The Erlang Multirate Loss Model With Batched Poisson Arrivals

This chapter considers 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. In the Erlang multirate loss model with batched Poisson arrivals, the chapter also considers 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. 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 z) than the Poisson process. The peakedness factor, z, is the ratio of the variance over the mean of the number of arrivals.