On Poisson Approximations for Superposition Arrival Processes in Queues
Management Science · 1982 · Volume 28 · Issue 2
Abstract
We report on simulations of Σ i GI i / 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 Σ i GI i / 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 Σ i GI i / 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
queues, approximations, superposition arrival processes
Enable JavaScript for citation tools and additional paper interactions.