The significance of transients following failures and repairs in packet-switched networks
Kobza, John E.
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A system composed of unreliable components can experience different levels of performance as its configuration changes due to failures and repairs. One approach used to measure overall system performance is to weight the level of performance measured for each system state by the probability that the system is in that state and then sum across all system states. Many performance measures have a transient behavior following a change in the state of the system. Because of the difficulty associated with transient analysis, the system is often assumed to be in steady state when measuring the performance for each system state. When this approach is used to analyze packet-switched communication networks, which consist of highly reliable high-speed links and switching nodes, it is argued that the steady-state assumption is justified on the basis of the large difference in rates of traffic-related events, such as call completions and packet transmissions, compared to component-related events, such as failures and repairs. To investigate the validity of this assumption, we define lower bounds for the length of the transient phase fol1owing link failures and repairs. For both cases, we obtain a distribution for the length of the lower bound. The transient phase is significant when its length exceeds a given fraction of the time until the next change in network state. Using the distributions for these lengths, we derive an expression for the probability that the transient phase is significant in tenns of the amount of traffic on the link and the ratio of the rates for traffic-related events and network state changes. These results show that the difference in rates between traffic-related events and component related events is not enough by itself to justify the steady-state assumption. The amount of traffic carried on the link and the size of the network must also be considered. These results indicate some situations where the steady-state assumption is inappropriate. We also obtain sufficient conditions for transient-phase significance following link failures. Although these results do not indicate when it is safe to use the steady-state assumption, they provide a measure of the risk associated with using it.
- Doctoral Dissertations