End-to-end queuing delay assessment in multi-service IP networks

Packet-based networks are more and more used to transport interactive streaming services like telephony and videophony. To guarantee a good quality for these services, the queuing delay and delay jitter introduced in the transport of voice or video flows over the packet-based network should be kept under control. Because data sources tend to increase their sending rate until (a part of) the network is congested, mixing real-time traffic and data traffic in one queue would lead to unacceptable high delays for real-time services. Therefore, voice and video packets need to get preferential treatment ( e.g. head-of-line priority) over data packets in the network nodes. Therefore, the queuing behavior of the voice and video packets can be studied more or less independently from the traffic generated by data services. Simple methods to assess the end-to-end delay are primordial. Since it is well known that an aggregate of voice (and CBR video) sources is accurately modeled by a Poisson arrival process and that delays in consecutive nodes are more or less statistically independent, this boils down to developing methods to calculate quantiles of the total queuing delay through a system of N statistically independent M/G/1 nodes. This paper develops four methods to calculate quantiles of the total queuing delay: a Gaussian method, a method based on the numerical inversion of the moment generating function of the total queuing delay developed by Abate and Whitt and two methods based on the assumption that the tail distribution of the individual queuing delay of one node is approximately exponential. The Gaussian method is the simplest, but only gives crude results. The method of Abate and Whitt is the most complex and breaks down for large quantiles. The methods based on the assumption of an exponential tail produce results that are more or less equally accurate as long as there is a node where the load is high enough.