Abstract
The stationary workload W φA+B of a queue with capacity φ loaded by two independent processes A and B is investigated. When the probability of load deviation in process A decays slower than both in B and \(e^{ - \sqrt x } \), we show that W φA+B is asymptotically equal to the reduced load queue W φ−bA , where b is the mean rate of B. Given that this property does not hold when both processes have lighter than \(e^{ - \sqrt x } \) deviation decay rates, our result establishes the criticality of \(e^{ - \sqrt x } \) in the functional behavior of the workload distribution. Furthermore, using the same methodology, we show that under an equivalent set of conditions the results on sampling at subexponential times hold.
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Jelenković, P., Momčilović, P. & Zwart, B. Reduced Load Equivalence under Subexponentiality. Queueing Systems 46, 97–112 (2004). https://doi.org/10.1023/B:QUES.0000021143.87779.3f
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DOI: https://doi.org/10.1023/B:QUES.0000021143.87779.3f