A review on hypercube queuing model's extensions for practical applications

In this study, we review some extensions of the well-known hypercube queuing model for applications to real life emergency services in server-to-customer systems. Given that many of these systems usually have their own distinct characteristics and dispatching policies, the classic hypercube model can be modified to incorporate these particularities allowing a more effective system analysis. In general, the hypercube model is extended by relaxing one or more of its limiting assumptions. We present different extended hypercube models of the literature, also motivated by our own experience with practical applications, pointing out the basic characteristics of these models. These extensions incorporate unique dispatching policies such as multiple dispatch hypercube models with identical and differentiated servers, dispatching policies using server reservation (cut-off model) to increase the availability of servers to high priority calls, hypercube models considering distinct priority policies to queued users, and hypercube models considering cross-trained servers that can provide two different kinds of emergency services (e.g., medical and fire control). To illustrate this review, describe how the equilibrium equations and the main performance statistics are evaluated, and provide useful insights into problems of interest, we use the smallest and non-trivial structures as systems’ examples, referred to as “toy-models”.