The ballot theorem strikes again: Packet loss process distribution
The probability distribution of the number of lost packets within a block of consecutive packet arrivals into a finite buffer is an important quantity in various networking problems. In a recent paper, Cidon, Khamisy, and Sidi introduced a recursive scheme to derive this distribution. In this paper, we derive explicit expressions for this distribution using various versions of the powerful Ballot Theorem. The expressions are derived for a single source M/M/1/K queue.
ballot theorem packet loss processes blocking probability finite queues forward error recovery high-speed networks