This paper appears to investigate the optimal joining strategies of arriving customers under different scenarios in the single-server Markovian queueing systems with three types of retrial orbits: standard, deluxe, and business class. Customers who arrive at the system and find the server busy can join one of the retrial orbits based on their preference and paying capacity. The standard orbit is assumed to be the cheapest, and customers who want to pay less would choose this option. Customers whose paying capacity is higher would join the deluxe orbit, while those who can afford the high cost would join the business-class orbit. The probability-generating function technique is applied to solve the steady-state difference equations and derive the steady-state probabilities and other important system metrics for a probability distribution. The cost-reward function is framed and analyzed based on the joining strategies of the arriving customers. The arriving customers would decide whether to join the queue or not based on the cost-reward structure. The cost-reward function may reflect the trade-off between the profit for those joining the queue and the waiting cost in the queue. The numerical experiment is also done by taking a numerical example and comparing the results for the fully unobservable, partially unobservable, partially observable, and fully observable. The development of equilibrium and social strategies enabled to make a detailed study on the behavior of customers subject to profit. This study can provide insights into the behavior of customers in queuing systems and inform the design and management of such systems in various applications, such as service operations, transportation, manufacturing, or production, etc.
Antala et al. (Tue,) studied this question.