TITLE:
Exact Tail Asymptotics for a Queueing System with a Retrial Orbit and Batch Service
AUTHORS:
Huijun Lu
KEYWORDS:
Exact Tail Asymptotics, Batch Service, Censoring Technique, Matrix Analysis Method, Karamata Tauberian Theorem
JOURNAL NAME:
Applied Mathematics,
Vol.15 No.6,
June
26,
2024
ABSTRACT: This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution.