| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1702695 | Applied Mathematical Modelling | 2016 | 18 Pages |
•Investigate a retrial queueing system with complementary services.•This model is analyzed under three price structures and three scenarios of ownership.•The optimal arrival rate of customers and the prices set by the servers in equilibrium are derived.•It shows that the prices set by the monopolist in equilibrium reach the social optimization.•It provides managerial insights for optimal control of the retrial queues with complementary services.
An unobservable retrial queueing system with complementary services is studied, in which customers are risk neutral and they have no information of the system upon arrival, but have to make the decision to join the system or not to maximize their expected benefits. In our model, one server provides an instantaneous service while the other offers a service with delayed customers, which is modeled as an M/M/1 retrial queue. The two services are complementary and the customer has no benefit from obtaining just one of them. Under various pricing schemes, we investigate the customers’ reward-cost situations and the servers’ price strategies in equilibrium. In each pricing scheme three scenarios are studied according to the different ownership of the two servers: (1) they are owned and operated by two different private agents; (2) they are owned and operated by a common private agent; or (3) one is owned and operated by a private agent, and the other by a public agent. Some numerical experiments of the equilibrium solutions are presented.
