= David D. Yao
{c}
<David D. Yao> coauthored the 1992 work on <common random numbers> with <Paul Glasserman>. Their analysis gives conditions under which coordinated random inputs improve comparisons of simulated systems, emphasizing monotonicity and continuity of event times.<Some Guidelines and Guarantees for Common Random Numbers by Paul Glasserman and David D. Yao>[Primary byline and abstract; §1]{ref} The cited primary byline retains his middle initial without expanding it.
An original <queueing theory> calculation illustrates the event-time viewpoint. Start an initially empty, first-come-first-served single-server queue with arrivals $A=(0,1,3)$. For service times $S_n$, its <single-server queue departure-time recursion> is
$$
D_n=\max(A_n,D_{n-1})+S_n,\qquad D_0=0.
$$
This is the paper's service-completion recursion in renamed notation.<Some Guidelines and Guarantees for Common Random Numbers by Paul Glasserman and David D. Yao>[§3, equations8–9, p894; §4.2, Example4.6, p897]{ref} With service times $(2,2,2)$, the departures are $(2,4,6)$. Reducing all services to $(1,1,1)$ gives departures $(1,2,4)$ using the same arrival input.
At time $2.5$, the first system has completed one job and the second has completed two. The states differ even though corresponding job labels and arrival times are coordinated. In a stochastic comparison, random inputs should likewise be assigned consistently to the intended jobs or events; a raw position in a mixed event list need not identify the same physical event in both simulations.
The deterministic numbers above demonstrate the recursion, not a measured variance reduction. A useful random coupling must preserve each system's marginal input law and have the response properties required for the chosen performance comparison. Shared random seeds alone do not establish those properties.
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