Abstract—In this research, we consider a single server
queueing system with Poisson arrivals and multiple vacation
types, in which the server can choose one of several types of
vacations to take when he finishes serving all customers in the
system. Upon completion of a vacation, the server may either
take another vacation with a certain probability or check the
number of customers waiting in the system. In the latter case, if
the number of customers is greater than a critical threshold, the
server will resume serving the queue exhaustively; otherwise, he
will take another vacation. A variety of vacation types are
available and the choice is the discretion of the server. The cost
structure consists of a constant waiting cost rate, fixed costs for
starting up service, and reward rates for taking vacations. It is
shown that this infinite buffer queueing system can be
formulated as a finite state Semi-Markov decision process. With
this finite state model, we can determine the optimal service
policy to minimize the long-term average cost of this vacation
system. Some practical stochastic production and inventory
control systems can be effectively studied using this model.
Index Terms—Queueing systems, vacation models, threshold
policies, semi-Markov decision process.
Y. Song is with Business School, Manchester Metropolitan University,
on leave from Department of System Management, Faculty of Information
Engineering, Fukuoka Institute of Technology, Fukuoka, Japan (e-mail:
song@fit.ac.jp).
[PDF]
Cite: Yu Song, "The Optimal Service Policies in an M/G/1 Queue
with Consecutive Vacations," International Journal of Modeling and Optimization vol. 4, no. 2, pp. 100-103, 2014.
