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In this paper we study the reliability of a k-out-of-n system, with a single technician, who also renders service to external customers besides repairing the failed components in the system. For optimizing the revenue from external service without compromising the system reliability, we introduce the Npolicy in which the repair of the internal customers (failed components) starts only on accumulation of N failed components. The service to external customers is of preemptive nature in the sense that their service can be interrupted on accumulation of N failed components. It is assumed that an external customer, who finds the server busy with an external customer at the epoch of its arrival joins a queue of infinite capacity; whereas an external customer who finds the server busy with an internal customer leaves the system forever. The failure times of the components of the k-out-of-n system follow an exponential distribution; the arrival of external customers is according to a Poisson process and the service times of the internal and external customers follow non-identical phase-type distributions. Using matrix-analytic methods, we discuss the system stability and steady state distribution. A special case of the model where the underlying distributions are all exponential has been considered, to obtain an expression for the stability condition and a product form solution for the steady state have been obtained for this case. Also several system performance measures have been obtained explicitly. Analysis of a cost function indicates that N-policy does help to optimize the system revenue maintaining high system reliability. [ABSTRACT FROM AUTHOR]

This paper considers an (s,S) production inventory system with positive service time, with time for producing each item following Erlang distribution. Customers arrive according to a Poisson process. A customer who arrives when there is no inventory in the system is considered lost. On the other hand, a customer who finds a busy server with at least one inventory in the system joins a queue of infinite capacity. When the inventory level falls tos, production process is switched on, and it is switchedoffwhen the inventory level reaches back toS. Service time to each customer also follows an Erlang distribution. The service of acustomermay be interrupted, where the time for such a phenomenon follows an exponential distribution, whenever it occurs. An interrupted service, after repair, resumes from where it was stopped. The correction/repair time follows an exponential distribution. We assume that the service of a single customer may encounter any number of interruptions and that the customer being served waits there until his service is completed. Moreover, at a time the server is subject to at most one interruption. We also assume that no inventory is lost due to a service interruption. Like the service process, the production process also is subject to interruptions, where the duration to an interruption follows an exponential distribution. However, in contrast to the service interruption, in the case of interruption to production process, we assume that the item being processed is lost because of interruption. That is, the production process, on being interrupted, restarts from the beginning, after repair. The repair time of an interrupted production process follows exponential distribution. Few of the last service phases are assumed to be protected in the sense that the service will not be interrupted while being in these phases. The same is assumed for the production process also. The model is analysed as a level-independent quasi-birth–death process. We apply a novel method to obtain an explicit expression for the necessary and sufficient condition for the stability of the system under study. This method works even if we assume general phase-type distributions for the production as well as the service processes, and hence can be used to characterise the stability of inventory systems where the assumption of disallowing the customers to join the system, when there is a shortage of inventory has been made. Under stability, we apply matrix analytic methods to compute the system state distribution. In consequence to that, several system performance measures have been derived, and their dependence on the system parameters has been studied numerically. [ABSTRACT FROM AUTHOR]

This paper considers a production inventory with positive service time. The time for producing each item is assumed to follow a ‘Markovian production scheme’. Because of this, correlation automatically gets into the production process. The customer arrival process follows a Markovian arrival process. When inventory falls to s, the production process is switched on, and is switched off when the on-hand inventory reaches S. The service time to each customer has a phase-type distribution. We investigate the system stability. Under the condition of stability, we investigate the system state distribution. Next, several performance measures are computed, such as the fraction of time server is on vacation; fraction of time the inventory level is zero; fraction of time the production process is On; expected number of customers in the system while server is on vacation and also while it is busy. Numerical results indicate, among other things, the effect of the control variables s and S on the fraction of time the system goes out of inventory and on expected loss rate of customers. [ABSTRACT FROM AUTHOR]