A queueing system with n-phases of service and (n-1)-types of retrial customers

作者：Langaris Christos; Dimitriou Ioannis^*

来源：European Journal of Operational Research, 2010, 205(3): 638-649.

DOI：10.1016/j.ejor.2010.01.034

• Poisson arrivals
• n-Phase service
• Retrial queues
• General services
• Single vacation

A queueing system with a single server providing n-phases of service in succession is considered. Every customer receives service in all phases. Arriving customers join a single ordinary queue, waiting to start the service procedure. When a customer completes his service in the ith phase he decides either to proceed to the next phase or to join the K(i) retrial box (i = 1,2...,n - 1), from where he repeats the demand for the (i + 1)th phase of service after a random amount of time and independently to the other customers in the system. Every customer can join during his service procedure a number of retrial boxes before departs from the system. When at the moment that a customer, either departs from the system or joins a retrial box and so releases the server, there are no other customers waiting in the ordinary queue, then the server departs for a single vacation of an arbitrarily distributed length. The arrival process is assumed to be Poisson and all service times are arbitrarily distributed. For such a system, the mean number of customers in the ordinary queue and in each retrial box separately are obtained, and used to investigate numerically system performance.

• 出版日期2010-9-16