A limited clearing queueing model with an orbit and non-persistent customers

Abstract

In this paper, we study a limited clearing queueing model with an orbit and non-persistent customers, in which the space of service station is finite and the server can serve all customers in the service station simultaneously. If a customer (new arrival or retrial) finds the station is full, he/she will decide whether join the orbit or not with respective probabilities. We first analyze the necessary and sufficient condition for the stability of this system, then using matrix geometric analytic method and spectral expansion method, we obtain the stationary distribution of this model. Besides, we also give many important performance measures of this system which help managers to make wisdom managerial decisions and designs, such as the mean size of service station, the mean queue length of the orbit and the mean sojourn time of an arbitrary customer. Finally, some numerical examples are provided to show the impacts of various parameters on the system performance measures.

Keywords:

• Clearing system
• orbit
• non-persistent customers
• matrix analytic method
• spectral expansion method

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant number 61773014].