离散时间Erlang消失系统的重构与比较

讨论了两种入口协议下的离散时间Erlang消失系统Geom/Geom/c/c，通过对系统的重构，建立新模型，分别得到两种入口协议下的稳态分布、PGF、平均队长和损失率的表达式，并进行了新旧模型的数值比较。通过比较得到，新旧模型队长的计算方法，损失率不同，但是状态转移矩阵，PGF的表达式相同。最后，在新模型下对两种不同入口协议进行了对比，得出两种协议下顾客的损失率随到达率增加而增大；随服务台个数和服务率的增加而减小；两种协议下顾客的平均队长随服务率的增加而减小，随到达率和服务台个数的增加而增大；同一参数下，有直接入口的损失率低于有延迟入口的损失率，有直接入口的平均队长低于有延迟入口的平均队长。

Reconstruction and comparison of discrete-time Erlang loss systems

Discrete-time Erlang lose systems Geom/Geom/c/c in two main entrance protocols are discussed. The system is reconstructed, new models are proposed in different entrance protocols, and the formula of PGF, the loss rate and the mean queue are obtained in the steady state system respectively. With some numerical examples, the differences of the important stationary indices are compared in new models and existing models. The calculation methods of the queue and the loss rate are different, but the state transition matrix and PGF had the same expressions. Finally, the new models are compared in the two different entrance protocols. The loss rate increases with the increasing arrival rate and decreases with the increasing numbers of entrance websites and the service rate. The mean queue decreases with the increasing service rate and increases with the increasing of the arrival rate and the numbers of entrance websites. Under the same parameters, the loss rate in direct entrance protocols is less than the other; the mean queue in delayed entrance protocols is higher than the other.