Kouichi Adachi

A two-queue model with Bernoulli service schedule and switching times

In this paper, we present a detailed analysis of a cyclic-service queueing system consisting of two parallel queues, and a single server. The server serves the two queues with a Bernoulli service schedule described as follows. At the beginning of each visit to a queue, the server always serves a customer. At each epoch of service completion in the ith queue at which the queue is not empty, the server makes a random decision: with probability pi, it serves the next customer; with probability 1-pi, it switches to the other queue. The server takes switching times in its transition from one queue to the other. We derive the generating functions of the joint stationary queue-length distribution at service completion instants, by using the approach of the boundary value problem for complex variables. We also determine the Laplace-Stieltjes transforms of waiting time distributions for both queues, and obtain their mean waiting times.

Availability analysis of two-unit warm standby system with inspection time

Abstract This paper deals with two identical units warm standby system when a failure of unit is detected by actual inspection but a system down can be detected at any time without inspection. Where the lifetime distribution of unit is the bivariate exponential distribution and other distributions are arbitrary. The Laplace transform of the point-wise availability of the system and the steady state availability of the system are derived by using the supplementary variable method. Further, we discuss the optimum inspection period maximizing the steady state availability. A numerical example is presented.

A two-queue and two-server model with a threshold-based control service policy

Abstract This paper investigates a queueing system consisting of two-parallel queues and two servers. The service policy is a threshold-based control one such that two thresholds v (⩾0) and N (⩾v) called control level are set up in one of the two queues, say, the second queue. At each epoch of service completion, the server decides which queue is to be served next according to the control level the number of customers in the second queue reaches. For both queues, the arrival processes are Poisson, and the service times are exponentially distributed with different means. We derive the generating functions of the stationary joint queue-length distribution, and then obtain the mean queue length and the mean waiting time for each queue.

Optimal replacement under additive damage in a poisson random environment

We consider a system existing in a random environment. The randomly varying environment is described by a Poisson process called Poisson environment process(PEP). The system receives shocks at random points of time and is subject to failure. Each shock causes a random amount of damage which accumulates additively and depends on the environment state. The damage process is assumed to be a piecewise semi-Markov process (PSMP) which is constructed by the shock process and the environment process. Any of the shocks or the changes of the environment state may cause the system to fail. The optimal replacement problem of the system is examined. Sufficient conditions for the optimality of control-limit policies, the control-limit process and the corresponding bounded processes axe given

Inspection policy for two-unit parallel redundant system

Abstract This paper deals with a single-server two-unit parallel redundant system with non-negligible inspection time. We shall assume that a failure of a unit or the system failure is detected by inspection only. We consider two inspection policies and under each inspection policy the stationary availability is derived by applying Piecewise Markov Process. Optimum inspection schedule is discussed to maximize the stationary availability of the system. A numerical example is presented.

On some minimal repair model

Abstract This paper deals with a one-unit system under the new maintenance policy subject to a minimal repair and a preventive maintenance. Under this policy, the Laplace transform of the point-wise availability and the stationary availability of the system are obtained using the supplementary variable method. The special cases of the results obtained here coincide with earlier results given by R.E.Barlow and L.Huter etc.,. Further, the optimum policy in the sense of the availability is discussed.

An inspection policy for one-unit system subject to revealed and unrevealed failures

Abstract This paper deals with a single-server one-unit system subject to both revealed and unrevealed failures. We shall assume that a revealed failure is detected as soon as it occures but an unrevealed failure is detected by an inspection only. Under an inspection policy, the Laplace transform of the pointwise availability of the system and the stationary availability of the system are derived by using the supplementary variable method. Further, we discuss the optimum inspection schedule maximizing the stationary availability. Finally, some numerical examples are presented.

k-out-of-n: G system with simultaneous failure and three repair policies

Abstract This paper deals with a single-server k -out-of- n : G system with general repair distribution. The life-times of the active units depend on each other in having simultaneous failures. We consider three repair policies and under each repair policy, some relation between the reliability, pointwise availability and mission availability functions of the system. The mission availability, pointwise availability and reliability functions are obtained simultaneously. We use a suitable transformation to deduce the pointwise availability and reliability function from the mission availability function. Explicit expressions for steady-state availability of the system and the mean time to system failures are obtained.

An optimal state-age dependent replacement for a network system

Abstract We consider an optimal state-age dependent replacement problem for a network system composed of a main system and a sub-system with N components. The components functioning times are exponentially distributed random variables with the same parameters, and every failed component is repaired by one repairman by taking an exponentially distributed random time. Repaired components are as good as new. The main system is subject to a sequence of randomly occurring shocks and each shock causes a random amount og damage. Shock arrivals and magnitudes depend on the accumulated damage level of the main system itself and the number of the functioning components of the sub-system. Any of the shocks or components failures might cause the main system to fail. Upon failure of the main system, it is replaced and emergency repairs for all failed components are carried out. Our aim is to determine an optimal state-age dependent replacement policy which minimizes the long-run average cost over the infinite horizon.

Optimum policy of one-unit system with two types of maintenance and minimal repair

Abstract This paper deals with a one-unit system with minimal repair. Two policies (new Policy IV and Policy IV′) are considered. Under these policies, the Laplace transform of the point-wise availability and the stationary availability of the system are obtained using not the renewal theory but the supplementary variable method. And under new Policy IV, the optimum policy in the sense of the availability is discussed.