On Poisson Approximations for Superposition Arrival Processes in Queues
- 1 February 1982
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Management Science
- Vol. 28 (2) , 126-137
- https://doi.org/10.1287/mnsc.28.2.126
Abstract
We report on simulations of ΣiGIi/M/1 queues; the arrival process is the superposition (sum) of up to 1024 i.i.d. renewal processes and there is a single exponential server. As one might anticipate, the simulation estimate of the expected number of customers in a ΣiGIi/M/1 queueing system approaches the expected number in an M/M/1 queueing system as the number of arrival processes, n, increases. However, for a given n, the difference between the expected numbers in the M/M/1 and ΣiGIi/M/1 queueing systems dramatically increases as the traffic intensity increases from ρ = 0.5 to ρ = 0.9. This difference is approximated by a formula which is a function of the traffic intensity, the number of component arrival processes and the squared coefficient of variation of the component interarrival times.Keywords
This publication has 0 references indexed in Scilit: