Two problems in internet reliability

Abstract

This paper is motivated by two problems related to Internet reliability, where transient rather than traditional steady-state analysis is required. First, a failure and repair model for a router with active and redundant processors is considered. It is proved that the number of failed routers during given interval of time is asymptotically Poisson when the total number of routers is large and the parameter of the Poisson process is explicitly calculated. The second problem is related to reliability of a nationwide IP backbone. A situation, where operational links do not have enough spare capacity to carry additional traffic during the outage time, is referred to as <i>bandwidth loss.</i> We consider only one unidirectional backbone link and derive asymptotic aproximations 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.