1. Introduction

A link budget that lists mean polarization dependent loss (PDL) as 0.8 dB and mean differential group delay (DGD) as 4 ps has said nothing yet about how often the link fails. Both quantities are random variables that fluctuate with temperature, mechanical stress, and the random orientation of every discrete element along the path, and the number that matters to a service-level agreement is not the mean but the probability that the instantaneous value exceeds the margin the design carries. That probability, multiplied by the number of minutes in a year, is what a customer experiences as downtime.

Concatenated PDL elements follow a Maxwellian distribution once enough of them are strung together, and so does the instantaneous DGD produced by concatenated birefringent fiber sections. The same functional form governs both quantities, which means the same tail-probability arithmetic converts a mean value and a design margin into an outage probability for either impairment, and the same 525,600-minute reference period used for unavailable-seconds (UAS) reporting under ITU-T G.8201 converts that probability into minutes per year. This article builds that chain end to end: from the physical definitions of PDL and DGD, through the Maxwellian model that describes their statistics, to a worked outage-minutes figure for a representative coherent link, cross-checked against a tail probability the Optical Internetworking Forum (OIF) has itself published.

The scope covers first-order PMD and PDL statistics for a single amplified span or a small number of concatenated spans, the outage-probability framework classical PMD-tolerance engineering already uses, and the specific case of coherent client optics where digital signal processing (DSP) changes which of the two impairments binds the design. Higher-order PMD, joint PMD-PDL statistics, and multi-span restoration scenarios are outside what a single article can carry with the same numerical care, though the closing sections point to where that further work sits in the current literature.