 We consider a queueing system where the server is subject to failures and can be repaired within a random period of time. After an "imperfect" repair, the server (machine) will be in a state between "as good as new" and "as bad as old". The server state will determine either the failure rate or the service rate or both. A Quasi Birth Death process is developed for modeling such a system. We i...

This paper studies the machine repair problem consisting of M operating machines with S spare machines, and R servers (repairmen) who leave for a vacation of random length when there are no failed machines queuing up for repair in the repair facility. At the end of the vacation the servers return to the repair facility and operate one of three vacation policies: single vacation, multiple vacati...

This paper presents two methods to calculate the response time distribution of impatient customers in a discrete-time queue with Markovian arrivals and phase-type services, in which the customers’ patience is generally distributed (i.e., the D-MAP/PH/1 queue). The first approach uses a GI/M/1 type Markov chain and may be regarded as a generalization of the procedure presented in Van Houdt [14] ...

The objective of this paper is to study the M/M/R machine repair queueing system with mixed standbys. The life-time and repair time of units are assumed to be exponentially distributed. Failed units are repaired on FCFS basis. The standbys have switching failure probability q (0≤q≤1). The repair facility of the system consists of R permanent as well as r additional removable repairmen. Due to i...

This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model the limited capacity of the system, and routing is used to represent the need for additional service. The most significant result of the analysis is the derivation of the generating function for queue length when buffer sizes are limited and a representation of the system workload. The queue length...

This paper studies the single server repairable queueing system with variable service rate and failure rate. The rule of variation is that changes when number customers in reaches a certain value. may fail at any time, rates idle periods busy are different. has one reliable repairman to repair server. steady-state joint distribution states obtained by matrix geometric solution method, availabil...

This study aimed at presenting a method for formulating optimal production, repair and replacement policies. The system was based on the production rate of defective parts and machine repairs and then was set up to optimize maintenance activities and related costs. The machine is either repaired or replaced. The machine is changed completely in the replacement process, but the productio...

We consider a repair facility consisting of one repairman and two arrival streams of failed items, from bases 1 and 2. The arrival processes are independent Poisson processes, and the repair times are independent and identically exponentially distributed. The item types are exchangeable, and a failed item from base 1 could just as well be returned to base 2, and vice versa. The rule according t...

We consider a system of two separate finite-buffer M/M/1 queues served by a single server, where the switching mechanism between the queues is thresholdbased, determined by the queue which is not being served. Applications may be found in data centers, smart traffic-light control and human behavior. Specifically, whenever the server attends queue i (Qi ) and the number of customers in the other...

This paper analyzed the multi-machine repairable system with one unreliable server and repairman. The machines may break at any time. One oversees servicing machine breakdown. fail time different failure rates in idle busy repairman is responsible for repairing failure; repair rate variable to adapt whether are all functioning normally or not. All distributions exponential. Using quasi-birth-de...