Nationwide IP networks typically include nodes in major cities and the following elements: customer equipment, access routers, backbone routers, peering routers, access links connecting customer equipment to access routers, access routers to backbone routers, and backbone links interconnecting backbone routers. The part of this network consisting of backbone routers and related interconnecting links is referred to as the “backbone”. We develop a new approach for accurately computing the Availability measure of IP networks by directly simulating each type of backbone outage event and its impact on traffic loss. We use this approach to quantify availability improvement as a result of introducing various technological changes in the network such as IGP tuning, high availability router architecture, MPLS-TE and Fast Reroute. A situation, where operational backbone links do not have enough spare capacity to carry additional traffic during the outage time, is referred to as bandwidth loss. We concentrate on one unidirectional backbone link and derive asymptotic approximations for the expected bandwidth loss in the framework of generalized Erlang and Engset models when the total number of resource units and request arrival rates are proportionally large. Simulation results demonstrate good accuracy of the approximations.
We introduce the notion of customer bandwidth fulfillment in IP data networks and provide a quantitative characterization of the fulfillment using measurements of the router uplink (link connecting a router to the backbone) utilization. The threshold for the uplink utilization is calculated for a given probability of customer fulfillment based on the normal approximation. We use three different stochastic models to prove the normal approximation for the distribution of the uplink utilization. The convergence to the Gaussian diffusion prcess is proved in the framework of the nonstationary exponential Benes buffer model. In a special case of an alternating renewal process, we show that the fulfillment can be evaluated based on measurements of the mean uplink utilization. We also prove that the distribution for the number of busy links in a large generalized Engset model is asymptotically normal that provides another justification of the normal approximation for the uplink utilization. We analyze 5-minutes measurements of the uplink utilization and show that their empirical distribution is close to normal.
KEYWORDS: Picosecond phenomena, Feedback control, Data modeling, Asynchronous transfer mode, Internet, Network architectures, Control systems, Classification systems, Switches, Data communications
A particular closed queuing network consisting of two processor sharing servers and two types of customers with fixed routes, which are generated by two finite sources, is studied. A complete bottleneck classification is provided as the number of customers and service rates at processor sharing servers increase. Asymptotic approximations for the marginal distributions at the two processor-sharing nodes are derived, when both nodes are bottlenecks. These approximations imply the normal approximation whose mean and variance are explicitly expressed through network parameters. The results are applied to the problem of admission control in packet-switching communication networks.
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