Equilibrium balking strategies in Markovian queues with a single working vacation and vacation interruption

Abstract

In this work, we study customer equilibrium balking strategies in single-server Markovian queueing systems with a single working vacation and vacation interruption. That is, the server undertakes workload with a lower service rate rather than completely stops working during the vacation period. At the instant of completing the service during a vacation period, if there are any customers in the system, the server ends the vacation compulsively and returns to the normal working level, i.e. vacation interruption occurs. Upon arrival, the customers must make a decision whether to join or balk the system based on the information about the number of customers in the system and the server status, along with the reward–cost structure of the system. Accordingly, four cases with respect to different levels of information are introduced and the corresponding Nash equilibria are presented. In addition, the impact of the information levels, as well as of several system parameters, on the equilibrium thresholds and equilibrium joining probabilities is illustrated by numerical examples.

Keywords:

• Single working vacation
• vacation interruption
• equilibrium strategy
• balking