A Batch Arrival Queue with a Second Optional Service Channel Under N-Policy

Abstract

We consider an M ^X /G/1 queueing system with a second optional service channel under N-policy. The server remains idle until the queue size reaches or exceeds N (≥1). As soon as the queue size becomes at least N, the server immediately begins to serve the first essential service to all the waiting customers. After the completion of which, only some of them receive the second optional service. For this model, our study is basically concentrated in obtaining the queue size distribution at a random epoch as well as at a departure epoch. Further, we derive a simple procedure to obtain optimal stationary policy under a suitable linear cost structure. Moreover, we provide some important performance measures of this model with some numerical examples.

Keywords:

• First essential service
• M ^X /G/1 queue
• N-policy
• Optimal cost structure
• Second optional service

Mathematics Subject Classification:

• Primary 60K25
• Secondary 90B22

ACKNOWLEDGMENTS

The authors are thankful to the referee and the editor for their fruitful comments, which brings the paper to the present form. This work is supported by Department of Atomic Energy, Government of India, NBHM Project No. 48/2/2001/R&DII/1211.