Optimal design of measurements on queueing systems

Abstract

We examine the optimal design of measurements on queues with particular reference to the M/M/1 queue. Using the statistical theory of design of experiments, we calculate numerically the Fisher information matrix for an estimator of the arrival rate and the service rate to find optimal times to measure the queue when the number of measurements are limited for both interfering and non-interfering measurements.We prove that in the non-interfering case, the optimal design is equally spaced. For the interfering case, optimal designs are not necessarily equally spaced. We compute optimal designs for a variety of queuing situations and give results obtained under the D-and D s -optimality criteria.

Statistical Error Propagation Affecting the Quality of Experience Evaluation in Video on Demand Applications

“…Network measurement techniques are technically mature and discussed in detail in [9][10] and [20] but their accuracy is still the subject of ongoing research. Network measurement techniques were examined for statistical accuracy in [7][8].…”

“…Roughan [23] and [24] has also reported bounds on the accuracy and precision of using probes for measuring packet loss, and has tried to quantify the error in packet loss using statistical techniques. The size of the probes, sampling frequency of the probes and the load on the network can also cause inaccurate measurements as presented in [7][8][9][10], [20], [22] and [25].…”

“…Uncertainty analysis is vital for all measurements and as reported by the National Physical Laboratory, measurements are only complete with a complete reference to the uncertainty in the measurand [27]. In common with [7][8][9][10], we consider the uncertainty that derives from measuring QoS parameters using sampling, e.g. [20].…”

“…These measurements are made both passively and actively. The latter employs sampling, and will be subject to sampling errors [7][8][9][10]. In this paper, we use the data acquired by our industrial collaborator Teragence.…”

Bayesian Design of Experiments for Intractable Likelihood Models Using Coupled Auxiliary Models and Multivariate Emulation

“…specifying the design variables, has received significantly less attention. Under the frequentist approach to statistical inference, Pagendam and Pollett (2013) and Parker et al (2015) used numerical approximations to the Fisher information to find D-optimal designs (e.g., Atkinson et al, 2007, Chapter 11) for stochastic epidemic and queueing models, respectively. In this paper, the Bayesian approach to statistical inference is used.…”