Estimating tail probabilities of delays and queue lengths for telecommunication applications

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In most service industries, especially the telecommunication systems, service providers usually want to determine a single statistic associated with a performance measure, such as queue length or waiting times,to be used as an indicator of users' quality of service (QoS).  The statistic often used as a single measure is the mean value.  Mean values are however viewed as not good indicator of performance measure for purpose of determining QoS as far as a user is concerned.  Tail probabilities are more meaningful and accepted as better measures.  For example, telling a user that their waiting time will not exceed a given value with a certain probability (tail probability) is more meaningful than been told that their average (mean) waiting time is of a particular value. Estimating the tail probabilities of performance measures is critical for service providers in planning their systems.  They need such statistic in order to assess how successful their system is perceived to be by users and this is what in the end determines what users subscribe to the system which translates to revenue (and profit) to service providers. The challenge, however, is how to determine the tail probabilities of a measure without computing the whole distribution, since it is usually very cumbersome to obtain a whole distribution in a practical real life system.  The aim of this proposal is to develop exact and approximate techniques for estimating the tail probabilities for measures in systems that have light tails, i.e for which the tail has a geometric decay property.  For such cases we only need to compute two parameters; the decay rate and the decay (asymptotic) constant.  There are several methods for computing decay rates, but hardly any for computing decay constants. We plan to improve existing techniques for computing decay rates and develop approximate techniques for computing decay constants for single node queues, and then extend the results to tandem queues for applications in telecommunication systems.