This paper is concerned with performance models and approximations for very large, multi-media networks. Blocking is the traditional performance measure in circuit-switched networks, and will remain as such in multi-rate circuit-switched networks. It is also considered a likely performance measure candidate for resource management and dimensioning in broadband fast packet-switched networks, operated under virtual circuit mode.
rnTo gain some insight into network-wide blocking phenomena, we study in this paper the basic building block of any network, a single link. Multi-media traffic calls with Poisson arrivals, arbitrarily distributed service times, and different bandwidth requirements (in number of circuits), are offered to a system (link) of finite capacity. A call is rejected when the sharing policy doesn't allow it to be accommodated by the system.
rnUnder complete sharing policy, an aggregate state describing the number of occupied circuits is shown to exhibit a product form solution in steady state, when the capacity and traffic intensities become very large asymptotically. This structural property leads to the main result of this paper, an approximation which reduces the computation of the blocking probabilities for the different classes of traffic to the evaluation of a single Erlang formula and the determination of the root of a monotonous polynomial function.
rnWe provide comparison curves of the exact blocking probabilities and the approximations for some examples with 3 classes of traffic.
本文涉及非常大型的多媒体网络的性能模型和近似值。阻塞是电路交换网络中的传统性能指标,在多速率电路交换网络中将保持不变。它也被认为是在虚拟电路模式下运行的宽带快速分组交换网络中资源管理和规模确定的一种可能的性能指标。 P> rn
为了深入了解网络范围的阻塞现象,我们在本文是任何网络的单一链接的基本构建块。具有泊松到达,任意分配的服务时间和不同的带宽要求(以电路数量为单位)的多媒体业务呼叫被提供给容量有限的系统(链路)。在共享策略不允许系统容纳呼叫时,呼叫被拒绝。 P> rn
在完全共享策略下,描述占用电路数的汇总状态显示为产品形式解决方案在稳定状态下,当容量和流量强度渐近变大时。这种结构性质导致了本文的主要结果,该近似值减少了针对单个Erlang公式的求值和单调多项式函数的根的确定,从而减少了针对不同通信量的阻塞概率的计算。 P> rn
对于某些具有3类流量的示例,我们提供了精确的阻塞概率和近似值的比较曲线。 P>
Department of Electrical Engineering and Center for Telecommunication Research, Columbia University, New York, NY;
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