Oscillating Service System Between Conventional and Retrial Queues for Impatient Customers with Switch-off and Close-down Periods

Abstract

In this article, we analyze a single server dynamic service system between conventional and retrial queueing modes with impatient customers and switch-off and close-down periods of the server. In such a system, analytical expressions for the steady-state joint probabilities of the status of the server and the orbit size are derived in terms of hypergeometric functions. The factorial moments of the orbit size are also determined. Several interesting and key performance measures have been obtained. Moreover, the regenerative cycle length of the system and its related characteristics are discussed. Finally, extensive numerical results are presented graphically to illustrate the effects of the system parameters on the vital performance measures.

Keywords

• retrial queue
• reneging
• switch-off time
• close-down time
• regenerative analysis
• hypergeometric functions