Consider an aggregate arrival process A^N obtained by multiplexing N On-Off sources with exponential Off periods of rate \lambda and subexponential On periods \tau^{on}. For this process its activity period I^N satisfies \[ \Pr[I^N>t]\sim (1+\lambda \expect \tau^{on})^{N-1} \Pr[\tau^{on}>t] \;\; as \;\;t \rightarrow \infty, \] for all sufficiently small \lambda.When N goes to infinity, with \lambda N\rightarrow \Lambda, A^N approaches an M/G/\infty type process, for which the activity period I^\infty, or equivalently a busy period of an M/G/\infty queue with subexponential service requirement \tau^{on}, satisfies \Pr[I^\infty>t]\sim e^{\Lambda \expect \tau^{on}} \Pr[\tau^{on}>t] as t \rightarrow \infty.For a simple subexponential On-Off fluid flow queue we establish a precise asymptotic relation between the Palm queue distribution and the time average queue distribution. Further, a queueing system in which one On-Off source, whose On period belongs to a subclass of subexponential distributions, is multiplexed with independent exponential sources with aggregate expected rate \expect e_t, is shown to be asymptotically equivalent to the same queueing system with the exponential arrival processes being replaced by their total mean value \expect e_t.For a fluid queue with the limiting M/G/\infty arrivals we obtain a tight asymptotic lower bound for large buffer probabilities. Based on this bound, we suggest a computationally efficient approximation for the case of finitely many subexponential On-Off sources. Accuracy of this approximation is verified with extensive simulation experiments.
['Predrag R. Jelenkovic', 'Aurel A. Lazar']
Multiplexing On-Off Sources with Subexponential On Periods: Part I