随机环境下M/M/c重试丢弃的ATM网络排队性能分析

在ATM网络中顾客的到达率和服务率都随着环境的变化而变化.本文考虑的是具有随机环境的多服务台排队模型,在随机状态为i(1≤i≤m)时,到达时间间隔和服务时间分布分别是服从参数为λ_i和μ_1的指数分布,系统具有有限缓冲位置和无限位置的重试轨道,重试失败的顾客以一定概率被系统丢弃而永远离开系统.运用拟生灭过程方法,我们求得了稳态条件及在稳态下各个环境上各项条件排队指标及平均排队指标,通过数值模拟说明了高峰期到达率和其它参数对系统状态及忙期循环的影响.

Queuing Performance Analysis of ATM Network with Retrial Loss in a Random Environment

In ATM, arrival rate and service rate of customers vary randomly according to changes of the random environment. In the paper, we deal with a multi-server queueing system with random environment. During sojourns in the state i (1 ≤ i ≤ m), customers arrive to the system according to a Poisson process of rate λ_i. During sojourn intervals in the state i the service rate μi prevails. In the system, there are finite waiting positions and infinite positions of retry orbit, the customers who fail to retry will leave the system with a certain probability forever. Using quasi-birth-death (QBD) process, we obtain the necessary and sufficient condition for stability of the system, the conditional indexes and overall means of the queue in every state are obtained Additionally, the affect of various parameters of Rush-hour and other parameters on the system state and busy cycle are illustrated numerically.