Multi-server Queues With Batch Arrival And Its Simulation

The main theme of this paper is queue model with batch arrival and multi-server. At first, we study the case of exponential distribution serve time. We deduce equations about steady probability distribution of custom number in system by analyzing state transition and solve them with generation function. And then, we present waiting time distribution. We have known the fact that Erlang distribution with parameter r tends to fix-length distribution when r tends to infinite. So we gain approximation solution of M~ξ/D/m model thinking about the fact. We program emluator to simulate running of M~ξ/D/m using event-driven method arid compute corresponding value. Comparing the approximation with simulation show that our method is feasible. We present waiting time distribution of this model with analytical method. The application of our result in design of call centers is presented.