Abstract
This paper investigates a multi-server Markovian queueing system with an optional service, working vacations of servers and retention of reneged customers. When all the servers are busy, customers may renege from the system with probability r1 or may remain in the queue with probability After working vacation completion, the c servers return back to regular busy period if there is at least one customer in the system; otherwise, they continue the vacation. The steady-state probabilities of the model are obtained using the matrix geometric method. Numerical investigations with cost model and performance measures are illustrated with tables and graphs.
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Acknowledgments
The authors would like to thank the editors and the anonymous referees for their valuable comments and suggestions which have helped in improving the quality and presentation of the paper.