Search for: All records

This paper investigates a hybrid service system with a cloud server and an in-house server. We consider two different scenarios: a hybrid service system with orbit space and a hybrid service system without orbit space. In the hybrid service system with orbit space, customers who fail to enter the cloud server can choose to join the in-house subsystem or to enter an orbit space and retry the cloud server. An admission control mechanism based on queue-length limitation is adopted to adjust whether the cloud service resources are open to customers. When the cloud server cannot be accessed immediately, some customers send their jobs to the in-house subsystem, while others (called opportunists) try to send their jobs to the cloud server again. We obtain the optimal queue-length limitation for a given retrial rate. The service provider and customers are different stakeholders, and their market forces are also different. Therefore, it is more realistic to explore the game relationship between them by using dynamic game theory. We can also explore the joint optimums of the queue-length limitation and the retrial rate in the framework of the Stackelberg game. Finally, by comparing with the hybrid service system without orbit space, we discuss the significance of the existence of orbit space, and gain management insights. It is found that the existence of opportunists may benefit the service provider, although they significantly harm social interests, regardless of whether they are cooperative or non-cooperative; therefore, opportunists are encouraged in some situations. Numerical analysis shows that adding a retrial orbit to a hybrid cloud service system with certain input parameters may even more than triple the service provider’s revenue. 

Abstract Endohedral metallofullerenes are chemically more inert compared to empty fullerenes, primarily due to their intramolecular electron transfer. In this work, we report an inverse electron demand Diels–Alder (IEDDA) reaction on M₃N@C₈₀(M=Lu, Sc), where they show significantly higher reactivity than empty fullerenes. The molecular structures of the [4+2] cycloadducts were unambiguously characterized. Moreover, the cycloadducts can fully revert to pristine M₃N@C₈₀via retro‐cycloaddition upon thermal treatment. With the unusual reactivity and reversibility, the IEDDA reaction enables an effective separation approach for metallofullerenes from their soot extracts, opening path to efficient and economical scale‐up synthesis of metallofullerenes in laboratory and industrial settings.