  This paper continues the study, initiated by Cole and Fleischer, of the
behavior of a tatonnement price update rule in Ongoing Fisher Markets. The
prior work showed fast convergence toward an equilibrium when the goods
satisfied the weak gross substitutes property and had bounded demand and income
elasticities.
  The current work shows that fast convergence also occurs for the following
types of markets:
  - All pairs of goods are complements to each other, and - the demand and
income elasticities are suitably bounded.
  In particular, these conditions hold when all buyers in the market are
equipped with CES utilities, where all the parameters $\rho$, one per buyer,
satisfy $-1 < \rho \le 0$.
  In addition, we extend the above result to markets in which a mixture of
complements and substitutes occur. This includes characterizing a class of
nested CES utilities for which fast convergence holds.
  An interesting technical contribution, which may be of independent interest,
is an amortized analysis for handling asynchronous events in settings in which
there are a mix of continuous changes and discrete events.
