A Generalized Erlang-C Model for the Enhanced Living Environment as a Service (ELEaaS)

In this article, a full-access waiting multi-server queue with a statedependent arrival and departure processes is investigated and suggested for use as a generic traffic model of the novel concept of the Enhanced Living Environment as a Service (ELEaaS). The generalized arrival and service flows with nonlinear state dependence intensities are used. The idea is based on the analytical continuation of the Poisson arrival process and Bernoulli service process, and the classic M/M/n queuing system. Birth and death processes and state-dependent rates are applied. The suggested new queuing system is of a M(g)/M(g)/n/k type (in Kendal notation) with a generalized arrival and departure processes M(g). The input and output intensities depend nonlinearly on the system state with defined parameters - the socalled “peaked factors”. The state probabilities of the system are obtained using the general solution of the birth and death processes. The influence of the peaked factors on the queuing behavior is evaluated showing that state-dependent arrival and service rates may change significantly the characteristics of the queuing system. The simplicity and uniformity in representing both peaked and smooth behavior make this queuing model also attractive for future networks’ analysis and synthesis.