Numerical Analysis for Time - dependent Machine Repair Model with Threshold Recovery Policy and Server Vacations
نویسنده
چکیده
We consider a machine repair problem with server breakdowns, in which an unreliable server (repairman) operates the threshold recovery policy. When there are no failed machines in the system, the server leaves for a vacation. If the server returns from a vacation to find no failed machines in the system, he/she immediately takes another vacation. And the server continues in this manner until he/she finds at least one failed machine waiting in the queue upon returning from a vacation. It is assumed that the failure and service times of each machine are exponentially distributed. The server breaks down with a constant failure rate. The repair and vacation times obey exponential distributions. Using the Runge–Kutta method of fourth order, we solve the differential equations for this machine repair model numerically. Machine availability is developed in terms of transient probabilities. Finally, a sensitivity analysis is conducted to investigate the effects of system parameters on the machine availability with respect to time. Keywords—Machine repair problem, Runge–Kutta method, server vacation, threshold recovery policy
منابع مشابه
Vacation model for Markov machine repair problem with two heterogeneous unreliable servers and threshold recovery
Markov model of multi-component machining system comprising two unreliable heterogeneous servers and mixed type of standby support has been studied. The repair job of broken down machines is done on the basis of bi-level threshold policy for the activation of the servers. The server returns back to render repair job when the pre-specified workload of failed machines is build up. The first (seco...
متن کاملA time-shared machine repair problem with mixed spares under N-policy
The present investigation deals with a machine repair problem consisting of cold and warm standby machines. The machines are subject to breakdown and are repaired by the permanent repairman operating under N-policy. There is provision of one additional removable repairman who is called upon when the work load of failed machines crosses a certain threshold level and is removed as soon as the wor...
متن کاملPerishable Inventory Model with Retrial Demands, Negative Customers and Multiple Working Vacations
This paper presents the analysis of a continuous review perishable inventory system wherein the life time of each item follows an exponential distribution. The operating policy is (s,S) policy where the ordered items are received after a random time which follows exponential distribution. Primary arrival follows Poisson distribution and they may turnout to be posit...
متن کاملFinite Capacity Queuing System with Vacations and Server Breakdowns
This paper deals with finite capacity single server queuing system with vacations. Vacation starts at rate nu if the system is empty. Also the server takes another vacation if upon his arrival to the system, finds the system empty. Customers arrive in the system in Poisson fashion at rate lamda0 during vacation, faster rate lamdaf during active service and slower rate lamdas during the breakdow...
متن کاملAnalysis of an M/G/1 Queue with Multiple Vacations, N-policy, Unreliable Service Station and Repair Facility Failures
This paper studies an M/G/1 repairable queueing system with multiple vacations and N-policy, in which the service station is subject to occasional random breakdowns. When the service station breaks down, it is repaired by a repair facility. Moreover, the repair facility may fail during the repair period of the service station. The failed repair facility resumes repair after completion of its re...
متن کامل