Alternating Renewal Processes and Availability

A trading system, an exchange gateway, or a piece of hardware often cycles between two states: working ("up") for a random stretch of time, then failing or being taken down for maintenance ("down") for another random stretch, then back up again, repeating indefinitely. This is an alternating renewal process: each up-down pair is a cycle, and successive cycles are independent and identically distributed, though the up-time and down-time within a cycle can have different, unrelated distributions.

The quantity of practical interest is availability — the long-run fraction of time the system is up — and it has a remarkably simple form: if the average up-time per cycle is $\mu_{up}$ and the average down-time is $\mu_{down}$, then availability equals $\mu_{up}/(\mu_{up}+\mu_{down})$, regardless of the exact shape of either distribution. A system that averages 9 days up between failures and 1 day down for repair has availability $9/(9+1)=0.9$, i.e. 90% uptime, whether outages are always exactly one day or occasionally stretch to a week and other times last an hour, so long as the average holds. This is why capacity planning for trading infrastructure focuses on shrinking mean repair time as much as extending mean uptime — halving the average outage length improves availability just as much as doubling the average time between failures, and is often the cheaper of the two to achieve.