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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.^[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 isThis is the paper's service-completion recursion in renamed notation.^[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.