Abstract
We present a technique to estimate the arrival rate from delay measurements, acquired using single-packet probing. With practical applications in mind, we investigate a lower bound on the value of probe separation, to obtain a satisfactory estimate in a fixed amount of time. This leads to a problem: how long does it take for an M/D/1 queue to converge to its steady state as a function of the load? We examine this problem using three independent approaches: the time until the autocovariance of the transient workload process becomes negligible; the time it takes for the first transient moment of the workload process to get close to its stationary limit; and the convergence rate of the transient workload distribution to stationarity. These approaches yield different, yet strikingly similar results. We conclude with a recommendation for the probe separation threshold, and a practical approach to obtaining an arrival rate estimate using single-packet probing.
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Novak, A., Watson, R. Determining an adequate probe separation for estimating the arrival rate in an M/D/1 queue using single-packet probing. Queueing Syst 61, 255–272 (2009). https://doi.org/10.1007/s11134-009-9107-z
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DOI: https://doi.org/10.1007/s11134-009-9107-z