A utility based framework for optimal network measurement

Packet level measurement is now routinely used to evaluate the loss and delay performance of broadband networks. In active measurement, probe packets provide samples of the loss and delay and from these samples the performance of the traffic as a whole can be deduced. However this is prone to errors: inaccuracy due to taking insufficient samples, self-interference due to injecting too many probe packets, and possible sample-correlation induced bias. In this paper we consider the optimisation of probing rate by treating all measurements as numerical experiments which can be optimally designed by using the statistical principles of design of experiments. We develop an analytical technique that quantifies an overall utility function associated with: (i) the disruption caused per probe packet, (ii) the bias and (iii) the variance as a function of the probing (sampling) rate. Our numerical results show that the optimal probing rate depends strongly on what parameter the network engineer seeks to measure.</p

A Single Server Queue with Random Arrivals and Balking: Confidence Interval Estimation

35 pages, 1 article*A Single Server Queue with Random Arrivals and Balking: Confidence Interval Estimation* (Rubin, Gail; Robson, Douglas S.) 35 page

Optimal design of measurements on queueing systems

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

Fitting phase type distribution to service process with sequential phases

The work of this thesis is concerned with fitting Hypo-exponential and Erlang phase type distributions for modeling real life processes with non-exponential service time. There exist situations where exponential distributions cannot explain the distribution of service time properly. This thesis presents the application of two traditional statistical estimation techniques to approximate the service distributions of processes with coefficient of variation less than one. It also presents an algorithm to fit Hypo-exponential distribution for complex situations which can’t be handled properly with traditional estimation techniques. The result shows the effect of variation of sample size and other parameters on the efficiency of the estimation techniques by comparing their respective outputs. Furthermore it checks how accurately the proposed algorithm approximates a given distribution