The authors 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. The authors 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, the authors bring to light the connection between the model at hand and a method is proposed by L.E.N. Delbrouck (1983) for estimating blocking probabilities in an incompletely specified setting.>

We address the problem of estimating the time congestion on a finite trunk group from the size of the group and the mean and peakedness factor of the offered traffic. In order to be able to assess the relative merits of the various estimates, we adopt a common setting where the offered traffic is simple overflow traffic. Next to giving brief descriptions of earlier results, we elaborate on some of the earlier suggestions, and discuss some new approaches to the problem. Our numerical evaluation of the various approximations for time congestion induced by simple overflow traffic distinctly reveals the superiority of a variant of Frederieks' approximation procedure.

Delbrouck's recent estimates for the call blocking probabilities experienced by heterogeneous traffic streams on a common trunk group are brought to light in a new and simple manner. A link with earlier estimates by Delbrouck is established by means of a Manfield-Downstype approximation.