Cell loss and call blocking at an ATM multiplexor

We study an ATM access node which multiplexes on-off calls onto a common channel on a cell loss and call blocking basis. Calls arrive at a Poisson rate λ calls/sec and require an exponentially distributed holding time of mean 1/μ seconds. When on, a call generates traffic at a fluid rate R cells/sec and when off it generates no traffic. The on and off time intervals are exponentially distributed with means 1/α and 1/β second, respectively. When arriving cells can´t be transmitted immediately, they are queued in a common buffer of size B cells. Cells arriving when the buffer is full are assumed lost. Using a fluid model, we derive the cell loss and call blocking probabilities and apply them to provision the maximum call handling capacity, N, of the system. When N calls are already in progress, arriving calls are blocked. When call-level transition rates are much smaller than cell-level transitions, the input process is nearly completely decomposable (NCD). This NCD approximation greatly reduces the computational difficulty of the exact fluid model. Numerical results show that the NCD approximation is quite accurate over a wide range of traffic parameters