On the many-server fluid limit for a service system with routing based on delayed information

Pender, Rand and Wesson recently established a delay differential equation limit for a parallel service system with routing based on delayed information. We provide an interpretation of their scaling under which their limit can be regarded as an instance of a law of large numbers in the familiar many-server heavy-traffic scaling. It requires scaling in the probabilistic routing function. We also obtain related many-server heavy-traffic delay-differential-equation limits for more general models. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

Pender, Rand, and Wesson have recently established a delay differential equation limit for a parallel service system with routing based on delayed information. The interpretation provided in their study suggests that their limit can be seen as an example of the law of large numbers in the context of many-server heavy-traffic scaling. Scaling in the probabilistic routing function is required, and related many-server heavy-traffic delay-differential-equation limits for more general models have also been obtained.