Abstract:
In this paper, we consider a discrete time working vacation queue with a utility function
for the reward of receiving the service and the cost of waiting in the system. A more
flexible switching mechanism between low and regular service states is introduced to enhance
the practical value of the working vacation queue. Under different precision levels
of the system information, namely observable, almost unobservable and fully unobservable
cases, the utility function is studied from both the individual customer’s and the system
administrator’s points of view. By analyzing the steady-state behavior of the system, the
associated optimal joining decisions under different information scenarios are obtained. We
find that for the fully observable queue, the joining threshold for individual optimization
may be less than the one for social optimization in working vacation period. A similar
situation also appears in almost unobservable case. Such phenomenon is not possible for
the classic first come first served queue due to the fact that there is no vacation time and
thus will not cause large fluctuations in customers’ conditional waiting time. Additionally,
we also conduct some numerical comparisons to demonstrate the effect of the information
levels as well as system parameters on customer joining behavior.
