Transient solution of an M[X]/G/1 queueing model with feedback, random breakdowns, Bernoulli schedule server vacation and random setup time

Transient solution of an M[X]/G/1 queueing model with feedback, random breakdowns, Bernoulli schedule server vacation and random setup time

0.00 Avg rating0 Votes
Article ID: iaor2016152
Volume: 25
Issue: 2
Start Page Number: 196
End Page Number: 211
Publication Date: Dec 2016
Journal: International Journal of Operational Research
Authors: ,
Keywords: scheduling, combinatorial optimization, maintenance, repair & replacement
Abstract:

We consider an M[X]/G/1 queue with Poisson arrivals, random server breakdowns and Bernoulli schedule server vacation. Both the service time and vacation time follow general distribution. After completion of a service, the server may go for a vacation with probability θ or continue staying in the system to serve a next customer, if any, with probability 1 − θ. With probability p, the customer feedback to the tail of original queue for repeating the service until the service becomes successful. With probability 1 − p = q, the customer departs the system if service be successful. The system may breakdown at random following Poisson process and the repair time follows exponential distribution. Also, we assume that at the end of a busy period, the server needs a random setup time before giving proper service. We obtain the probability generating function in terms of Laplace transforms and the corresponding steady state results explicitly.

Reviews

Required fields are marked *. Your email address will not be published.