Blocking Probabilities In A Loss System with Arrivals in Geometrically Distributed Batches and Heterogeneous Service Requirements

We analyze a generalization of the classical Erlang loss model. Customers of several types contend for access to a service facility consisting of a finite number of servers. Each customer requires a fixed number of servers simultaneously during an exponentially distributed service time, and is blocked on arrival if this requirement cannot be met. Customers of each type arrive in geometrically distributed batches, while the arrival of batches of each type is governed by a Poisson process. All relevant parameters may be type-dependent. We obtain the steady-state distribution of the number of customers of each type in the system (which turns out to have product form), and the blocking probabilities experienced by each customer type. In addition, we bring to light the connection between the model at hand and a method proposed by Delbrouck for estimating blocking probabilities in an incompletely specified setting.