Retention of impatient customers in a multi-server Markovian queueing system with optional service and working vacations

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 $r_2(=1-r_1).$ 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.

Keywords:

• Multi-server queue
• working vacations
• first essential service
• second optional service
• reneging
• retention

MATHEMATICS SUBJECT CLASSIFICATION:

• 60K25; 65K30

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.

Additional information

Funding

The authors would also like to thank the Department of Science and Technology, Government of India, for providing the Lab facility in the department under the DST-FIST Project grant No. SR/FST/MS-I/2017/3(c).