@article{anjum_perros_2015, title={Bandwidth estimation for video streaming under percentile delay, jitter, and packet loss rate constraints using traces}, volume={57}, ISSN={["1873-703X"]}, DOI={10.1016/j.comcom.2014.08.018}, abstractNote={We present and use a CPU-efficient activity-based simulation model to calculate the sojourn time of a packet and the packet loss rate in a tandem queueing network that depicts the path of a video flow. The video flow is characterized by a packet trace. Background traffic, also characterized by a trace, is allowed in the tandem queueing network. In our analysis we used real video traces (Telepresence, WebEx, Jabber) and also generalized our results using traces generated by a theoretical model of a video arrival process depicted by a Markovian Arrival Process. Using this simulation model we calculate the bandwidth required for a video flow, so that a given set of constraints for the percentile end-to-end delay, jitter, and packet loss rate are satisfied. We also show that the bandwidth required for n identical video streams that follow the same path through an IP network, so that the end-to-end percentile delay remains the same, is a linear function of n. Further, it is experimentally depicted that for infinite-capacity queues the bandwidth required to satisfy the percentile end-to-end delay constraint also satisfies the jitter constraint. And for finite-capacity queues, the bandwidth required to satisfy both the percentile end-to-end delay and the packet loss rate constraints also satisfies the pair of jitter and packet loss rate constraints.}, journal={COMPUTER COMMUNICATIONS}, author={Anjum, Bushra and Perros, Harry}, year={2015}, month={Feb}, pages={73–84} }
 @inproceedings{anjum_perros_2012, title={End-to-end delay percentiles for video traces using a MAP2 approximation}, DOI={10.1109/netwks.2012.6381676}, abstractNote={Video traffic is widely expected to account for a large portion of the traffic in future wired and wireless networks. We propose an efficient and accurate approximation method for calculating a given percentile of the end-to-end delay of a video stream depicted by a trace. The queueing delay encountered in the network by the IP packets carrying the video is modeled by a tandem queueing network of infinite capacity queues. The video trace is approximated by a two-stage Markovian Arrival Process (MAP2), which is the arrival process to the tandem network. The proposed method uses only the first queue of the tandem queueing network to construct an upper and lower bound of a given percentile of the end-to-end delay. The percentile value is then approximated by interpolating between the two bounds. We used this method to estimate the 95th percentile of the end-to-end delay of two different types of video traces, Cisco's point-to-point presence and WebEx over a 10-node path. The results obtained were compared against simulation, and have an average relative error of 4.24%. Using this method, we then obtained the minimum amount of bandwidth required to be allocated on each link along the path of the video stream, so that a given 95th percentile of the end-to-end delay is satisfied.}, booktitle={2012 15th International Telecommunications Network Strategy and Planning Symposium (NETWORKS)}, author={Anjum, B. and Perros, H.}, year={2012} }
 @article{anjum_perros_2011, title={Adding Percentiles of Erlangian Distributions}, volume={15}, ISSN={["1089-7798"]}, DOI={10.1109/lcomm.2011.011011.102143}, abstractNote={In networking, enterprise computing and many other areas the issue of adding percentiles of a performance metric, such as the response time, arises regularly. Percentiles cannot be added using the arithmetic sum, and surprisingly there are no known formulae that permit us to do so correctly. In this paper, we obtain an exact analytical expression for adding percentiles of random variables which can be represented by a series of generalized exponential stages (e.g., Erlang, hypoexponential and two-stage Coxian). We demonstrate the applicability of our results by an example in which we use our expressions in the Dijkstra's algorithm to calculate the shortest 'percentile delay' path.}, number={3}, journal={IEEE COMMUNICATIONS LETTERS}, author={Anjum, Bushra and Perros, Harry}, year={2011}, month={Mar}, pages={346–348} }
 @article{anjum_perros_mountrouidou_kontovasilis_2011, title={Bandwidth allocation under end-to-end percentile delay bounds}, volume={21}, ISSN={["1099-1190"]}, DOI={10.1002/nem.783}, abstractNote={SUMMARY}, number={6}, journal={INTERNATIONAL JOURNAL OF NETWORK MANAGEMENT}, author={Anjum, Bushra and Perros, Harry and Mountrouidou, Xenia and Kontovasilis, Kimon}, year={2011}, pages={536–547} }