A Token-Based Central Queue with Order-Independent Service Rates

We study a token-based central queue with multiple customer types. Customers of each type arrive according to a Poisson process and have an associated set of compatible tokens. Customers may only receive service when they have claimed a compatible token. If, upon arrival, more than one compatible token is available, then an assignment rule determines which token will be claimed. The service rate obtained by a customer is state-dependent, that is, it depends on the set of claimed tokens and on the number of customers in the system. Our first main result shows that, provided the assignment rule and the service rates satisfy certain conditions, the steady-state distribution has a product form. We show that our model subsumes known families of models that have product-form steady-state distributions, including the order-independent queue of Krzesinski and the multi-type customer and server model of Visschers et al. Our second main contribution involves the derivation of expressions for relevant performance measures such as the sojourn time and the number of customers present in the system. We apply our framework to relevant models, including an M/M/K queue with heterogeneous service rates, the MSCCC queue, and multiserver models with redundancy. For some of these models, we present expressions for performance measures that have not been derived before.