2 research outputs found
Equilibrium joining strategies in M/M/1 Queues with working vacation and vacation interruptions
We study the equilibrium joining strategies for customers in an M/M/1 queue with working
vacations and vacation interruptions. The service rate switches between a low and a high
value depending on system dynamics. The server will take a multiple working vacation when
the system is empty, during which a low service rate is provided to the arriving customers
if any. Upon completion of the first customer’s service, given that the system is not
empty, the working vacation will be terminated which means the server comes back and
serves the following customers with a higher service rate. Otherwise, if the system is
found empty upon completion of the first service, the server will continue his working
vacation. Arriving customers may or may not know the state of the server and/or the number
of the customers upon arrival, but they have to decide whether to enter the system or balk
based on a linear reward-cost structure. We investigate customer behavior according to
different levels of information regarding the system state. The equilibrium strategies for
the customers are derived and the stationary behavior of the system under these strategies
are analyzed. Finally, the effect of different levels of information on equilibrium
thresholds and equilibrium entrance probabilities is illustrated by several numerical
examples