RenewalProcess[rdist]
represents a renewal process with interarrival times distributed according to rdist.


RenewalProcess
RenewalProcess[rdist]
represents a renewal process with interarrival times distributed according to rdist.
Details

- RenewalProcess is a continuous- or discrete-time and discrete-state process.
- RenewalProcess is a discrete-state and continuous-time or discrete-time process depending on rdist.
- The state
is the number of events in the interval 0 to
and
.
- The distribution rdist can be any continuous or discrete distribution with positive domain.
- RenewalProcess can be used with such functions as Mean, PDF, Probability, and RandomFunction.
Examples
open all close allScope (6)
Continuous Interarrival Distributions (2)
Applications (1)
Messages arrive at a communication line according to a two-phase hyperexponential distribution with phase probabilities 0.4 and 0.6. The average arrival times for the two phases are 4.8 milliseconds and 0.8 milliseconds, respectively. Simulate the process for 100 milliseconds:
Mean number of arrivals during the first 10 milliseconds:
Compare with the value obtained from simulation of the time slice distribution:
Properties & Relations (2)
Related Guides
History
Text
Wolfram Research (2012), RenewalProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/RenewalProcess.html.
CMS
Wolfram Language. 2012. "RenewalProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RenewalProcess.html.
APA
Wolfram Language. (2012). RenewalProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RenewalProcess.html
BibTeX
@misc{reference.wolfram_2025_renewalprocess, author="Wolfram Research", title="{RenewalProcess}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/RenewalProcess.html}", note=[Accessed: 11-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_renewalprocess, organization={Wolfram Research}, title={RenewalProcess}, year={2012}, url={https://reference.wolfram.com/language/ref/RenewalProcess.html}, note=[Accessed: 11-August-2025]}