT FROM AUTHOR]