Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Transforming renewal processes for simulation of nonstationary arrival processes
AU - Gerhardt, Ira
AU - Nelson, Barry L.
PY - 2009/10
Y1 - 2009/10
N2 - Simulation models of real-life systems often assume stationary (homogeneous) Poisson arrivals. Therefore, when nonstationary arrival processes are required, it is natural to assume Poisson arrivals with a time-varying arrival rate. For many systems, however, this provides an inaccurate representation of the arrival process that is either more or less variable than Poisson. In this paper we extend techniques that transform a stationary Poisson arrival process into a nonstationary Poisson arrival process (NSPP) by transforming a stationary renewal process into a nonstationary, non-Poisson (NSNP) arrival process. We show that the desired arrival rate is achieved and that when the renewal base process is either more or less variable than Poisson, then the NSNP process is also more or less variable, respectively, than an NSPP. We also propose techniques for specifying the renewal base process when presented properties of, or data from, an arrival process and illustrate them by modeling real arrival data.
AB - Simulation models of real-life systems often assume stationary (homogeneous) Poisson arrivals. Therefore, when nonstationary arrival processes are required, it is natural to assume Poisson arrivals with a time-varying arrival rate. For many systems, however, this provides an inaccurate representation of the arrival process that is either more or less variable than Poisson. In this paper we extend techniques that transform a stationary Poisson arrival process into a nonstationary Poisson arrival process (NSPP) by transforming a stationary renewal process into a nonstationary, non-Poisson (NSNP) arrival process. We show that the desired arrival rate is achieved and that when the renewal base process is either more or less variable than Poisson, then the NSNP process is also more or less variable, respectively, than an NSPP. We also propose techniques for specifying the renewal base process when presented properties of, or data from, an arrival process and illustrate them by modeling real arrival data.
KW - arrival counting process
KW - phase-type distribution
KW - nonstationary Poisson process
U2 - 10.1287/ijoc.1080.0316
DO - 10.1287/ijoc.1080.0316
M3 - Journal article
VL - 21
SP - 630
EP - 640
JO - INFORMS Journal on Computing
JF - INFORMS Journal on Computing
SN - 1091-9856
IS - 4
ER -