The objective of this paper is to analyze an queueing model with multiple vacation, closedown, essential and optional repair. Whenever the queue size is less than , the server starts closedown and then goes to multiple vacation. This process continues until at least customer is waiting in the queue. Breakdown may occur with probability when the server is busy. After finishing a batch of service, if the server gets breakdown with a probability , the server will be sent for repair. After the completion of the first essential repair, the server is sent to the second optional repair with probability . After repair (first or second) or if there is no breakdown with probability , the server resumes closedown if less than ` ' customers are waiting. Otherwise, the server starts the service under the general bulk service rule. Using supplementary variable technique, the probability generating function of the queue size at an arbitrary time is obtained for the steady-state case. Also some performance measures and cost model are derived. Numerical illustrations are presented to visualize the effect of various system parameters.
Ayyappan, G. and Deepa, T.
Analysis of batch arrival bulk service queue with multiple vacation closedown essential and optional repair,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 13,
2, Article 2.
Available at: https://digitalcommons.pvamu.edu/aam/vol13/iss2/2