Efficient Multirate Teletraffic Loss Models Beyond Erlang

10The Erlang Multirate Loss Model With Batched Poisson Arrivals

In this chapter we consider multirate loss models of batched Poisson arriving calls with fixed bandwidth requirements and fixed bandwidth allocation during service. In the batched Poisson process, simultaneous call‐arrivals (batches) occur at time‐points which follow a negative exponential distribution. A batched Poisson process can model overflow traffic.

10.1 The Erlang Multirate Loss Model with Batched Poisson Arrivals

10.1.1 The Service System

In the Erlang multirate loss model with batched Poisson arrivals (BP‐EMLM) we consider a link of capacity C b.u. that accommodates K different service‐classes under the CS policy. Calls of all service‐classes arrive in the link according to a batched Poisson process.

In the batched Poisson process, one basic principle of random arrivals, according to which no simultaneous arrivals occur (Figure 10.1a), is abolished, while another basic principle of random arrivals, according to which arrivals (the batches) occur at time‐points following a negative exponential distribution, is kept (Figure 10.1b) [1–4]. The batched Poisson process is important not only because in several applications calls arrive as batches (groups), but also because it can represent, in an approximate way, arrival processes that are more “peaked” and “bursty” (expressed by the peakedness factor ) than ...