A Time-Sharing Queue with a Finite Number of Customers
Journal of the ACM (JACM)
Steady-state simulation of queueing processes: survey of problems and solutions
ACM Computing Surveys (CSUR)
Initial transient problem for steady-state output analysis
WSC '05 Proceedings of the 37th conference on Winter simulation
Issues in simulation and modelling of communication systems
ICOSSE'06 Proceedings of the 5th WSEAS international conference on System science and simulation in engineering
Proceedings of the Winter Simulation Conference
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This paper presents a perspective on the initial transient problem in steady-state simulation. In particular, it enumerates five generally accepted facts: 1) Conditions prevailing at the beginning of a simulation influence sample paths. 2) The extent of influence is a function of the strength of autocorrelation. 3) Some initial conditions are less detrimental than others are. 4) Truncation reduces bias but usually increases variance. 5) So far no complete solution exists. The remainder of the paper describes a proposal for solving the problem. It relies on the relatively weak assumption that the conditional means in a stochastic process of interest are related linearly. An estimator of the steady-state mean is described which has considerably less bias than one can achieve via conventional trunction. An interval estimator is also described which follows from standard regression theory. A test for residual bias is presented which enables a user to judge whether or not sample data meet the minimal requirements for the proposed technique to apply. A second test allows a user to judge whether or not a more efficient estimation technique can be used.